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APPLICATIONS OF HILBERT HUANG TRANSFORM (HHT) TO THE ANALYSIS OF EEG AND OTHER NON-STATIONARY TIME SERIES
A Thesis Presented to The Faculty of the College of Graduate Studies Lamar University
In Partial Fulfillment of the Requirements for the Degree Master of Engineering Science by Sumanth Reddy Yeddula August 2012
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APPLICATIONS OF HILBERT HUANG TRANSFORM (HHT) TO THE ANALYSIS OF EEG AND OTHER NON-STATIONARY TIME SERIES SUMANTH REDDY YEDDULA Approved:
_________________________ Gleb V. Tcheslavski Supervising Professor
_________________________ Selahattin Sayil Committee Member
_________________________ Cristian Bahrim Committee Member
_______________________________ Harley R. Myler Chair, Department of Electrical Engineering
________________________________ Jack R. Hopper Dean, College of Engineering
________________________________ Victor A. Zaloom Interim Dean, College of Graduate Studies
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© 2012 by Sumanth Reddy Yeddula No part of this work can be reproduced without permission except as indicated by the “Fair Use” clause of the copyright law. Passages, images or ideas taken from this work must be properly credited in any written or published materials
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ABSTRACT APPLICATIONS OF HILBERT HUANG TRANSFORM (HHT) TO THE ANALYSIS OF EEG AND OTHER NON-STATIONARY TIME SERIES by Sumanth Reddy Yeddula
Nonlinear and non-stationary nature of biomedical signals, such as Electroencephalogram (EEG) that is of critical importance in understanding brain functions, dictates necessity for proper and accurate analysis techniques. Hilbert Huang Transform (HHT) is one of the algorithms suitable for such nonlinear and nonstationary signal analysis. In present project, a new HHT algorithm was implemented with a novel boundary condition for spline-interpolated envelopes during the decomposition. An improved approach to estimate the instantaneous frequency from the HHT’s analytical signal output was used in obtaining the time-frequency data. A new method of estimating power-related features from the HHT time-frequency data was developed and used in analyzing various EEG signals, such as Epileptic EEG, SSVEP BCI EEG, Alcoholic and Control VEP EEG. Various features were extracted, analyzed, and compared using the modified Kruskal-Wallis test that minimizes the effect of sub-group selection during the evaluation of the intra-group and inter-group H-statistics. The power-based features extracted by HHT from the EEG signals were utilized next in classification. k – Nearest Neighbor method based on Manhattan distance with the Leave-One-Out-Cross validation scheme was predominantly used in this project for classification of EEG signals in three independent experiments. First, Epileptic EEG
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signal analysis was performed and the signals were successfully classified with the accuracy of 95% for the realistic classification problem. Next, SSVEP BCI EEG signal analysis was conducted and the classification results obtained were on par to the output of advanced algorithms that use preprocessed filtered input signal with an accuracy around 70% for a three class classification problem and 92% for a two class classification problem. Finally, VEP EEG collected from alcoholics and controls were analyzed and the classification results based on Gamma-band power achieved 96% accuracy. The results from these three independent applications justify usage of the improved methods that were devised and implemented in the present project. We conclude that HHT-based analysis of EEG may be successfully implemented in various practical clinical and biomedical systems.
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ACKNOWLEDGEMENTS First I need to thank the Lamar University for giving me such a wonderful opportunity to prove myself and for providing all the resources and the support needed. Also, I need to specially thank the interlibrary loan program of Mary & John Gray Library for helping me in the desperate times. I am grateful to all of those with whom I have had the pleasure to work during this and other related projects. Each of the members of my Graduate Committee has provided me with extensive personal and professional guidance. My supervising professor Dr. Gleb V. Tcheslavski helped me to gain immense knowledge in various domains related to academics and general life by sharing his experiences and thoughts. I need to sincerely thank him for patiently bearing all my blabbering, directionless thoughts and guided me in right direction during the times I am off the track. It is my deepest pleasure to work under such a great person who gives additional support and space for the students in both personal and professional fronts. He always helped me in shaping up crucial ideas and provided the support needed for improving my thesis. With all my gratitude, I thank him once again for accepting me and guiding me as his student. My graduate committee member Dr. Selahattin Sayil is the first professor under whom I have taken my first course in Lamar University. Undoubtedly, he is the one who sow the seed in my heart and mind to always learn, to do research, to share the thoughts and to improvise with hard work. It is my deepest pleasure to work under his valuable guidance on various research domains and also need to thank him for giving me the opportunity to have my first publication by including me in his research.
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My graduate committee member Dr. Cristian Bahrim is the one who completely radicalized my thought process in a positive way and helped me in shaping up my research career by sharing his philosophy of being a ‘rebel’ in science fields by respectfully questioning, verifying the proven facts and acknowledging them with a sense of inquisitiveness and his ideology to accommodate new school of thoughts for explaining the facts in a completely different manner, has helped me to think beyond and out of the box. I would like to thank Dr. Harley Myler, Chair of the Electrical Engineering Department for indirectly helping and supporting this work in the form of various approvals and providing financial aid during my coursework. I take this as an opportunity to thank Dr G.V. Marutheeswar who helped me to understand various technical aspects of Electrical Engineering and spiritual aspects about the life during my Bachelor’s period 2002-2006 and his continued support in my life till date. I am undoubtedly indebted my whole life to all these mentors and great personalities. I would also like to convey my gratitude to the folks in the Department of College Readiness for giving me On-Campus employment that helped me to have some extent of financial freedom and thereby wholly concentrated on my research work. Jane Stanley Capps deserves the appreciation and warmth of love for being such a wonderful motherly figure for our electrical engineering department. She took all our concerns, corrected our mistakes and helped us in overcoming our known “deadline laziness” and always never forgot to share the light hearted moments to cheer her sons and daughters. Also, from my deepest heart, I need to thank Mr. Mike Fuller and Mr.
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Max Morgan for their valuable help and support in providing the needed equipment, and providing the timely access to the electronic workshop during this thesis work. This thesis would not have shaped in this way if I had no technical/philosophical discussions during my stay in Lamar University with Abhilash, Ali, Dinesh, Firat, Raghuram, Ravi, Srikanth, Vinay, Zheng Xu, Late Mr. Rajesh Puli (one of the dearest friends whom I lost during my thesis work), and many others. Also, I need to thank and became indebted to all of my friends who helped me in all fronts during all these times in my life. I need to thank my Parents (Raja Ram Reddy Yeddula and Kanaka Durga Ramani Yeddula), In-laws (Y. Dhananjaya Reddy and Y. Bhavani), grandparents, and my sister (Sri Kalyani Reddy Yeddula) and their family for supporting in ups and downs of my life. Last but not least, my whole thesis and in fact whole Master’s is impossible for me without the support and encouragement of my wife. She is the driving force behind me to pursue Masters and always been there with me in all the hard and cheerful times. Hence, I proudly and humbly dedicate my thesis work to my beloved wife “Anusha”.
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TABLE OF CONTENTS Page List of Tables
ix
List of Figures
x
CHAPTER 1.
2.
3.
INTRODUCTION
1
1.1
Motivation
1
1.2
General Objective
2
1.3
Organization of the Project
2
1.4
Literature Review
4
BRAIN AND EEG INTRODUCTION
12
2.1
Brain and Neuron
12
2.2
Electroencephalogram (EEG)
17
2.2.1
History
17
2.2.2
EEG Usage
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2.2.3
EEG Rhythms
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2.2.4
EEG Electrodes and Data Acquisition
22
2.2.5
Various Artifacts and Their Removal
26
2.2.5.1 Artifact Removal and Preprocessing Techniques
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HILBERT HUANG TRANSFORM (HHT) IMPLEMENTATION
29
3.1
HHT Introduction
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3.2
HHT Implementation
32
3.3
Features from HHT Analytic Signal
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3.3.1
Instantaneous Frequency Estimation
34
3.3.2
Energy and Power Estimations based on HHT
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3.3.2.1 Power Related Features based on Decomposition
36
3.3.2.2 Importance of Scaling
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Hilbert Weighted Frequency (HWF) Computation
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3.3.3 3.4 4.
Comparison, Validation and Testing of HHT
REVIEW OF STATISTICAL TESTS AND CLASSIFICATION METHODS
USED
52 4.1
5.
6.
7.
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Kruskal – Wallis H – Test
52
4.1.1
53
Usage in present project
4.2
kNN Classification
57
4.3
Leave-One-Out Cross-Validation Scheme
59
EPILEPTIC EEG ANALYSIS
60
5.1
Data Description
60
5.2
Analysis Methods
60
5.3
Results and Discussions
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SSVEP BCI EEG ANALYSIS
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6.1
Data Description
74
6.2
Analysis Methods
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6.3
Results and Discussions
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DISCRIMINATING BETWEEN ALCOHOLIC AND CONTROL USING THE
VEP EEG ANALYSIS 7.1
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Data Description
88
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7.2
Analysis Methods
89
7.3
Results and Discussions
92
8.
CONCLUSIONS
111
9.
FUTURE SCOPE
114
REFERENCES
116
APPENDICES
136
APPENDIX – A
136
A1: Confusion matrices for Epileptic EEG Classification APPENDIX – B
136 141
B1: Biosemi layout and Electrodes order APPENDIX – C
141 143
C1: Alcoholic and Control VEP classification
143
C2: Standard term calculation for a 2-class classifier
146
APPENDIX – D
148
D1: Matlab Code for Synthetic Signal
148
D2: Links for HHT implementations
148
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LIST OF TABLES Table 3.1: Selected parameters of various HHT methods
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Table 5.1: Classification problems
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Table 5.2: HSTATS for HWF IMF1 using the HHT implemented
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Table 5.3: HSTATS for Total Average Power of the decomposed signal
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Table 5.4: HSTATS for Total δ-band (0.5-4Hz) power of the decomposed signal
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Table 5.5: HSTATS for Total θ-band (4-8Hz) power of the decomposed signal
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Table 5.6: HSTATS for Total α1-band (8-10Hz) power of the decomposed signal
66
Table 5.7: HSTATS for Total α2-band (10-12Hz) power of the decomposed signal 66 Table 5.8: HSTATS for Total β1-band (12-20Hz) power of the decomposed signal 67 Table 5.9: HSTATS for Total β2-band (20-30Hz) power of the decomposed signal 67 Table 5.10: HSTATS for Total γ1-band (30-40Hz) power of the decomposed signal
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Table 5.11: Classification results
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Table 5.12: Sens, Spec, Sel for 5 classification problems based on 8 powers
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Table 5.13: Sens, Spec, Sel for 5 classification problems based on 7 powers
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Table 6.1: SSVEP stimulation frequency deviations
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Table 7.1: Alcoholic and Control VEP signal count for analysis based on stimuli
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Table 7.2: Classification results based on power based features using HHT decomposition on CAR applied – no DC VEP signal
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Table 7.3: Accuracy results for various classification schemes
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Table 7.4: Classification results compared for various stimuli
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LIST OF FIGURES Figure 2.1: General division of Brain Forebrain/Midbrain/Hindbrain
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Figure 2.2: (a) Mid sagittal view (b) The Human Brain
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Figure 2.3: Cerebral cortex lobes and their functions
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Figure 2.4: Structure of mammalian Neurons
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Figure 2.5: Action potential (a) Measured (b) Propagation
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Figure 2.6: First recorded Human EEG signal
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Figure 2.7: EEG Rhythms as function of time (in seconds)
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Figure 2.8: Electrode based different classes of BCI
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Figure 2.9: (A) and (B) International 10 – 20 System’s Electrode measurement
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Figure 2.10: 64 electrode system based on 10-20 International System
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Figure 2.11: (A) Bipolar (B) Unipolar Measurement
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Figure 3.1: Average (b) or Extrema (a) boundary condition illustration
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Figure 3.2: Input signal for HHT analysis and comparison
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Figure 3.3: IMF decomposition using boundary tied to zero based HHT
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Figure 3.4: IMF decomposition using boundary tied to signal based HHT
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Figure 3.5: IMF decomposition using average or extrema boundary based HHT
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Figure 3.6: IMF decomposition using Rato’s HHT
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Figure 3.7: Time frequency data for all the IMFs and residue using average or extrema
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Figure 3.8: Time frequency data for IMFs alone using average or extrema
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Figure 3.9: Synthetic Signal
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Figure 3.10: Synthetic signal for 0.1 second duration after frequency transition
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Figure 3.11: DFT spectrum of synthetic signal
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Figure 3.12: STFT based time-frequency representation of synthetic signal
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Figure 3.13: IMF decomposition of the synthetic signal
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Figure 3.14: HHT based Time-Frequency information of synthetic signal
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Figure 4.1: (a) Sample Subgroup observations and (b) their corresponding box plots
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Figure 4.2: (a) Sample Subgroup observations and (b) their corresponding box plots with another repetition of arbitrary division
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Figure 4.3: (a) Hstats value in each repetition (b) Histogram of Hstats
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Figure 4.4: kNN example (a) represents training examples and query instance and (b) represents the decision induced for 1-Nearest Neighbor
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Figure 5.1: HWF of IMF1 vs HWF of IMF2 using the HHT implemented
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Figure 5.2: HWF of IMF1 vs HWF of IMF2 using Rato’s HHT
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Figure 6.1: First 5 IMFs based HHT spectral plot for SSVEP=8Hz for EEG (5-20 sec)
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Figure 6.2: First 5 IMFs based HHT spectral plot for SSVEP=14Hz for EEG (5-20 sec)
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Figure 6.3: First 5 IMFs based HHT spectral plot for SSVEP=28Hz for EEG (5-20 sec)
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Figure 6.4: Comparison of energies in various bands for three mean signals calculated from their HHT time-frequency data
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Figure 6.5: Classification accuracies for128 electrodes based on energies around ±1.5Hz range SSVEP frequency
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Figure 6.6: Average Powers for various bands (±1.5Hz) with SD error for A23 (Oz) electrode
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Figure 6.7: Classification accuracies for128 electrodes based on energies around ±0.5Hz range SSVEP frequency
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Figure 6.8: Average Powers for various bands (±0.5Hz) with SD error for A23 (Oz) electrode
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Figure 6.9: Classification accuracies for128 electrodes based on energies around ±0.1Hz range SSVEP frequency
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Figure 6.10: Average Powers for various bands (±0.1Hz) with SD error for A23 (Oz) electrode
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Figure 6.11: Classification accuracies for128 electrodes based on energies using first 5 IMFs around ±0.1Hz range SSVEP frequency for a 2 class problem 86 Figure 7.1: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using raw VEP signals
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Figure 7.2: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using raw VEP signals with Cz ignored
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Figure 7.3: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using no-DC VEP signals with Cz ignored
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Figure 7.4: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using CAR applied and no-DC VEP signals
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Figure 7.5: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using CAR applied and no-DC VEP signals with Cz ignored
95
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Figure 7.6: Mean of Averaged EEG Power of Alcoholics and Controls for different Visual Stimuli evaluated for CAR applied no-DC VEP signals
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Figure 7.7: Histogram Plot showing Number of Input Signals (CAR no-DC VEP) 97 Figure 7.8: Mean of HHT-based Total Average power for (a) Alcoholic (b) Controls
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Figure 7.9: Mean of HHT based Total Average power for (a) Alcoholic (b) Controls using scaling factor
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Figure 7.10: Various band powers for CAR applied no-DC VEP signals based on HHT decomposition
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Figure 7.11: Various scaled band powers for CAR applied – no DC VEP signals based on HHT decomposition
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Figure 7.12: Mean of Averaged EEG power for the first IMF (a) Alcoholics (b) Controls
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Figure 7.13: Mean of various band powers for the first IMF
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Figure 7.14: Hstats (Kruskal-Wallis Test results) evaluated for various HHT based band powers
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Figure 7.15: ROC graph for various classification features from Table 7.2
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Figure 7.16: ROC graph for (a) Scaled Power based features for decomposed signal (b) Power based features (c) scaled power based features for first IMF using CAR applied no-DC VEP
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Figure 7.17: ROC graph for (a) Power based features for raw VEP (64 channels) (b) Power based features for raw VEP (61 channels)
107
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Yeddula 1 1
Chapter 1 INTRODUCTION
1.1
Motivation “The most beautiful thing we can experience is the mysterious. It is the source of
all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed” – Albert Einstein. The Brain, one of the most complex organs in human body, is still a mystery (Eagleman 2007; Hemmen and Sejnowski 2006). Understanding the basic fundamentals of the brain in terms of its physiology and functionality shall be the key to solve many real world problems. This research needs the support from various domains such as neuroscience, bio-chemistry, signal processing, computation, statistics and etc., and attracts a large number of researchers to work in tandem for betterment of mankind. The multi-disciplinary research in the field related to human brain helps to design and develop neuroprosthetics and Brain-Computer Interfaces (BCI) for aiding the disabled (Birbaumer 2006; Koralek, et al. 2012; Lebedev and Nicolelis 2006), in diagnosis and treatment of epilepsy and other neural disorders such as autism, Parkinson’s disease etc. (Bosl, et al. 2011; Detre 2004; Stam, et al. 1994) and in understanding various phenomena that are useful in unlocking the mysteries related to cognition, underlying neuronal connections and etc. Electroencephalogram (EEG), a measure of the brain’s electrical activity, is widely used in Brain-related research studies (Hughes 1994; Sanei and Chambers 2007). Being an Electrical Engineer, I am interested in applying signal processing algorithms on
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Yeddula 2 EEG for understanding the brain functionality under various conditions. As EEG is highly nonstationary and nonlinear signal (Paluš 1996), the advanced signal processing techniques such as Hilbert Huang Transform (HHT) can be used in analyzing EEG signals (Lo, et al. 2009). The latter serves as the key motivation for the present project titled “APPLICATIONS OF HILBERT HUANG TRANSFORM (HHT) TO THE ANALYSIS OF EEG AND OTHER NON-STATIONARY TIME SERIES.” 1.2
General Objective The general objective was to implement an HHT-based signal processing
framework using Matlab that would be used in analyzing the EEG signals considering intrinsic nonlinear and nonstationary nature of EEG. The project implementation included (i) a detailed study of existing HHT-based algorithms and their implementation using Matlab with few improvements, (ii) analyzing epileptic EEG and classifying them using the HHT implementation, (iii) analyzing and classifying Steady-State Visual Evoked Potentials (SSVEP) signals, widely used in BCI, using HHT implementation, (iv) Studying the effects of Alcoholism on EEG using HHT implementation and extending the work to the classification of Alcoholics and Controls. 1.3
Organization of the Project The present chapter explained the motivation behind this project, the general
objective of this thesis and presents a detailed Literature review with a clear visibility on the process flow of this thesis.
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Yeddula 3 The organization of the remaining chapters is explained below. PART I (includes the present Chapter 1) Chapter 2 covers the background concepts needed for this thesis from the Brain and EEG perspective. It also contains a brief overview on few techniques, such as Common Average Referencing, artifact removal, DC removal and other preprocessing steps. Chapter 3 explains the theory behind HHT. It covers a detailed explanation on how the HHT has been implemented in this project and is compared with other methods as well as other HHT implementations. Instantaneous frequency estimation, marginal band power estimation using frequency sub bands and other methods related to HHT that are used in this thesis are also discussed. Chapter 4 briefly introduces the classification methods used in this project and also covers an overview of cross validation mechanisms used to measure the accuracy of those classifiers. PART II Chapter 5 documents the HHT analysis of Epileptic EEG. It has the detailed explanation of the EEG data used, methods used in analysis, results obtained and their discussion. Chapter 6 documents the HHT analysis of SSVEP BCI EEG signals. Similar to chapter 5, it has the detailed explanation of EEG data, methods used and the results obtained.
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Yeddula 4 Chapter 7 documents the HHT analysis of Alcoholic VEP signals. Similar to chapter 5 and chapter 6, it has the detailed explanation of the EEG data, analysis methods and the results obtained. PART III Chapter 8 has all the generalized conclusions from the results of Part II with proper justification for the usage of implemented HHT algorithm Chapter 9 provides the information on the areas that can be further improved and lists them in future scope. References have the centralized bibliographic details that are cited in all the above chapters. PART IV Appendix lists the Programs and other support information that are used in the thesis. 1.4
Literature Review Human mind is mysterious; it is a key for various activities, such as control,
thinking, emotion, reaction, etc. and has the ability of effortlessly crossing the space and time in terms of cognition, memory etc. (Berlinski 2004; Geary 2005; Suddendorf and Corballis 1997). The brain is the control center that receives and sends millions of signals every second from and to all over the body in the form of chemical transmitters, electrical signals, hormones etc. The activity of the brain can be measured and monitored using various methods, such as Electro-Encephalography (EEG), Magneto-Encephalography (MEG), Positron-Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT), Magnetic Resonance Imaging (MRI), functional Magnetic
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Yeddula 5 Resonance Imaging (fMRI) (Kamitani and Tong 2005; Liu, Ding and He 2006). Of the above methods, EEG is one of the least expensive methods to monitor and measure the brain activity with a good temporal resolution (Cohen and Cuffin 1983; Gevins, et al. 1994; Tcheslavski and Gonen 2012). EEG is widely used in the brain research studies that involve Brain-Computer Interfaces (Nielsen, Cabrera and do Nascimento 2006), Diagnosis of neuro-pathological conditions (Bosl, et al. 2011; Detre 2004; Stam, et al. 1994), understanding the functional neuronal connectivity (David, Cosmelli and Friston 2004) and etc. As of now, classical signal processing methods were widely used to analyze the EEG signals where stationarity and linearity were approximated from nonstationary and non-linear EEG sequences wile extracting short segments respectively (Rampil 1998; Tcheslavski and Gonen 2012). Kaplan, et al. (2005) had discussed the paradigm shift from considering EEG as stationary to nonstationary time series and had also extensively reviewed the integrated approaches to detect the quasi-stationary segments for EEG signal analysis. Klonowski (2009) had explained the need to consider EEG as nonstationary and nonlinear time series and suggested the application of simple nonlinear methods for signal analysis, such as Higuchi’s fractal dimension method. It has been reported and verified in various sources (Huang, et al. 1998; Huang and Shen 2005) that (i) classical data-analysis methods, such as Fourier transform, are based on linear and stationary system assumption, (ii) Non-stationary data analysis methods, such as wavelet analysis, Wigner-Ville distribution and etc., yield valid realistic results for linear systems (Flandrin 1999), (iii) Nonlinear time series analysis methods (Diks 1999; Kantz and Schreiber 2004; Schreiber 1999) produce physically meaningful results for nonlinear but
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Yeddula 6 stationary data. Recent signal processing methods, such as wavelet-based transformations for nonlinear signal analysis (Nowak and Baraniuk 1999), Hilbert-Huang Transform (HHT) (Huang, et al. 1998), and other methods as described in Li (2006) and Fitzgerald, et al. (2000), were expected to work well on both nonstationary and nonlinear data. HHT: Huang, et al. (1998) phenomenal work had introduced the concept of Empirical Mode Decomposition and application of Hilbert transform, which was collectively called Hilbert-Huang Transform, to extract time-frequency information from a nonlinear and nonstationary signal. Their work had also compared the other non-stationary signal processing methods, such as, Spectrogram, Wavelets, Wigner-Ville distribution, and Evolutionary spectral methods, with HHT and concluded the advantages of HHT over them. HHT method was widely used as a nonlinear signal processing tool in various fields (Huang and Attoh-Okine 2005; Huang and Shen 2005; Yan and Gao 2007), such as analyzing seismic data in geophysics (Battista, et al. 2007; Loh, Wu and Huang 2001), analyzing waves and currents in oceanography (Hwang, Huang and Wang 2003), biomedical signal processing (Wu and Huang 2009), power system quality studies (Senroy, Suryanarayanan, and Ribeiro 2007) etc. HHT had its own limitations, such as end-point effects, interpolation issues etc., which were extensively studied and improvements were suggested in various reports (Dätig and Schlurmann 2004; Huang and Shen 2005). Rato, Ortigueira, and Batista (2008) have presented a detailed review on the limitations and drawbacks of traditional HHT and introduced a new framework for HHT algorithm with a number of improvements. In the present work, a new simple HHT algorithm was implemented with average-or-extrema end point conditions and was
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Yeddula 7 further used in EEG signal analysis where the signals related to epilepsy, SSVEP BCI, alcoholics and control VEP were used. Epileptic EEG: Epilepsy is one of the most common chronic neurological disorders that affect around 50 million people worldwide (WHO 2012). Epileptic EEG signal has a dominant nonlinear dynamic evolutionary system and nonstationary characteristics (Andrzejak, et al. 2001; Tzallas, Tsipouras and Fotiadis 2009). Srinivasan, Eswaran and Sriraam (2007) used Approximate Entropy (ApEn) that is a time domain feature reflecting the nonlinear dynamics of a time series and it was estimated for every sliding window segment of EEG data. Thus estimated ApEn was used in designing an Artificial Neural Network (ANN) based automated epileptic EEG detection system. The design was based on the fact that the value of ApEn decreases during epileptic activity as the large group of neurons involve in a synchronously discharge activity during epilepsy (Diambra, de Figueiredo and Malta 1999). Tzallas, Tsipouras and Fotiadis (2009) used fractional energy of specific signal segments, which were calculated using the time windows and the frequency sub bands applied on spectral density plot obtained from time-frequency analysis, as the parameters for ANN-based classification of EEG segments to identify epileptic activity. They compared the results for various time-frequency analysis techniques, such as Short Time Fourier Transforms (STFT), Pseudo Wigner-Ville distribution, etc. Bao, et al. (2009) used a combination of Power spectral features based on Fast Fourier Transform (FFT) with the parameters outlining the nonlinear chaotic signal characteristics, such as Higuchi Fractal Dimension, Petrosian Fractal Dimension measuring the fractal properties, and Hjorth mobility and complexity modeling the
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Yeddula 8 chaotic properties, on the segments of interictal scalp EEG signal to automatically diagnose the epilepsy with the help of Neural Network based classifier. Pachori (2008) used Empirical Mode Decomposition (EMD), a step in HHT, to decompose the EEG signal into various band-limited Intrinsic Mode Functions (IMF) and used Fourier-Bessel expansion to compute mean frequency for the IMFs. The computed mean frequency was used as the parameter for discriminating the ictal and seizure-free EEG signal. Oweis and Abdulhay (2011) used Hilbert Weighted Frequency (HWF) of IMFs, calculated using the instantaneous frequency and amplitudes obtained from HHT, as the parameter to compare the healthy EEG and seizure EEG using student’s t-test and implemented Supervised Euclidean clustering for their classification. In the present work, EEG epileptic signals were analyzed using the implemented HHT algorithm. Similar to the Oweis and Abdulhay (2011) work, HWF parameters were calculated for various EEG signals, but were compared using Kruskal-Wallis test which doesn’t make any assumptions about normality of data unlike student’s t-test in their work which needs the observations to be normally distributed. Additionally, the marginal powers estimated from the HHT output, using frequency sub bands, were compared using Kruskal-Wallis test and classified using k – Nearest Neighbor algorithm. SSVEP EEG: Brain-Computer Interfaces are the systems that control the external devices, such as neuro-prosthetics, wheel chairs, computers etc., using the brain activity (Martinez, Bakardjian and Cichocki 2007). They are used widely in various applications related to rehabilitation for the disabled people (Birbaumer 2006; Gao, et al. 2003). Additionally, it has profound usage in multimedia and virtual reality applications especially gaming,
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Yeddula 9 virtual environment, driving simulation, aircraft simulation etc. (Allison, Graimann and Gräser 2007; Krepki, et al. 2007; Lalor, et al. 2005; van de Laar 2009). Allison, et al. (2010) studied various BCI demographics based on different approaches such as SSVEP, P300, SensoriMotor Rhythms (SMR) and concluded that SSVEP-based BCI system could be used with most people having no prior BCI experience and in noisy environment. Volosyak, et al. (2011) as an extension to Allison, et al. (2010) work, had studied SSVEP-based BCI system for various flickering frequencies of the stimuli and concluded that Higher-frequency SSVEPs had reduced the user fatigue and risk of photosensitive epileptic seizures. Lin, et al. (2006) had used Canonical Correlation analysis (CCA), an array signal processing technique, on EEG signals from multiple channels and extracted CCA coefficients for all stimulus frequencies and assumed the frequency with the largest coefficient as the SSVEP’s frequency. Huang, et al. (2008) had used wavelet and HHT-based analysis on SSVEP signal and contrasted the result. Diez, et al. (2011) had implemented a simple SSVEP BCI system, using high frequency stimuli, to control a mobile object on the screen to reach its final destination where FFTbased signal processing methods were used on three EEG channels and reported 65%100% classification accuracy. Bakardjian, Tanaka, and Cichocki (2010) had designed an eight command online BCI system based on SSVEP. In their implementation, Blind Source Separation approach utilizing modified Robust Second Order Blind Identification with Joint Approximate Diagnolization and automatic Hoyer sparsity ranking of the components were used to remove the eye-blink, muscular and other artifacts. The preprocessed signal was processed through a bank of narrow band elliptic IIR filters and the features corresponding to the SSVEP were extracted and used in implementing an
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Yeddula 10 eight-command BCI system. In the present work, the data used in Bakardjian, Tanaka and Cichocki (2010) have been used without any preprocessing and the HHT analysis was performed on selective channels. Alcoholic EEG: Alcohol consumption is one of the most dominant risk factors for many health and socio-economic problems, especially for the people with heavier drinking habits (Gururaj, Girish and Benegal 2006; Rehm 2011). There has been considerable research being done to study the effects of Alcoholism on the Brain (Oscar-Berman and Marinkovic 2003; Porjesz and Begleiter 2003; White 2003). It has been identified with substantial evidence that alcoholism and epilepsy are clearly related, as alcoholism can cause unprovoked seizures (Rehm 2011; Samokhvalov, et al. 2010). Hayden, et al. (2006) in their research study to understand the vulnerability to alcoholism, had used EEG as a tool to find out the asymmetrical behavior in the brain hemispheres based on α-band (812Hz) power which varies inversely with cortical activity (Coan and Allen 2004) and concluded that the people suffering alcohol dependence exhibit decreased activity in left anterior cortex than in the right. Various research studies on resting EEG had reported increased power levels for chronic alcoholics in θ-band (4-8Hz) (Porjesz and Begleiter 2003; Porjesz, et al. 2005; Rangaswamy, et al. 2003) and in β-band (12-30Hz) (Porjesz and Begleiter 2003; Rangaswamy, et al. 2002; Rangaswamy, et al. 2004). Tcheslavski and Gonen (2012) used the quasi-stationary assumption for short segments of EEG in their analysis to study the alcoholism effects on spectral properties of EEG with the usage of Burg Autoregressive parametric model, effects on coherence properties of EEG with the help of parametric coherence estimator, and effects on phase synchrony and had
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Yeddula 11 reported that the average power, coherence and phase synchrony between certain electrodes can be affected by the subject’s drinking habits in a statistically significant manner which was verified using Kruskal-Wallis tests. Palaniappan, Raveendran, and Omatu (2002) had used γ-band (32-48 Hz) power of Visual Evoked Potential (VEP) from the specific scalp EEG channels, which were optimally selected using Genetic algorithm, as the classification parameter to classify Alcoholics and Controls using neural networks. Ravi and Palaniappan (2006) had evaluated the feasibility of using Late Gamma Band (LGB) features of EEG for classifying the subjects related to alcoholism with the help of back propagation and simplified fuzzy ARTMAP neural networks. Palaniappan (2003) had used ROOT-MUSIC algorithm on γ-band filtered VEP to extract the power of the dominant frequency as the feature and used the extracted feature for the purpose of classifying the subjects into alcoholics and controls with the help of k – Nearest Neighbor and artificial neural networks. Lin, et al. (2009) had demonstrated the application of HHT for time-frequency analysis of Alcoholics and Controls. In the present work, inspired from Tcheslavski and Gonen (2012) report, EEG Spectrum between alcoholics and controls under various bands would be compared. However this will be implemented considering VEP signals as nonlinear and nonstationary in nature unlike quasi-stationary as in their work. HHT was applied to analyze the VEP signal and the marginal band powers estimated from the HHT output, using frequency sub bands, were classified using k – Nearest Neighbor algorithm.
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Yeddula 12 2
Chapter 2
BRAIN AND EEG INTRODUCTION 2.1
Brain and Neuron The Brain is the most important organ and complex creation in the Human body
and sometimes is referred to as the ‘GOD’ (Meshberger 1990; Davis n.d.). It is the major part of the nervous system. Nervous system is the body’s decision, communication and control center that has two major components: (1) the central nervous system (CNS) – consisting of the Brain and the spinal cord, (2) the peripheral nervous system (PNS) – consisting of nerves. Generally, CNS and PNS work in tandem to control every part of daily human life from breathing to memorization, from sensing to providing responses etc. Nerves run from the brain to the face, ears, eyes, nose, spinal cord, and other body parts. Nerves also run from spinal cord to various parts and the rest of the body (Serendip 2005). Nerves connected to the sensory organs are generally referred to as Sensory Nerves, while those nerves connected to the muscle are generally called Motor Nerves. Sensory nerves gather the information from the surroundings using sensory organs and pass this information to the brain either directly or through the spine depending on the location of the sensory organ. The Brain processes this information and generates and delivers the response to the corresponding muscles either through the direct Motor nerves or Motor nerves originating from Spine (Noback, et al. 2005). The Brain is divided into three various parts such as (1) Forebrain representing cerebrum or cortex along with thalamus and hypothalamus, (2) Midbrain consisting of tectum and tegmentum and (3) Hindbrain that includes cerebellum, pons and medulla. Pons and Medulla are collectively called Brain Stem.
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Yeddula 13 The anatomical structures of the brain is illustrated in the Figures 2.1, 2.2, 2.3
Figure 2.1: General division of Brain Forebrain/Midbrain/Hindbrain (Edelman 2011)
Figure 2.2: (a) Mid sagittal view (Serendip 2005) (b) The Human Brain (Vista 2010) The various important parts of the brain can be easily located from the anatomical figures shown in Figures 2.1 and 2.2. Cerebrum is the largest part of the brain and consists of two hemispheres that are joined by dense band of nerve fibers (Corpus Callosum). The cerebrum has sensory areas, association areas and motor areas and is divided into various lobes as shown in Figure 2.3.
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Yeddula 14
Figure 2.3: Cerebral cortex lobes and their functions (Vista 2010) Cerebrum is divided into six lobes: Frontal lobe, Parietal lobe, Temporal lobe, Occipital lobe, Insular lobe, and Limbic lobe. In Figure 2.3, frontal, parietal, temporal and occipital lobes are shown and their functionalities are briefly explained. Cerebellum is an essential part of the brain that controls body movements and maintains the equilibrium. Voluntary muscles are coordinated by cerebellum in their contraction and relaxation to ensure a smooth movement. Cerebellum receives a continuous supply of unconscious information from muscles, tendons, and joints. Thalamus coordinates the sensory impulses from eyes, ears, and skin and then relays them to cerebrum. Hypothalamus receives the taste and the smell impulses and relays them to cerebrum. It also takes active role in controlling heart rate, blood pressure, and blood temperature. It includes emotional and mood control centers. A more detailed anatomical description and their functionalities can be found elsewhere (Jacobson and Marcus 2011; Noback, et al. 2005; Patestas and Gartner 2006).
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Yeddula 15 Also, it has been reported that the brain can form new connections based on the new learning experiences. This is generally referred to Neuronal Plasticity. The neuronal plasticity is used to explain how the brain can change its physiological structure (Glick 2011). From cellular point of view, Neurons are the basic building blocks and functional units of the nervous system. Adult Human brain has approximately 100 billion neurons (Koch and Laurent 1999). The following Figure 2.4 illustrates the structure of typical mammalian neurons.
Figure 2.4: Structure of mammalian Neurons (Lodish, et al. 2000)
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Yeddula 16 As seen in Figure 2.4, a typical neuron includes a cell body (Soma) with a nucleus, dendrites and axon. Axons are specialized conductors of the electric impulse (an Action potential) in the outward direction away from the cell body toward axon terminals. An action potential is a sudden change of voltage or electric potential across the cell’s plasma membrane. A detailed description of the Ion pump cycle generating the action potential is beyond the scope of this work and can be found elsewhere (Karp 2010; Lodish, et al. 2000). In a non-stimulated resting state, the potential across axonal membrane of a neuron is generally -60mV while the inside part is negative with respect to the outside. This membrane potential can be changed to as high as +50mV during the peak of the action potential as shown in Figure 2.5.
Figure 2.5: Action potential (a) Measured (b) Propagation (Lodish, et al. 2000) The action potential causes a net change of approximately +110 mV. These action potentials generated at the axon hillock are actively conducted down the length of the axon toward axon terminals. Few axon terminals form the synapses or connections with other cells as shown in Figure 2.5 (b). In human central nervous system, a typical single axon can synapse with multiple neurons and further induce a simultaneous response in all
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Yeddula 17 of them. In general, the synapses are chemical synapses using neurochemical transmitters and it is very rare to find electric synapses. The dendrites are specialized to receive chemical signals from the axon terminals of other neurons and convert these chemical signals to electrical signals for transmitting them inward toward the cell body. This continues as a chain process and as a result a weak electric current is induced inside the brain. Different instruments such as EEG, MEG, MRI, CT scan, etc. are being used to measure and analyze the brain’s electromagnetic activity. EEG is used in the present project for various analysis as EEG is the least expensive and offers a higher temporal resolution in its measurements when compared to other methods (Cohen and Cuffin 1983; Gevins, et al. 1994; Tcheslavski and Gonen 2012). Hence, our discussion will be focused on and limited to EEG. 2.2
Electroencephalogram (EEG) Electroencephalogram or Electroencephalograph is a recording (“graph”) of
electrical signals (“electro”) from the brain (“enchephalo”). 2.2.1
History In 1875, Richard Caton first discovered electric brain signals in apes and rabbits
by directly probing on the surface of the animal’s exposed brain. In 1877, Vasili Yakovlevich Danilevsky had published his doctoral thesis based on electric stimulation as well as on spontaneous electrical activity in the brains of animals at the University of Kharkov.
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Yeddula 18 In 1890, Adolph Beck had published his results in a physiological journal about the brain-wide interruption of the slow even pattern waves because of sensory stimuli such as clap or a light flash. In 1912, Vladimir V. Pravdich-Neminsky recorded the animal EEG. He published his results and photographic recordings of the brain waves in dogs in the year 1913. In 1929, Dr. Hans Berger, a German physiologist and psychiatrist, had successfully recorded and published the Human EEG for the first time using his own instrument on his son and found the regular waves repeating at 10 approximate cycles per second and named them as Alpha waves (Berger 1929; Haas 1992).
Figure 2.6: First recorded Human EEG signal (Berger 1929) In 1934 Edgar Adrian and B.H.C Mathews worked on human EEG and nervefibers. They verified and confirmed Berger’s basic research. Adrian had been awarded with Nobel Prize for his work on electrophysiological activity of nerves (Collura 1993; Niedermeyer and Da Silva 2005). 2.2.2
EEG usage After its discovery, EEG was used for research studies in psychophysiology for
better understanding of the brain during various states such as sleep, seizures, etc. (Borb and Achermann 1999). It is also used widely for analyzing the effects of drug abuse on human mind (Essig and Fraser 1958). It is also widely used in various clinical studies for the diagnosis of neural disorders (Bosl, et al. 2011; Detre 2004; Stam, et al. 1994). EEG
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Yeddula 19 is widely used in diagnosis and treatment of epilepsy (Logar, Walzl and Lechner 1994). It is also used in various Brain-Computer Interfaces for aiding the disabled (Nielsen, Cabrera and do Nascimento 2006). EEG is widely used in various fields related to neurosciences such as Neurophysiology, Affective Computing, Psychophysiology, Clinical Neurosciences, Neuropharmacology, etc. for various purposes. 2.2.3
EEG Rhythms Electric potential recorded at the surface of human scalp changes spatially due to
varied activity of the brain occurring in different regions. Also, these potentials change temporally in chaotic fashion as the state of brain is dynamic in nature. This varying potential signal is made up of different frequency signals. Alpha rhythms and Beta rhythms were distinct harmonic oscillations observed and named by Hans Berger. Because of various interferences from different parts of the brain, the scalp potential is not easy to analyze. In order to efficiently and effectively evaluate the recorded potentials, EEG waves (recorded potentials) were generally divided into six different rhythms based on their frequency content. These rhythms do not have fixed demarcations or universal definitions. Depending upon the considerations of the researcher/author, slight variations in the frequency ranges considered for these rhythms may be encountered. Generally, 0.5 – 4 Hz is considered as delta rhythm δ; 4 – 8 Hz is considered as theta rhythm θ; 8 – 12 Hz is considered as alpha rhythm α; 12 – 30 Hz is considered as beta rhythm β; 30 – 100 Hz is considered as gamma rhythm γ; and 8 – 13 Hz is considered as Mu rhythm µ. In the present project, additional divisions in α and β were
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Yeddula 20 considered such as α1 (8 – 10 Hz), α2 (10 – 12 Hz), β1 (12 – 20 Hz), and β2 (20 – 30 Hz). EEG rhythms are illustrated in Figure 2.7.
Figure 2.7: EEG Rhythms as function of time (in seconds) (Gautham 2011) Delta rhythms are generally the slow but strong waves that are associated with the deep sleep and are dominant wave patterns in infants. Any brain injury or damage produces high-amplitude rhythmic delta waves in adults. Delta rhythm may also be related to attention-deficit hyperactivity disorder (ADHD) condition in children (Clarke, et al. 2002).
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Yeddula 21 Theta rhythms are dominantly related to cognitive and memory associated tasks (Michels, et al. 2012) and are prominent in children compared to the adults. These are generally related to fuzzy thinking, impulsivity, poor decision making and slowed reaction time. These rhythms are also found in the subjects suffering with depression and attention deficit-disorder. Theta rhythms are generally used to refer to two different ‘hippocampal theta’ and ‘human cortical theta’ signals. Alpha rhythms are the ones first discovered by Hans Berger and are also called Berger’s waves. These waves are predominantly generated from occipital lobe during wakeful relaxation with closed eyes. They decrease in amplitude with open eyes, sleep, and drowsiness. The amplitude of alpha rhythm is enhanced during mental calculations and active working memory (Palva and Palva 2007). Mu rhythm, while occupying a similar frequency range that Alpha rhythm, exhibits the maximum amplitude only when the somatosensory cortices are at rest. Mirror neuron activity in premotor cortex has an indirect effect on Mu band powers. Mu rhythm is dominant during imaginary actions (Ulloa and Pineda 2007). Beta rhythms are generally associated with normal waking consciousness. Beta rhythms with lower amplitudes and multiple and varying frequencies are generally associated with active, busy, or anxious thinking and active concentration. Local field Beta waves are generally observed in various parts of the brain including primary motor, somatosensory and posterior parietal cortices in the neocortex (Takahashi, et al. 2011). Gamma rhythms have been associated with the sensory processing especially in visual cortex. . These waves also correlate with transcendental mental state after
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Yeddula 22 meditation (Lutz, et al. 2004). These waves are inhibited or reduced in individuals having learning disorders and mental deficiency. 2.2.4
EEG Electrodes and Data Acquisition Based on the placement of electrodes, various classes of EEG has been identified
such as Surface/scalp EEG, intracranial EEG or Electrocorticography (iEEG or ECoG). Generally implanted EEG electrodes are used in identifying epileptogenic zone (Blume 2004). Now-a-days, ECoG is also widely used for BCI purposes (Kotchetkov, et al. 2010). The typical EEG recorded from scalp electrodes is about 10µV to 100µV and the EEG recorded from implanted subdural electrodes is about 10-20mV. Various electrode placements are compared in Figure 2.8
Figure 2.8: Electrode based different classes of BCI (Kotchetkov, et al. 2010) Although the Figure 2.8 is based on BCI related work (Kotchetkov, et al. 2010), it is helpful in understanding the various electrode placements, their advantages and limitations. Although scalp EEG might be more prone to interference and various
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Yeddula 23 artifacts, EEG recordings from the scalp are the safest compared to the implanted electrode based EEG recordings. As the size and shape of human head changes from subject to subject and variations in the physiological structures of the brain, it is difficult to develop a universal and perfect system to access exactly the specific regions in the brain. The International 10-20 system standardizes EEG scalp electrode placements and is widely used and adopted for EEG studies. The 10-20 notation indicates that each electrode should be 10 – 20 – 20 – 20 – 20 – 10 percent away from each other when measured from Nasion to Inion. As per the standard notation, ‘F’ – Frontal lobe, ‘C’ – Central lobe, ‘T’ – Temporal lobe, ‘P’ – Parietal lobe, and ‘O’ – Occipital lobe. The detailed positioning of electrodes are shown in Figure 2.9
Figure 2.9: (A) and (B) International 10 – 20 System’s Electrode measurement (Malmivuo and Plonsey 1995)
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Yeddula 24 In addition to these electrodes as shown in Figure 2.9, extra electrodes can also be placed based on the available head cap size, the research study requirements and other additional parameters. Also, besides the international 10-20 system, there are many other electrode systems that exist for EEG recordings. Figure 2.10 illustrates a 64 electrode system that is widely used and is an extended version of International 10-20 based on 10% intermediate electrodes.
Figure 2.10: 64 electrode system based on 10-20 International System (Malmivuo and Plonsey 1995) The electrode nomenclature used in Figure 2.10 has additional ‘A’ – ear lobe, ‘N’ – Nasion, ‘I’ – Inion apart from those mentioned earlier. A similar system was employed in VEP EEG acquisition for the data used in the Alcoholic and Control VEP analysis
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Yeddula 25 (Zhang, et al. 1997). Therefore, we have used the same system to generate the 2-D interpolated brain plots in Chapter 7. Various research studies are using Active electrodes for EEG acquisition, where the microelectronic circuit amplifier is integrated in the electrode itself. Such systems are reported to yield a higher Signal-to-Noise ratio compared to convenient passive systems (Bakardjian, Tanaka and Cichocki 2010). These active electrodes also provide more accurate EEG scalp recordings and are comparable to ECoG. While acquiring the EEG, various measurement schemes can be used; some of them are shown in Figure 2.11.
Figure 2.11: (A) Bipolar (B) Unipolar Measurement (Malmivuo and Plonsey 1995) The acquired EEG signals are normally passed through a series of active filters and amplifiers and are converted to digital signals using advanced ADC. Thus converted digital EEG signals are stored and used for analysis by running various algorithms implemented in different environments. As the digital signals are stored, the montages can be changed. Though the Figure 2.11 (A) seems to differ from (B), they can be mathematically converted from one montage to the other. Average reference montage is
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Yeddula 26 also widely used: where all the outputs are summed up and averaged and the average signal is used as common reference for all the channels. Apart from the mentioned montages other montages such as Laplacian, etc. are also used. In present project, EEG signals acquired and digitally stored were used and signal processing algorithms developed in Matlab environment were implemented for analysis. 2.2.5
Various Artifacts and Their Removal As mentioned earlier, the scalp EEG is usually in the range of 10 – 100 µV. These
low voltage signals are easily subjected to various noise contaminations. These noise contaminations or unwanted signal in the EEG are called the artifacts. They may be of biological origin with in the subject or from errors in experimental setup and surrounding environments. Biological artifacts are of biological origin. Ocular artifacts – include eye blinking, eye ball movement, unwanted Visual evoked potential, etc. Eye blink introduces a very large variation in both amplitude and frequency of the EEG data. Eye ball movement produces distortion in the EEG signal and it may be present even when eyes were closed during the EEG acquisition to reduce eye blink artifacts. Unwanted VEP are the additional artifacts that contaminate the EEG (especially the desired Evoked Potentials) and are elicited by unwanted visual stimuli. Muscle artifacts, include – the limb movement artifacts, facial muscle artifacts and the contamination from other Electromyography (EMG) sources distorting the EEG signal. Cardio artifacts are EEG contaminations by the Electrocardiogram (ECG) signal.
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Yeddula 27 Swallowing artifacts may cause severe contaminations of EEG by involuntary or voluntary swallowing actions of the subject. These contaminations are large in both amplitude and frequency and may contaminate all the EEG channels severely. Non-Biological Artifacts include AC power line noise, DC noise, thermal noise in the amplifiers, etc. and may also contaminate the EEG recordings. Any errors/faults in the experimental setup, such as improper grounding, can also severely contaminate the EEG recordings. AC power line noise arises from the Electromagnetic interference with surrounding equipment or the power line and also from the carried over harmonic distortions at the power line frequency through power supply. DC offset may also be frequently observed in EEG recordings because of experimental hardware errors. 2.2.5.1 Artifact Removal and Preprocessing techniques Various advanced signal processing techniques may be used to reduce or remove the artifacts present in EEG. The biological artifacts are very hard to remove without losing the EEG data/information during the contamination period or window. The advanced signal processing techniques based on Independent Component Analysis can be implemented to remove the Eye blink, ECG, EMG and other biological artifacts. Various digital filters can be applied to reduce specific portions of frequency contents to reduce the Power line artifacts, DC drifts, and other band limited biological artifacts such as ECG. In the present project, although no advanced artifact removal techniques were considered, few simple preprocessing techniques, such as DC removal, Common Average Reference filter application, etc., are used.
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Yeddula 28 DC removal can be accomplished using Discrete Fourier Transform where the first term in the series is a DC component. This term is reduced to zero and by performing the inverse DFT a signal with no DC component may be recovered DC removal can also be achieved in time domain. Here, the average of the signal over total time is computed and subtracted from the original signal at each time instant to produce no-DC (DC removed) signal. CAR Application Common Average Reference filter is a spatial filter that can be applied to a multichannel signal such that the average of all the electrodes including the reference electrode at any point in time is always a zero. For an example, consider the N channels C1 to CN, where the recordings were performed using Referential montage/unipolar electrode measurement with the reference CR. The procedure to produce a CAR applied signals CX1 to CXN, such that CXR is the reference that needs to satisfy CAR constraint, ,
1 ,
2.1
1, . .
2.2
The new CAR applied signals CX1 to CXN satisfy the common average reference condition that may be verified as follows:
,
,
,
,
.
…
1 0 .
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Yeddula 29 3
Chapter 3
HILBERT HUANG TRANSFORM (HHT) IMPLEMENTATION 3.1
HHT Introduction Hilbert Huang Transform (HHT) is an adaptive and data dependent time-
frequency analysis method proposed by Norden E. Huang where Empirical Mode Decomposition (EMD) and Hilbert Spectral Analysis (HSA) are used together. It is widely used in the analysis of nonlinear and nonstationary signals (Huang, et al 1998). HHT does not need any requirements or assume any conditions regarding the linearity and stationarity of the signal. EMD is the core algorithm of HHT that decomposes the nonlinear and nonstationary signal into various Intrinsic Mode Functions (IMFs). In general, EMD algorithm is described as follows (Huang and Shen 2005; Bajaj and Pachori 2011; Lin, et al. 2009): Step (1): Local maxima, Local minima, and zero crossing are determined from the input signal. Step (2): Using interpolation techniques with proper boundary conditions, an upper envelope #$ going through the local maxima points and a lower envelope #% going through the local minima points are calculated. Step (3): The mean &#' #$ ' #% '/2 is calculated and used to
extract the detail component )' *' &#'. The steps (1) to (3) are generally referred to as Sifting Process. Sifting is the important process of the HHT algorithm that separates the central signal from various other random or noisy signals in an empirical way (Meeson 2005).
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Yeddula 30 Step (4): )' is checked for IMF requirements and other stopping criteria.
Step (5): If )' satisfies the requirements, then the sifting process is stopped
considering )' as an IMF '. If not, the process is repeated while considering )' as the input signal. The sifting process and decomposition is continued till the original signal *' is
decomposed into a set of IMFs and the residue signal '. The residue signal is the one that cannot be further decomposed into IMFs.
*' ' '
3.1
The components that satisfy the following two basic conditions/requirements are considered IMFs: (i) the number of extrema and the number of zero crossings must be the same or differ at most by one, (ii) the mean value of local maxima envelope and local minima envelope should be zero at any point (Huang, et al 1998; Bajaj and Pachori 2011; Lin, et al. 2009). Hilbert Transform is applied next to each of the IMF and residue to obtain a set of analytic signals. The estimation of the analytic signal ,' using Hilbert transform for a real signal *' is specified as follows (Johansson 1999; Kschischang 2006): 8 2 8 /2 *7 *7 1 7 6 7 -' lim5 6 '7 . 234 8 /2 ' 7 8 2
,' *' -' '. # 98
where -' is the Hilbert transform of *',
3.2
3.3
' :* ' - ' -' 9' arctan @ A *'
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Yeddula 31
The instantaneous angular frequency B' can be estimated from 9' such that B'
9 '
3.4
This brief overview of general HHT implementation above is widely used in the analysis of various practical signals (Huang and Shen 2005; Bajaj and Pachori 2011; Lin, et al. 2009). Different stoppage criteria can be used in the sifting process such as Cauchy SD convergence, S-method, etc. Their detailed description can be found elsewhere (Huang, et al 2003; Huang and Attoh-Okine 2005; Huang and Shen 2005). Different versions of HHT algorithms have been implemented using various interpolation algorithms in the sifting process to evaluate the envelopes, such as Cubic spline interpolation (Huang, et al 1998; Rilling, Flandrin and Gonçalves 2004), Akima cubic spline interpolation (Radić, Pasarić and Šinik 2004), etc. Various boundary conditions may also be considered during interpolation such as tied to zero, mirroring nearest extrema boundary conditions (Rilling, Flandrin and Gonçalves 2004), tied to signal, etc. In order to reduce the end point effects due to miscalculated boundary conditions during interpolation, several envelope estimation algorithms are used in practice including those based on neural networks (Lee and Lee 2010), etc. Improved algorithms such as Bi-variate EMD (Rilling, et al 2007), Complex EMD (Tanaka and Mandic 2007) and Multivariate EMD (Rehman and Mandic 2010) for multi-channel and multi-dimensional signal analysis, Ensemble EMD for a higher accuracy in noisy data (Wu and Huang 2009), etc., are also available. Few freely available implementations of EMD were obtained from Internet and are listed in Appendix D.
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Yeddula 32 Each implementation has its own advantages and drawbacks. Rato, Ortigueira and Batista (2008) presented a detailed overview of various algorithms. End point effects, boundary conditions, and various interpolation schemes were compared and their shortfalls were addressed while implementing the HHT algorithm using energy based operators. Therefore, Rato’s HHT implementation was adopted for the present project as a benchmark EMD algorithm for comparing the HHT algorithms designed and implemented in the present project. 3.2
HHT Implementation In present project, HHT was implemented in Matlab environment with custom-
built codes. Strict local extrema were calculated and used as maxima or minima. For example, assuming ‘x’ as a random signal, that has x(n)>x(n-1) and x(n+1)=x(n), few implementations consider x(n) as a local maximum. However, in the present implementation, it is considered as local maximum, only if x(n+1)>x(n+2). Cubic spline interpolation was used in the envelope construction. Three different boundary conditions for interpolated envelopes were considered during implementation. Zero boundary condition assumes that the envelopes were tied to zero at the ends. Signal boundary condition implies that the envelopes were tied to the signal at the end points. These two are used in various existing EMD implementations. A novel Average or Extrema boundary condition assumes that the end points of extrema envelope can be either an average of the signal at end point and the nearest extremum, or the signal at the endpoint itself is considered to be an extremum. This idea was devised and implemented in the present project. Figure 3.1 illustrates the application of Average
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Yeddula 33 or Extrema boundary condition for an arbitrary signal at one of the end points (starting point).
Figure 3.1: Average (b) or Extrema (a) boundary condition illustration As seen in Figure 3.1 (a), in the vicinity of the signal starting point, signal is decreasing and hence x1 is compared with first maximum M1. As the starting point x1 is greater than the first maximum (M1) and, therefore, this should be considered as a maximum at the starting point and included as a boundary point during interpolation for maxima or upper envelope. The boundary point for minima or lower envelope is estimated as an average of the signal at starting point (x1) and the first minimum (m1). As seen in Figure 3.1 (b), the signal is decreasing in the vicinity of the starting point and hence it is compared to the first maximum M1. As the starting point (x1) is lesser than the first maximum (M1), there is a chance that x1 could not be considered as a maximum at the starting point and hence the average of the signal point (x1) and first maximum (M1) is considered as boundary point during the interpolation for maxima or upper envelope. The boundary point for minima or lower envelope is considered as an average as explained earlier. If the signal is increasing in the vicinity of the starting point, x1 is compared with the first minimum to extract the boundary point for minima or lower envelope and the
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Yeddula 34 boundary point for maxima or upper envelope is estimated as the average of x1 and the first maximum M1. Similar procedure shall be applied to the other end point of the signal but compared with last occurring extrema set instead of first extrema set as seen in the above illustrated example. The EMD Matlab code developed in present project for HHT implementation can be found in the links listed in Appendix D. Analytic signal generation based on the Hilbert transform was performed using fft() routine of Matlab (Marple Jr 1999). 3.3
Features from HHT Analytic Signal
3.3.1
Instantaneous Frequency Estimation The instantaneous frequency is estimated from the set of HHT analytic signals by
differentiating the instantaneous phase of the analytic signal with respect to time as in equation E3.4. This is similar to the instantaneous frequency estimations in Hilbert Spectral Analysis. The instantaneous phase sequence of the analytic signal should be unwrapped before applying difference or differentiation to avoid negative frequencies (Freeman 2007). Simple difference operator, approximate differentiation using continuous derivative of phase at discrete points (Long 1995), Savitzky-Golay differentiation (Savitzky and Golay 1964), and other methods can be used to estimate frequency from the phase sequence. It is always preferable to bound the instantaneous frequency to D0 , EF /2 (where EF is the sampling frequency) In present project, the system was assumed to be evolving in time, which results in a never decreasing phase sequence. This highlights the need to unwrap the phase. A simple difference operator was used to estimate instantaneous frequency as
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Yeddula 35 GDH
9D 1H 9DH I EF 2.
J D0, 1H
3.5
L)#M# EF N N&OPQ GM#RS#T-, 9 N O)N#, GDH N N''#USN GM#RS#T- . It is important to note that for a – point analytic signal, we obtain 1
instantaneous frequency points. Also, if any instantaneous frequency point GDH V EF /2 ,
GDH is subtracted from EF to make GDH J D0, EF /2H.
This process is time consuming especially in the phase unwrapping stage. So, another method based on the similar procedure was implemented in present project for the fast estimation of instantaneous frequency. Here, an unwrapped phase sequence was used to estimate the instantaneous frequency. The steps were: 1. Difference operator is applied on instantaneous phase of discrete analytic signal to estimate frequencies. 2. If the frequency is negative, i.e. GDH W 0, then GDH GDH EF so that EF /2, 0H is
mapped to EF /2, EF H by adding EF . This is similar to phase unwrapping that takes care of negative frequencies. 3. Then an anti-aliasing step is performed to limit the frequency within D0, EF /2 by
subtracting the frequencies that are in the EF /2, EF H range from EF .
As explained earlier in this section, if unwrapped instantaneous phase is used, only positive frequencies within D0, EF range are obtained. So, step 2 can be skipped and the anti-aliasing step 3 can be used to limit the signal D0, EF /2. 3.3.2
Energy and Power Estimations based on HHT In general, the energy of a uniformly sampled time series *DH, 1 'U is [
specified as ∑Y Y *DH and the average power Z is estimated as Z .
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Yeddula 36 Hilbert transform can be used to obtain the complex analytic signal of a time series, whose real part is represented by the original time series. Hence, similar concepts of energy and average power can be applied to the analytic signal. 3.3.2.1 Power Related Features based on Decomposition In the present project, the amplitude of the analytic signal was used in power estimations. Using Hilbert transform on time series *DH, an analytic signal \ is
constructed and denoted by DH. # ]DYH , 1 'U as in equation E3.3. The average power was estimated as Z ∑Y Y DH /
As from the instantaneous frequency estimations, it is noted that only ( 1)
points are obtained for instantaneous frequency. In order to build a time-frequency data, new 1 point amplitudes are constructed using the original analytic signal \. The new amplitude points are denoted by ^ DH DH DH/2 where DH
DH, 1 'U 1 and DH D 1H, 1 'U 1. These new amplitude points are used in power estimations in the present project. Similarly, other ways of obtaining ( 1) amplitude points can also be used such as considering DH or DH alone, etc. In present project, the marginal band power for a frequency band having limits G (lower) and G (upper) are estimated using the ^ DH and GDH. The set of points _ are collected such that _ `a|a ^ D&H L)#M# GD&H c G GD&H V G , GUM PP & d D1, 1He. The marginal band power is specified by |a| ZG , G , ad_
3.6
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Yeddula 37 These computations are applied to each IMF and the residue of a decomposed signal. In the present project, ZG , G for each IMF is extracted and referred as a band power of first IMF, second IMF and etc. The total band power of the decomposed signal is estimated as the sum of the corresponding band powers across all the IMFs and the residue. Similarly, the total average power of the decomposed signal is estimated as the sum of the average power of all the IMFs and the residue. The estimations done above use the analytic signal amplitude rather than the original signal amplitude that is the real part of the analytic signal. 3.3.2.2 Importance of Scaling Scaling is crucial when comparing the power related features of the decomposed signal estimated by the HHT method with the power obtained by other methods, such as wavelets, STFT etc. Therefore, the scaling of analytic signal in power calculation is important to minimize discrepancy from reducing the point data to 1 point data, deviation because of summation of the IMF and the residue powers to obtain the total average power, etc. The sum of each IMF’s energy and residue energy may be either higher or lower than the energy of the original signal: i.e. the sum of IMFs and the residue. This can be proved using a simple mathematical explanation as shown below \ _ \, _ 0 3 \ _
W \ _ GUM \. _ W 0, UOOUN'# NQN
V \ _ GUM \. _ V 0, N&# NQN
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Yeddula 38 The scaling factor is computed using the average power from the original time series Zg , the total average power of the decomposed signal Z. Scaling factor is selected
as Zg /Z and could be used to convert the powers estimated in the present project based on HHT decomposition to the corresponding scale of the powers evaluated using other methods, such as FFT, STFT, wavelets, etc. 3.3.3
Hilbert Weighted Frequency (HWF) Computation The instantaneous frequency and amplitude information extracted from the
analytic signal can be used to compute Hilbert Weighted Frequency. As specified in earlier sections, for an point analytic signal constructed using Hilbert transform, we can have 1 instantaneous frequency points G and modified amplitudes h. The
HWF Gi can be computed as (Van Zaen, et al. 2010; Oweis and Abdulhay 2011) Gi
^ ∑ G ^ ∑ G
3.7
This Gi can be viewed as the average frequency derived from the instantaneous information. In case of HHT, the instantaneous frequency information is extracted for all the IMFs and, therefore, HWF for each IMF can be estimated. As HHT decomposes the wide-band signal into various narrow-band IMFs, HWF for each IMF has even more meaningful representation as the HWF for a narrow-band IMF can be considered as dominant frequency (Oweis and Abdulhay 2011). 3.4
Comparison, Validation and Testing of HHT HHT implemented in this project with various boundary conditions, such as tied
to zero, tied to signal, average-or-extrema boundary conditions, were compared. Also, these methods were compared with the Rato’s HHT.
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Yeddula 39 An experimental Electro-Dermal Response (EDR) signal acquired in our lab using TI MSP430 Launchpad was utilized in this comparison and is shown in Figure 3.2.
Figure 3.2: Input signal for HHT analysis and comparison The maximum value of the signal amplitude occurs during the start of the signal and had a value around 700 units. This signal is analyzed by using various HHT implementations. Rato’s HHT is assumed as a comparison benchmark, as Rato’s implementation tried to address various drawbacks of the conventional (or traditional) HHT algorithm. HHT implemented in present project while using various boundary conditions, such as tied to zero, tied to signal, average or extrema were used to analyze the EDR signal. The IMFs obtained as a result of HHT decomposition of EDR signal are illustrated in Figures 3.3, 3.4, 3.5, and 3.6.
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Yeddula 40
Figure 3.3: IMF decomposition using boundary tied to zero based HHT
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Yeddula 41
Figure 3.4: IMF decomposition using boundary tied to signal based HHT
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Yeddula 42
Figure 3.5: IMF decomposition using average or extrema boundary based HHT
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Yeddula 43
Figure 3.6: IMF decomposition using Rato’s HHT
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Yeddula 44 The numbers such as (1) in the Figures 3.3 – 3.6 represent the IMF number and (R) represents the residue. We observe in Figures 3.3 – 3.6 that the HHT implementation using zero boundary condition produces more signal distortions compared to the others. The amplitude of original signal is around 700 units while those obtained in zero boundary condition are in 1000 – 10000 units. Also, across all the decompositions, the IMF1 contains the high frequency information and residue represents the low frequency or DC component information. Therefore, the Empirical Mode Decomposition acts as an inherent filter bank structure representing the high frequency information in the first IMF, with the frequency range decreasing with the order of IMFs (increasing IMF number), and while storing the DC or low frequency signal components in the residue (Flandrin, Rilling and Gonçalves 2004). It should also be noted that the EMD is very sensitive to the boundary conditions used (so called end point effects) and can be easily distorted. To facilitate the selection of the HHT analysis method, selected decomposition parameters are illustrated in table 3.1.
Table 3.1: Selected parameters of various HHT methods Details
Method 1
Boundary condition Run time(in seconds)
tied to tied to average or Rato's HHT zero signal extrema based 89.603281 84.225081 96.135385 243.89422
# of IMFs (without residue)
Method 2
Method 3
Method 4
14
14
15
14
Max Amplitude value of IMFs
7071.6
20.8966
19.9426
14.3386
Max Amplitude value of IMFs & residue
7071.6
682
664.799
676.3886
Max Amplitude (from HHT time-freq data)
7282
734.754
712.4232
733.7836
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Yeddula 45 Zero boundary condition of Method 1 indicates several draw backs and the most important disadvantage is that the signal may be contaminated by the end point effects leading to a large variation in amplitudes as observed in Figure 3.3. Method 2 and Method 3 show the results similar to Rato’s HHT. Although Rato’s HHT was assumed as the comparison benchmark, Method 2 and Method 3 were selected for this project instead of Rato’s HHT for their considerable higher computation speed. The Method 2 assumes that both the maximum and minimum at the end points (both starting and ending) are same as that of the signal at end points. This assumption is not realistic as the same point cannot be both the local maximum and minimum. Also, of these two methods, Method 3 was considered as the best choice since the average or extrema boundary condition is logically better than tying the boundary extrema points to the signal. Therefore in the present project, HHT implemented with average or extrema boundary condition shall be used in the upcoming chapters for HHT analysis. Also, the time-frequency data were computed for the experimental EDR signal using average or extrema boundary HHT method and the results are illustrated below in Figures 3.7 and 3.8 for all the IMFs including the residue and excluding the residue respectively.
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Yeddula 46
Figure 3.7: Time frequency data for all the IMFs and residue using average or extrema
Figure 3.8: Time frequency data for IMFs alone using average or extrema It is seen in Figures 3.7 and 3.8 that the residue contained large DC component that is also observed in Figure 3.5. We observe in Figure 3.7 that the noise contamination can be easily noticed if the residue is eliminated while plotting.
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Yeddula 47 Next, a synthetic signal was generated in Matlab using the code in Appendix D. The generated signal is shown in Figure 3.9
Figure 3.9: Synthetic Signal The synthetic signal represents a non-stationary sequence where frequency changes after every 5 seconds interval (10 Hz for 0-5 sec, 25 Hz for 5-10 sec, 50 Hz for 10-15 sec, 100 Hz for 15-20 sec). Each frequency component was shown for 0.1 sec in the following Figure 3.10
Figure 3.10: Synthetic signal for 0.1 second duration after frequency transition
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Yeddula 48 Discrete Fourier Transform (DFT) analysis (using the Fast Fourier Transform Matlab routine) was performed on the signal shown in Figure 3.9 and the obtained amplitude-frequency plot is illustrated in Figure 3.11.
Figure 3.11: DFT spectrum of synthetic signal We conclude from Figure 3.11, that DFT does not provide time-frequency representation of the signal analyzed. Instead, DFT may indicate the major frequency components that are present in the signal. Additionally, the spectral information might be contaminated by the spectral leakage in most cases. In the present results, the amplitude pertaining to the frequencies present is not in accordance with the input. Therefore, DFT is not suitable for the spectral analysis of non-stationary signals (Huang, et al. 1998; Huang and Shen 2005; Klonowski 2009; Senroy, Suryanarayanan, and Ribeiro 2007). Short Time Fourier Transform (STFT) using 256 point rectangular window with 255 overlap points was used next to obtain the spectrogram plot shown in Figure 3.12 for the same input signal.
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Yeddula 49
Figure 3.12: STFT based time-frequency representation of the synthetic signal As seen in Figure 3.12, STFT produces the time-frequency representation of the signal. Based on the window size, the time-frequency resolution can be adjusted. The drawback of STFT is that, time resolution and frequency resolution are inversely related. Also, it can be observed in Figure 3.12 that during the transition, the frequency and time information is blurred. Also, STFT inherent assumption of piece-wise stationarity may be inappropriate for many practical sequences. HHT analysis discussed above was performed next on the synthetic signal and results are shown in Figures 3.13 and 3.14.
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Yeddula 50
Figure 3.13: IMF decomposition of the synthetic signal
Figure 3.14: HHT based Time-Frequency decomposition of the synthetic signal The spikes in IMF2 seen in Figure 3.13 may be used in determining the transition instances when frequency of the sinusoidal signal undergoes changes. As seen early in
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Yeddula 51 Figures 3.5 and 3.6, HHT generally acts as an inherent filter bank structure in decomposing wide band non-stationary signals into narrow band IMFs. It is seen in Figure 3.13, that IMF1 retains the original sinusoidal signal without much decomposition of signal in further IMFs as seen in Figures 3.5 and 3.6. However, the high frequency spike information characteristic to the transition is dominant in the first part of the decompositions i.e., IMF2 and IMF3 compared to the latter part of the IMFs and residue. Therefore, we conclude that HHT is a highly adaptive and data-dependent time frequency analysis method that can be used for variety of real world signals. As seen in Figure 3.14, the time-frequency data based on the HHT decomposition indicates the transition time more clearly and accurately than STFT results shown in Figure 3.12. Although the frequency content estimate shown in the Figure 3.14 may contain minor errors, the result is far superior to those obtained by either STFT or DFT. The comparisons and validations reported in the present section justify the HHT based signal analysis and illustrate its efficient use in analyzing various real-world signals that are inherently non-stationary and nonlinear.
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Yeddula 52 4
Chapter 4
REVIEW OF STATISTICAL TESTS & CLASSIFICATION METHODS USED 4.1
Kruskal-Wallis H-test Kruskal-Wallis H-test is a non-parametric method of testing that is generally used
in comparing three or more unrelated or independent samples. It is used in testing whether the samples originate from the same distribution or not. Similar to the most of the non-parametric methods, it also uses the ranked data and examines the medians of the samples (Gibbons and Chakraborti 2003). It is widely considered to be an extension to the Mann-Whitney U-test. However, Mann-Whitney U-test is limited to compare two unrelated samples; while more than two samples could be compared using KruskalWallis H-test. One way Analysis of Variance (ANOVA) is the parametric equivalent method of Kruskal-Wallis H-test (Corder and Foreman 2009). The following steps provide a general implementation of Kruskal-Wallis test as mentioned in various sources (Corder and Foreman 2009; Gibbons and Chakraborti 2003; Lowry 2012). SPP k-OU')#NN k4 : PP ')# m N&OP# QMUSON M# #'TP
\P'#M'# k-OU')#NN kn : PP ')# m N&OP# QMUSON M# U' #'TP 1. All the samples were combined and ranked. These were rank ordered. 2. H-test statistic was computed as o
12 3 1 k 1
4.1
where is the total number of values across all the samples, is the sum of ranks from
the particular 8i sample, is the number of values in the corresponding 8i sample and m is the number of sample groups.
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Yeddula 53 3. If ranking of the values across all the samples resulted in any ties, a tie correction factor p is computed as
∑q r q p 1 r
4.2
where is the total number of values across all the samples, q is the number of values in a set of ties. The corrected k is computed using the correction factor p where the
original k computed in step 2 is divided by the correction factor p as given below. TUMM#T'# k
k p
4.3
4. H-statistic approximates the s distribution and as a result the critical values
for a particular significance level t can be computed or looked up from s distribution with (m 1 degrees of freedom.
If the computed H-statistic is greater than the value looked up from s
distribution, then the null hypothesis will be rejected and thereby concluding a significant difference between the sample groups. Kruskal-Wallis test does not make any assumptions of the data normality unlike ANOVA and hence widely used for any type of generic real world data that do not follow a specific distribution. On the other hand, it assumes that the observations in each sample group come from the population with the same shape of distribution. If different groups have different distributions, the Kruskal-Wallis test results might not be accurate (McDonald 2009). 4.1.1
Usage in present project Based on the idea from Tcheslavski and Gonen (2012) work, Intra-group and
Inter-group H-statistics (Hstats) were computed using Kruskal-Wallis test. For example,
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Yeddula 54 two groups of observed data Group A and Group B were considered. Intra-group Hstats for group A (HsAA) was computed by arbitrarily dividing the Group A into A1 and A2 subgroups and by using Kruskal-Wallis test on A1 and A2. Similarly, Intra-group Hstats for Group B (HsBB) was also calculated. The inter-group Hstats (HsAB) was computed by using Kruskal-Wallis test on group A and group B. The Intra-group Hstats HsAA and HsBB were used to draw conclusions on the homogeneity of the observed data within the groups A and B respectively. If inter-group Hstats (HsAB) is considerably higher than the intra-group Hstats (HsAA and HsBB), we may conclude that groups A and B are significantly different. While calculating the intra-group Hstats, it has been observed that: although the division process of the groups into subgroups is performed arbitrarily, this process has affected the computed Hstats. Hence, a new simple and novel way of calculating the Hstats was implemented and used in the present project. For an example, the epileptic EEG data used in chapter 5 was used to demonstrate the effect of division on intra-group Hstats. The HWF for IMF1 of the normal EEG data with eyes open (SET B or O – having 100 data points) was divided into two sub-groups of 50 data points each. The observations in each subgroup were plotted in Figure 4.1.
Figure 4.1: (a) Sample Subgroup observations and (b) their corresponding box plots
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Yeddula 55 Kruskal-Wallis test was performed on the two subgroups as shown in Figure 4.1 to obtain a Hstats value as 22.23, which is greater than the critical value 6.6349 (degrees of freedom=1 and significance level α=.01). This concludes that subgroup 1 and subgroup 2 were having 99% statistically significant differences. Next, another arbitrary division was performed on the same data considered above and divided into two subgroups as shown in Figure 4.2
Figure 4.2: (a) Sample Subgroup observations and (b) their corresponding box plots with another repetition of arbitrary division Kruskal-Wallis test was performed on the two subgroups as shown in Figure 4.2 to obtain a Hstats value of 0.0023, which is considerably lower than the critical value 6.6349 (degrees of freedom=1 and significance level α=.01). This concludes that subgroup 1 and subgroup 2 were not having any statistically significant differences. This result is in direct contradiction to the result mentioned above from the data in Figure 4.1. Also, it seems to have Type I error for the results due to data in Figure 4.1 if results in Figure 4.2 were considered correct and Type II error for the results due to data in Figure 4.2 when Figure 4.1 results were considered correct. Hence, the arbitrary division of the
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Yeddula 56 data into two subgroups had a negative impact on the analysis done using Kruskal-Wallis test as mentioned in Tcheslavski and Gonen (2012) work. In order to overcome this, a novel simple method is implemented in this project where a repetitive process of randomly dividing the observations into subgroups, calculating the Hstats for each repetition and using the mean value of all repetitions to obtain the final Hstats value. Within the present project, this method shall be referred to as Kruskal-Wallis test with repetition and random selection. Now, using this method with a repetition rate of 1000, Hstats value was calculated for the data used in the above demonstration. The obtained Hstats values during each repetition was stored and used for further analysis as shown in Figure 4.3
Figure 4.3: (a) Hstats value in each repetition (b) Histogram of Hstats The mean value of the Hstats obtained from the above results was 1.0221. From Figure 4.3, it was evident that there were few times when Hstats was greater than the critical value, but majority of the times it was quite lesser than the critical value 6.6349. As a result, the final Hstats value 1.0221 (which was the mean of the Hstats for all repetitions) is considerably lower than the critical value 6.6349. Hence the intra-group Hstats obtained clearly concludes that the two subgroups were not having significant differences.
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Yeddula 57 This present method will also be verified in upcoming chapters 5 and 7. KruskalWallis test with repetition and random sampling can also be used in calculating Intergroup Hstats when a sample of data from the total available data for each group is considered in Hstats calculation. 4.2
kNN Classification k – Nearest Neighbor (kNN) is one of the instance-based supervised learning
methods, that is widely used in classifying the objects based on the closest or nearest neighbor training examples. The nearest neighbors of an instance are defined in terms of the various distance measures, such as Euclidean distance, Manhattan distance, and etc. Each instance is represented as a point in the feature space. A simple algorithm uses the majority class of the first nearest k training instances as the class of the queried instance.
Figure 4.4: kNN example (a) represents training examples and query instance and (b) represents the decision induced for 1-Nearest Neighbor (Mitchell 1997) It is seen in Figure 4.4 (a) that for a 5-Nearest Neighbor classification: the query instance *u can be attributed to the majority negative class and for a 1-Nearest Neighbor
classification: the query instance *u can be grouped with positive class. In Figure 4.4 (b),
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Yeddula 58 the convex polygon regions surrounding each training instance illustrate the region of influence for 1-Nearest Neighbor algorithm. If any query instance is within such region, it shall be classified to the class based on the training instance of that region. This simple algorithm fails when the query instance is on the polygon boundary. In order to address this limitation, few improvements were made to the simple kNN by considering the weights from all the training instances. The latter is widely known as distance-weighted kNN (Mitchell 1997). Distance-weighted kNN is widely used in various practical problems and is robust to noisy training data. It is generally accurate and effective in classification when large training data are provided. In contrary to this, for a large training dataset, it requires large memory resources to store all training data and is computationally expensive as distance measures are calculated for each of the query/test instance to all of the training data. A detailed discussion on kNN algorithms, its improvements and other pattern recognition or classification mechanisms are beyond the scope of this project. Palaniappan (2003) had implemented kNN of order 5 using Manhattan distance measure to successfully classify alcoholic and control VEP EEG. Inspired from Palaniappan (2003) work, kNN algorithm of order 5 using Manhattan distance was implemented in the present project as a classifier. “knnclassify” function from the Matlab Bio-Informatics tool box can be used for this purpose (The Mathworks 2012). For the present project, Seo (2005) work was used and the code was modified to implement the kNN classifier using Manhattan distance measure.
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Yeddula 59 4.3
Leave-One-Out Cross-validation Scheme Cross-validation is a statistical method of comparing and evaluating the learning
algorithms using two sets of data such as the training or learning set and the validating set. There are various cross-validation schemes such as k-fold cross validation, Resubstitution validation, Hold-Out validation, Leave-One-Out cross-validation, repeated k-fold cross-validation, etc. (Refaeilzadeh, Tang and Liu 2009). Leave-One-Out crossvalidation is implemented in the present project to compare various features used for classification purposes. In Leave-One-Out cross-validation scheme, a single observation is considered as a test or validation case and the remaining observations are considered as a training class. This shall be repeated such that each observation is used once as validation/test case. This is a special case of k-fold cross-validation where k equals to the length of the total available observations. Though it has very large variance, it does not over fit the data and it does not overlap the training and validation sets. Although this method was simple to implement, such implementations take lot of time considering the fact that it was repeated by the length of the observations. Leave-One-Out cross validation scheme was chosen in present project because of its unbiased performance estimation of the classifier (Refaeilzadeh, Tang and Liu 2009).
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Yeddula 60 5
Chapter 5
EPILEPTIC EEG ANALYSIS 5.1
Data Description EEG data for the present study were downloaded as compressed files from a
webpage at “http://epileptologie-bonn.de/cms/front_content.php?idcat=193&lang=3 &changelang=3” which was accessed and verified the latest on June 24th 2012. The downloaded data consist of five datasets SET A (Z.zip), SET B (O.zip), SET C (N.zip), SET D (F.zip) and SET E (S.zip) with each set containing 100 time series. Each time series was a single-channel EEG segment of 23.6 seconds duration selectively extracted by visual inspection from a continuous 128 channel EEG signal, recorded with a sampling rate of 173.61Hz. SET D represents inter-ictal activity recorded from hippocampal section, which was the epileptogenic zone. SET C also includes inter-ictal activity recorded from the zone similar in location to epileptogenic zone but on the opposite hemisphere of the brain. SET E includes the EEG recorded during seizure activity. SET A, and B were recorded with eyes open and closed states respectively from healthy subjects after surgically treating their epileptogenic zones. SET C, D, and E were intracranial readings while SET A and B were scalp EEG readings. The more details regarding data collection methodology used to produce these five sets can be found elsewhere (Andrzejak, et al. 2001). 5.2
Analysis Methods Without any preprocessing, the HHT based on average-extrema boundary
condition with standard deviation and a limit on number of siftings-based stopping
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Yeddula 61 criteria as explained in section (3.2) was used to analyze the EEG data. Standard deviation and the upper limit of siftings were chosen as .05 and 1000 respectively. Instantaneous frequency and Hilbert weight frequency were estimated from the HHT analytic signal output. Marginal band powers across various bands, such as δ (0.54Hz), θ (4-8Hz), α1 (8-10Hz), α2 (10-12Hz), β1 (12-20Hz), β2 (20-30Hz) and γ1 (3040Hz), were estimated using the HHT time-frequency data as explained in section (3.3). Other power-related features based on the decomposition, such as total average power of decomposed signal and etc., were also extracted. Kruskal-Wallis test with repetition and random selection as specified in section (4.1) was implemented to assess the inter-group and intra-group differences in all the five sets and for various features, such as HWF of first IMF and power-related features based on the decomposition. In the present study, a repetition of 10000 was used. For intragroup calculations, 100 points of extracted features from each set were randomly ordered and divided into two groups containing 50 points. For inter-group calculations, 50 points were randomly selected from each of the two sets under consideration. As only two groups at a time were used during calculations, degree of freedom was considered to be 1, which made the threshold value of Hstats to be 6.63490 for 99% significance. When the calculated value of Hstats was greater than the threshold, the two groups were deemed different with 99% statistical significance. Based on Tzallas, Tsipouras and Fotiadis (2007; 2009) works, five different classification problems were created. PROBLEM (a): Normal/healthy EEG (A, B) as C1, interictal (C, D) as C2 and ictal (E) activity as C3 were considered as three different classes.
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Yeddula 62 PROBLEM (b): The data from SET A, B, C, D were grouped to represent NonSeizure activity as C1 and data from SET E was considered as other group representing Seizure activity as C2. PROBLEM (c): similar to (a) but only one data set was selected for each of two classes’ i.e. Normal/healthy EEG (A) as C1 and interictal activity (D) as C2, while the third class was retained the same (E) ictal activity as C3. PROBLEM (d): similar to (b) but only one data set was chosen for Non-seizure activity (A) as C1. PROBLEM (e): A special case where each data set was treated as a separate group and classified. Various features – such as HWF of IMFs and power-related features based on decomposition obtained using the present HHT algorithm implemented in this project and HWF of IMFs obtained using Rato’s HHT method – were used for classification purposes. K-Nearest Neighbor classification algorithm based on Manhattan distance was used with order 5 and the results were compared using Leave-One-Out cross validation scheme.
Table 5.1: Classification problems
SET FILE
Description
Classification PROBLEM (a) (b) (c) (d) (e)
A
Z
Healthy scalp EEG eyes closed
C1
C1
C1
C1
C1
B
O
C1
C1
-
-
C2
C
N
C2
C1
-
-
C3
D
F
Healthy scalp EEG eyes open Intracranial interictal activity from non-epileptogenic zone Intracranial interictal activity from epileptogenic zone
C2
C1
C2
-
C4
E
S
Ictal activity or Seizure activity
C3
C2
C3
C2
C5
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Yeddula 63 5.3
Results and Discussions The HWF of first IMF and HWF of second IMF obtained using the HHT
implemented for all five different data sets are shown in Figures 5.1 and 5.2.
Figure 5.1: HWF of IMF1 vs HWF of IMF2 using the HHT implemented
Figure 5.2: HWF of IMF1 vs HWF of IMF2 using Rato’s HHT
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Yeddula 64 By visual comparison from the above two Figures, SET C and D indicate a considerable overlap, while every other SET exhibits distinguishable dominant regions with slight overlaps with other sets. Comparing Figure 5.1 and Figure 5.2, Rato’s output shows a reduced overlap and clear distinguishable features while the output from the HHT indicates a spread out and increased overlap between various sets. Kruskal-Wallis test results were calculated for five different data sets based on HWF of first IMF using the implemented HHT and are tabulated in Table 5.2.
Table 5.2: HSTATS for HWF IMF1 using the HHT implemented HSTATS SET A SET A 1.0282 SET B 29.994 SET C 57.1783 SET D 25.479 SET E 68.4606
SET B SET C SET D 29.8227 57.181 25.6476 1.0043 70.1808 50.685 70.2202 0.996 4.2313 50.673 4.2303 0.9891 21.1008 73.3311 70.4639
SET E 68.4463 21.2381 73.347 70.4516 0.989
We conclude from Table 5.2 that SET C and D are not significantly different. Though SET A and B were derived from healthy subjects’ EEG, they illustrate significant difference. We also observe that each of the SETs A, B, C and D are significantly different compared to SET E. Kruskal-Wallis test results were evaluated next for five different data sets for Total Average Power of the decomposed signal obtained using the implemented HHT and are tabulated in Table 5.3.
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Yeddula 65 Table 5.3: HSTATS for Total Average Power of the decomposed signal HSTATS SET A SET B SET C SET D SET A 1.0104 27.9806 3.948 4.6344 SET B 27.9385 1.0096 7.8142 3.0908 SET C 3.9458 7.7911 0.9721 0.98 SET D 4.5561 3.0915 0.9684 0.9805 SET E 74.0224 71.478 72.6313 63.2468
SET E 74.0221 71.48 72.6467 63.3265 1.0041
The total average powers of the decomposed signal for SET A, C, and D are not significantly different with each other. Similarly, SET B, C, and D are also not significantly different with each other. On the other hand, SET E is significantly different compared to all other datasets. Kruskal-Wallis test results evaluated for five different data sets and for various bands are illustrated in tables 5.4 – 5.10.
Table 5.4: HSTATS for Total δ-band (0.5-4Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A 0.9863 2.9895 28.4609 23.0692 74.2574
SET B 2.9909 0.9567 19.3855 15.4744 73.9408
SET C 28.4787 19.5548 1.0184 0.7514 68.0265
SET D 23.0027 15.4676 0.7588 1.0014 54.3828
SET E 74.2574 73.9032 68.0187 54.4479 0.9817
SET A and B are not significantly different, while every other dataset is significantly different from each other.
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Yeddula 66 Table 5.5: HSTATS for Total θ-band (4-8Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A SET B SET C SET D 0.995 45.552 9.6978 16.6778 45.5858 0.9983 10.0931 1.6472 9.7175 10.1205 0.9926 3.4674 16.7067 1.6714 3.4111 0.9961 74.2574 72.9786 73.435 70.1583
SET E 74.2574 73.0016 73.4261 70.131 1.0345
SET C and D indicate no significant difference. Similarly, SET B and D also show no significant difference. On the other hand, SET E is significantly different compared to other datasets.
Table 5.6: HSTATS for Total α1-band (8-10Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A 1.018429 60.8536 12.27595 1.199257 73.49194
SET B 60.81936 0.98311 57.34821 30.98689 59.07209
SET C 12.22048 57.42901 1.022112 3.023629 73.65159
SET D 1.159586 30.89772 3.03908 1.018574 70.78798
SET E 73.48624 59.15413 73.65949 70.78596 0.984351
SET A and D show no significant difference. Similarly, SET C and D are not significantly different. As previously, SET E is significantly different compared to other datasets.
Table 5.7: HSTATS for Total α2-band (10-12Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A 1.005299 57.98704 33.24569 12.60711 73.7875
SET B 58.0996 0.990457 68.19962 56.05592 49.24413
SET C 33.27931 68.21038 1.014337 2.745178 73.90293
SET D SET E 12.55279 73.776 56.07536 49.3764 2.752641 73.90139 1.004257 71.6216 71.58774 1.008483
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Yeddula 67 SET C and D show no significant difference. SET E is significantly different from other datasets.
Table 5.8: HSTATS for Total β1-band (12-20Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A 1.011928 50.08831 36.55693 23.4423 74.0188
SET B 50.08524 0.999222 63.40295 55.83833 52.84166
SET C 36.62039 63.39083 0.99384 1.364767 73.57521
SET D 23.42009 55.85118 1.361444 1.015994 71.75264
SET E 74.0179 52.93808 73.57159 71.75334 0.988164
SET C and D indicate no significant difference. SET E is significantly different from other datasets.
Table 5.9: HSTATS for Total β2-band (20-30Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A 1.017923 11.91019 38.37325 29.18348 67.51481
SET B 12.06227 1.003895 51.78165 44.9597 65.84877
SET C 38.44922 51.78353 1.023821 1.153566 72.55107
SET D SET E 29.09975 67.5132 44.92025 65.82156 1.114824 72.56327 0.993344 70.3704 70.37944 0.9847
SET C and D show no significant difference. SET E is significantly different from other datasets.
Table 5.10: HSTATS for Total γ1-band (30-40Hz) power of the decomposed signal HSTATS SET A SET B SET C SET D SET E
SET A 0.996413 0.513087 31.5525 29.73713 42.54829
SET B 0.522578 1.020564 27.74721 28.0608 43.22896
SET C 31.56329 27.71265 0.955444 0.499965 61.21399
SET D 29.6976 28.04861 0.503843 1.00746 61.56967
SET E 42.54216 43.18056 61.17488 61.56527 0.997033
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Yeddula 68 SET A and B show no significant difference. SET C and D also indicate no significant difference. SET E is significantly different from other datasets. From the above results in Tables 5.3 – 5.10, it is evident that SET E representing ictal activity group can be distinguished, while using the various marginal band powers, from healthy EEG group represented by SET A and B and by inter-ictal activity data group represented by SET C and D. We also observe that the corresponding upper triangular and lower triangular elements in the tables have similar values. The latter justifies the Kruskal-Wallis test with repetition and random selection methodology used in this project. For example from Table 5.10, SET A and B inter-group Hstats were calculated as 0.522578 and this is fairly close to SET B and A inter-group Hstats value i.e., 0.513087. We conclude that Hstats is not affected by the selection of sub groups from the original data set as it was negated by repetition and random sampling used in the present testing. Various extracted features were used in the classification and their confusion matrices obtained for different classification problems mentioned earlier are illustrated in the Appendix A. The estimated accuracies are shown in the Table 5.11.
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Yeddula 69 Table 5.11: Classification results
Classification Problem (a) Problem (a) Problem (a) Problem (a) Problem (a) Problem (a) Problem (a) Problem (a) Problem (b) Problem (b) Problem (c) Problem (c) Problem (d) Problem (d) Problem (d) Problem (d) Problem (d) Problem (d) Problem (d) Problem (d) Problem (e) Problem (e)
Features used HWF for first IMF HWF for first IMF HWF for first, second IMF HWF for first, second IMF Total average power of the decomposed signal Total average power and various band powers of the decomposed signal Total various band powers of the decomposed signal Average power and various band powers of first IMF Total average power and various band powers of the decomposed signal Total various band powers of the decomposed signal Total average power and various band powers of the decomposed signal Total various band powers of the decomposed signal HWF for first IMF HWF for first, second IMF HWF for first, second, third IMF HWF for first, second, third IMF Total average power and various band powers of the decomposed signal Total various band powers of the decomposed signal Average power and various band powers of first IMF various band powers for first IMF Total average power and various band powers of the decomposed signal Total various band powers of the decomposed signal
Accuracy (%) 71.4 75.8 58.4 60.8 58.0
HHT method Present Rato Present Rato Present
93.8
Present
95.8
Present
86.0
Present
97.6
Present
97.6
Present
92.0
Present
94.3 92.0 93.5 94.5 97.5
Present Present Present Present Rato
99.5
Present
100.0
Present
98.0 97.5
Present Present
73.2
Present
80.2
Present
Problem (d) was rather simple as only two groups were compared. Though it was similar to the classification performed by Oweis and Abdulhay (2011), the present work,
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Yeddula 70 more signals were considered, k-Nearest Neighbor classification algorithm was implemented, and various features in classification were used compared to the referred work. We conclude that HWF information from first three IMFs is sufficient for classification as indicated by Oweis and Abdulhay (2011). From problem (a) and problem (d), the results obtained using power-related features based on the decomposition exhibit better classification results compared to the Hilbert Weighted Frequency based classification. Also, Rato’s HHT implementation based HWF shows better results for classification than the HWF based on the implemented HHT. Comparing all the classification problems from Problem (a) to Problem (e), classification based on Total various band powers (7 features: δ, θ, α1, α2, β1, β2, γ1 band powers) showed higher classification accuracy compared to Total average power and various band powers (8 features: Total average power, δ, θ, α1, α2, β1, β2, γ1 band powers) of decomposed signal. Although in both the present project and in the work by Tzallas, Tsipouras, and Fotiadis (2007; 2009) power-related information based on timefrequency analysis was used; the underlying process implemented in time-frequency analysis was completely different. Tzallas, Tsipouras, and Fotiadis (2009) have reported 75.88% classification for problem (e) using k-Nearest Neighbor method of order 5. They also have achieved 89% accuracy while using the artificial neural network based classification. In present work, 80.2% classification accuracy was observed using the Total various band powers (7 features) with k-Nearest Neighbor method of order 5. Therefore, the power-related features evaluated in this project based on HHT decomposition are useful for accurate classification of the epileptic EEG signals. Problem (a), problem (c), and problem (e) were observed as showing a slightly reduced accuracy.
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Yeddula 71 The latter can be attributed to the complexity of the classification problems involving three or more groups compared to two groups as in problem (b) and problem (d). Sensitivity (sens), selectivity (sel), and specificity (spec) for a classifier in % values were also calculated as described in Tzallas, Tsipouras, and Fotiadis (2007) from confusion matrices for all classification problems that were classified using the powerbased features. v#N vO#T v#P
S&a#M UG O''#MN UG TPNN TPNNG# TPNN qU'P S&a#M UG O''#MN TPNN
S&a#M UG O''#MN U' TPNN TPNNG# U' TPNN qU'P S&a#M UG O''#MN U' TPNN
S&a#M UG O''#MN UG TPNN TPNNG# TPNN qU'P S&a#M UG O''#MN TPNNG# TPNN
Table 5.12: Sens, Spec, Sel for 5 classification problems based on 8 powers
Sens(%) Spec(%) Sel(%)
Sens(%) Spec(%) Sel(%)
Sens(%) Spec(%) Sel(%)
PROBLEM (e) A B C D E 87.00 74.00 66.00 43.00 96.00 92.25 98.00 87.00 91.00 98.25 73.73 90.24 55.93 54.43 93.20 PROBLEM (a) PROBLEM (b) (A,B) (C,D) E (A,B,C,D) E 93.00 94.00 95.00 98.25 95.00 98.00 94.00 98.25 95.00 98.25 96.88 91.26 93.14 98.74 93.14 PROBLEM (c ) PROBLEM (d) A D E A E 92.00 88.00 96.00 100.00 99.00 96.50 94.00 97.50 99.00 100.00 92.93 88.00 95.05 99.01 100.00
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Yeddula 72 Table 5.13: Sens, Spec, Sel for 5 classification problems based on 7 powers
Sens(%) Spec(%) Sel(%)
Sens(%) Spec(%) Sel(%)
Sens(%) Spec(%) Sel(%)
PROBLEM (e) A B C D E 94.00 88.00 77.00 48.00 94.00 96.25 99.50 87.25 93.75 98.50 86.24 97.78 60.16 65.75 94.00 PROBLEM (a) PROBLEM (b) (A,B) (C,D) E (A,B,C,D) E 97.00 95.50 94.00 98.50 94.00 98.67 96.33 98.50 94.00 98.50 97.98 94.55 94.00 98.50 94.00 PROBLEM (c ) PROBLEM (d) A D E A E 96.00 92.00 95.00 100.00 100.00 98.50 95.50 97.50 100.00 100.00 96.97 91.09 95.00 100.00 100.00
It is evident from tables 5.12 and 5.13 that the total average power could be used in classification of epileptic seizure (ictal) activity and non-seizure activity. However, it might not be useful in classifying the interictal activity and healthy EEG. WE conclude that the classification results obtained using the 7 power features (δ, θ, α1, α2, β1, β2, γ1 band powers) that were evaluated based on HHT decomposition of EEG signals are the best of all the methods implemented in the present project. As Problem (a), Problem (c), and Problem (e) were closer to the realistic clinical conditions, the methods and processes used in the present project could be utilized in clinical diagnosis and especially the features, such as various band powers, seem as most suitable for diagnosing the onset of epilepsy. We also notice that the EEG signals used in the present research were artifact free and selectively collected. Thus we may expect that the accuracy of the proposed methods might be reduced when EEG is contaminated by artifacts in practical epilepsy detection situations. Nonetheless, the present HHT implementation and the novel power-
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Yeddula 73 based feature extraction from the time-frequency data can definitely be applied for highly nonlinear and nonstationary epileptic EEG data analysis.
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Yeddula 74 6
Chapter 6
SSVEP BCI EEG ANALYSIS 6.1
Data Description SSVEP EEG data used in the present analysis were downloaded from
“http://www.bakardjian.com/work/ssvep_data_Bakardjian.html” accessed on June 28, 2012. This database was copyrighted to Brain Science Institute RIKEN and Dr. Hovagim Bakardjian. EEG data have been acquired from four healthy subjects with an average age of 38.2 ± 2.4 years and either with normal or corrected-to-normal vision. The subjects were screened for history of epilepsy and photosensitivity. Each subject had acknowledged in writing that she/he had no known neurological disorders. Also, before the data collection, visual stimuli with increasing frequency were shown to each subject to test for photosensitive epilepsy and thereby to decrease the probability of seizure. Biosemi EEG system with Ag/AgCl active scalp electrodes was used for data acquisition. Active electrodes had miniaturized electronic circuits that help increasing the EEG signal-to-noise ratio; therefore, enhancing the sensitivity for weak brain signals. The experiment was performed using 128 conventional electrodes, a passive Driven Right Leg (DRL) electrode, and an active Common Mode Sense (CMS) electrode. Both of the additional electrodes were positioned just posterior to the vertex. The CMS electrode was used to determine the common mode voltage of the Biosemi EEG system, with respect to which all other electrode measurements were recorded. Biosemi 128 electrode cap position diagram is shown in Appendix-B. The EEG recording was performed at a sampling rate of 256 Hz. To prevent excessive contamination of the EEG data with
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Yeddula 75 muscular artifacts, a chin rest was used by all subjects. The subjects were seated comfortably at 90cm away from a 21” Cathode-Ray-Tube computer display which had been set to operate at a high vertical refresh rate of 170 Hz (measure 168±0.4 Hz). SSVEP stimulation was performed using small reversing black and white checkerboards with 6 x 6 checks. The detailed description on the SSVEP stimulation generation, illumination strengths, and other experimental parameters can be found in (Bakardjian, Tanaka, and Cichocki 2010). Five trials were conducted on each subject for each SSVEP stimulus. In each trial, a black screen was shown for 5 seconds and then SSVEP stimulation was shown to the subject for 15 seconds followed by a black screen for approximately 5 seconds. Three different frequencies, 8 Hz, 14 Hz, and 28 Hz, were considered for SSVEP Stimuli. The measured stimulation frequencies were slightly deviated and are presented in Table 6.1.
Table 6.1: SSVEP stimulation frequency deviations SSVEP Frequency 8 Hz 14 Hz 28 Hz
Measured SSVEP stimulation frequency (Hz) SUBJ1 SUBJ2 SUBJ3 SUBJ4 7.99 8.084762 7.99 8.016667 13.9825 14.14833 14.02917 14.005833 27.965 28.29667 27.965 27.965
The data downloaded from the website only contains 128 EEG channels without two additional channels (DRL and CMS). The electrode order can be determined using the Biosemi Position coordinates downloaded from “http://www.biosemi.com/download/Cap_coords_all.xls”.
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Yeddula 76 6.2
Analysis Methods DC removal as explained in section (2.2.5) was performed on all the SSVEP EEG
signals. The reference montage was also changed to Cz (A1) electrode, such that Common-Averaging reference condition was satisfied as explained in section (2.2.5). The change in reference to Cz was necessary as the downloaded data had no information pertaining to CMS electrode as explained in section (6.1). The reason for considering Cz as the reference was that it would be the most generally acceptable reference electrode. These operations of DC removal and reference change were considered as the preprocessing steps. Apart from these steps, no other preprocessing to remove any artifacts was implemented. The output of these steps was analyzed using the HHT algorithm implemented in present project based on average or extrema boundary condition and having SD=.05 and MAXSIFT=1000 as the stopping criteria as explained in section (3.2). The HHT output was used to compute the instantaneous frequency as explained in section (3.3) to obtain the time-frequency data that was used in comparing various SSVEP EEG signals recorded based on SSVEP stimuli having frequencies around 8 Hz, 14 Hz, and 28 Hz. The time-frequency data from HHT analysis were used in extracting the powerrelated features as explained in section (3.3.2). The marginal band powers of the decomposed signal were extracted for all the electrodes for various frequency bands centered around SSVEP frequencies, such as ±0.1 Hz bands (7.9 – 8.1, 13.9 – 14.1, 27.9 – 28.1), ±0.5 Hz bands (7.5 – 8.5, 13.5 – 14.5, 27.5 – 28.5), and ±1.5Hz bands (6.5 – 9.5, 12.5 – 15.5, 26.5 – 29.5). The obtained three dimensional vector (Powers in bands centered at 8Hz, 14Hz, 28Hz) features were used to classify the SSVEP signal into
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Yeddula 77 various classes based on their SSVEP stimulus frequency using k-Nearest Neighbor classification algorithm with order 5. The kNN algorithm used in present classification process implements the Manhattan distance. Especially, two different classification problems were created where the first one considers classifying into three classes (SSVEP 8 Hz, 14 Hz, and 28 Hz) and the other one considers classifying into two classes(SSVEP 8 Hz and 14 Hz). The classification results were verified using Leave-One Out cross validation scheme. The classification accuracy for various electrodes were obtained and compared to determine the region of the brain having the highest response for SSVEP stimuli. 6.3
Results and Discussions Channel A23 (Oz electrode – Occipital region) was selected, since it was assumed
that occipital region would have good response to visual stimuli (Srinivasan, Bibi and Nunez 2006). The mean signal for each SSVEP set (8 Hz, 14 Hz, and 28 Hz) for the above mentioned electrode were calculated and HHT implemented in present project was used on these three mean signals to generate the HHT plots based on first 5 IMFs. These plots were generated to contain the information within the visual stimulus window, which was from the seconds 5 to 20 of the total signal and were shown in Figures 6.1 to 6.3. .
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Yeddula 78
Figure 6.1: First 5 IMFs based HHT spectral pplot lot for SSVEP=8Hz for EEG (5-20 (5 sec)
Figure 6.2:: First 5 IMFs based HHT spectral plot for SSVEP= SSVEP=14Hz Hz for EEG (5-20 ( sec)
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Yeddula 79
Figure 6.3:: First 5 IMFs based HHT spectral plot for SSVEP= SSVEP=28Hz Hz for EEG (5-20 (5 sec) It is quite evident from the Figures igures 6.1 to 6.2, that SSVEP 8 Hz set and 14 Hz set contain the dominant activity in 00-10 Hz and 10-20 20 Hz respectively. On the other hand, we observe in Figure igure 6.3, although it represents the HHT plot for SSVEP 28 Hz, no dominant activity in 20-30 30 Hz frequency range. We also observe reduced activity in other frequency ranges compared to Figure 6.1 and Figure igure 6.2. The obtained time-frequency time data is used to compute the energy in various frequency ranges as explained in section (3.3) such as 7.9 – 8.1 Hz, 13.9 – 14.1 Hz and 27.9 – 28.1 Hz. Thus computed energy in various bands for various experiments are shown in Figure 6.4.
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Yeddula 80
400 350 E n e r g y
300 250 200
E1 (7.9-8.1Hz)
150
E2 (13.9-14.1Hz)
100
E3 (27.9-28.1Hz)
50 0 8Hz
14Hz
28Hz
Experiments
Figure 6.4: Comparison of energies in various bands for three mean signals calculated from their HHT time-frequency data We observe from Figure 6.4 that the SSVEP with frequency 8 Hz and 14 Hz produce stronger responses compared to SSVEP with frequency 28 Hz. This observation agrees with the previous reports indicating that brain produces the strongest occipital responses for SSVEP stimuli in the 5 – 15 Hz range (Bakardjian, Tanaka and Cichocki 2010; and Srinivasan, Bibi and Nunez, 2006). The energy in three different bands 6.5 – 9.5 Hz (denoted as E1), 12.5 – 15.5 Hz (E2), and 26.5 – 29.5 Hz (E3) were evaluated next for each electrode from the HHT timefrequency data. These energy estimates were used as features for the classification into three classes. The classification accuracies were obtained and plotted versus electrodes as shown in Figure 6.5.
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Yeddula 81
Figure 6.5: Classification accuracies for128 electrodes based on energies around ±1.5Hz range SSVEP frequency The classification yielded the maximum accuracy of 66.67% and this had occurred at the occipital electrode Oz (A23). The 10 electrodes showing the highest accuracy were A23, A28, A30, A14, B6, A16, A21, D7, A15, and A26, of which most of them are near to the occipital region. The electrode labels/names corresponding to the numbers 1 to 128 as shown in Figure 6.5 are given in the Appendix B. There are 5 trials performed on each of the 4 subjects resulting in the 20 trials for each SSVEP stimuli experiment. These are used to compute the average powers for various bands in each of the three SSVEP stimuli experiments. Powers for various bands of Oz electrode are compared in Figure 6.6.
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Yeddula 82
Figure 6.6: Average Powers for various bands (±1.5Hz) with SD error for A23 (Oz) electrode Next, narrower frequency bands, i.e., 7.5 – 8.5 Hz, 13.5 – 14.5 Hz, and 27.5 – 28.5 Hz, were assumed. As previously described, energy estimates were evaluated from HHT time-frequency data within three different bands and for each electrode. These estimates were used as features for a three-class classification. The classification accuracies obtained are plotted electrode-wise in Figure 6.7.
Figure 6.7: Classification accuracies for128 electrodes based on energies around ±0.5Hz range SSVEP frequency
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Yeddula 83 The classification yielded a maximum accuracy of 70.00% and at A15 electrode. The 10 electrodes showing the highest accuracy were A15, A21, A29, A14, A9, A24, D7, A16, A23, and A26. We notice that most of these electrodes are near the occipital region. Power estimates for various bands of Oz (A23) electrode are illustrated in Figure 6.8.
Figure 6.8: Average Powers for various bands (±0.5Hz) with SD error for A23 (Oz) electrode Narrower frequency bands, i.e., 7.9 – 8.1 Hz (E1), 13.9 – 14.1 Hz (E2), and 27.9 – 28.1 Hz (E3) were assumed next. The energy estimates in these bands and for each electrode were evaluated from HHT time-frequency data and were used next as features for a three-class classification. The classification accuracies obtained are shown electrode–wise in Figure 6.9.
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Yeddula 84
Figure 6.9: Classification accuracies for128 electrodes based on energies around ±0.1Hz range SSVEP frequency The classifier achieved the maximum accuracy of 68.33% at A22 electrode. The 10 electrodes yielding the highest accuracy were A22, A15, A16, A23, A21, A24, A25, A14, A17, and A26. We notice again that all of these electrodes are from or near to the occipital region. Power estimates for various bands and for Oz electrode are illustrated in Figure 6.10
Figure 6.10: Average Powers for various bands (±0.1Hz)with SD error for A23 (Oz) electrode
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Yeddula 85 We conclude from Figures 6.6, 6.8, 6.10 that, as the band range decreases from ±1.5 Hz to ±0.5 Hz and then to ±0.1 Hz, average power for the frequency bands also decreased in their magnitudes. On the other hand, the average powers in various bands for various experiments almost retained their trend or shape in terms of their relative band powers irrespective of the bandwidth used in power computation (power in E1 > power in E3 > power in E2 band for SSVEP 8 Hz stimulus experiment across all the frequency ranges considered). From the Figures above, average power estimate for the band centered around 8Hz E1 is the highest when SSVEP 8 Hz stimulus is present and power estimate centered around 14Hz (E2) is the highest during SSVEP 14 Hz. These results are similar to ones in Figure 6.4. We also observe that all the bands show high variance. Perhaps, the latter observation accounts for non-perfect classification accuracy. A two class (8 Hz and 14 Hz) classification problem with SSVEP 8 Hz and SSVEP 14 Hz data was considered next while using a similar classification procedure as before. In this classification process, energy estimates were estimated based on the first 5 IMFs instead of all IMFs and residue as was considered before. Figure 6.11 shows the resultant classification accuracies.
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Yeddula 86
Figure 6.11: Classification accuracies for128 electrodes based on energies using first 5 IMFs around ±0.1Hz range SSVEP frequency for a two class problem The highest percentage of correct classification, 92.50%, was achieved for the A28 electrode. The 10 electrodes showing the highest classification accuracy are A28, A15, A25, A24, A27, A13, A26, A22, A23, and A21. All these electrodes are from or near the occipital region. Therefore, we may conclude that the strongest response from a human brain originates from the occipital region for the SSVEP stimuli with the frequency around 5-15 Hz (Bakardjian, Tanaka and Cichocki 2010; Srinivasan, Bibi and Nunez 2006). We further conclude that the classification of SSVEP EEG signals based on the energy estimated from the present HHT implementation may be fairly accurate and comparable to the previously reported results (Bakardjian, Tanaka and Cichocki 2010). However, the referred work reported superior accuracy levels and allowed to build an eight command real time BCI prototype. The present work did not achieve those superior accuracy levels, but still produced valuable results although no complex preprocessing algorithms were implemented to eliminate any artifacts and no filter banks were designed to extract the features. The present work showed that the HHT implementation could be
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Yeddula 87 used successfully, as seen in Figure 6.11, for a BCI based on SSVEP of the frequencies within the peak-response region of the brain. We further hypothesize that implementation of the artifact removal algorithms before analyzing the signal with HHT could provide better results and can, therefore, be used in building a real-time BCI application.
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Yeddula 88 7
Chapter 7
DISCRIMINATING BETWEEN ALCOHOLIC AND CONTROL USING THE VEP EEG ANALYSIS 7.1
Data Description E EG recordings were downloaded from the open database hosted on University
of California Irvine’s Machine Learning repository accessed on June 28, 2012 at “http://archive.ics.uci.edu/ml/datasets/EEG+Database”. These data were originally used to study genetic predisposition to the alcoholism by Henri Begleiter at SUNY Downstate Medical Center in Brooklyn and were also used in other projects (Zhang, et al. 1997; Palaniappan 2003; Tcheslavski and Gonen 2012). EEG data have been collected from 48 male control subjects and 77 male alcoholic subjects. The control group members were selected from hospital employees having no personal/family history of alcohol/drug abuse and also with no history of known neurological or psychiatric disorders. All control subjects were right handed and had normal or corrected-to-normal vision. The age of the control group members had a range from 19.4 to 38.6 years with a mean age of 25.81 years and SD=3.38. The alcoholic group had a mean age of 35.83 years with a SD=5.33 and had a range from 22.3 to 49.8 years. The alcoholic group consisted of hospitalized individuals, who were assessed by clinical psychiatrists and were diagnosed with alcoholic abuse or dependence during the initial intake diagnostics. Majority of the alcoholic group had been drinking heavily for atleast 15 years. All alcoholic group members were hospitalized for a minimum of 30 days and had no alcohol administered during their period of stay in hospital, which resulted in making them fully detoxified.
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Yeddula 89 A subset of visual stimuli taken from Snodgrass and Vanderwart (1980) picture set were presented on a white background at the center of a computer display forming a visual angle of 0.05º - 0.1º. The visual stimuli were presented in such a way that first a picture was shown as stimulus S1 and then, after some time, another picture was shown as stimulus S2 that either matched S1 (denoted as S2M) or did not match S1 (denoted as S2N). EEG recordings were performed using 61 electrodes placed according to the extended 10/20 International montage while using three additional electrodes: i.e. nose electrode, horizontal and vertical electro-oculogram electrodes. Visual Evoked potential (VEP) recordings of these 64 channels were performed at a sampling rate of 256 Hz, such that each electrode had impedance less than 5KΩ, with an amplification gain of 10000, pre-filtered from 0.02 Hz to 50 Hz and referenced to Cz electrode. Detailed description of the acquisition process can be found elsewhere (Zhang, et al. 1997). The downloaded EEG data were converted into a suitable format that would be used for further analysis using Matlab. There were total 10958 trials having 64 channel EEG signals with each signal lasting for 1 second, i.e. consisting of 256 samples. 7.2
Analysis Methods The trials with voltage levels in any of 64 channels exceeding 100 µV at any point
of time within the 1 second duration were discarded. This decision was based on the fact that artifact-free VEP is expected to have amplitude below 100 µV (Palaniappan 2003). Zhang and colleagues suggested that this threshold could be lowered to 70 µV (Zhang, et al. 1997). We also observed that for some trials, there was at least one channel where the signal was zero for all the time. Such trials were also discarded. Therefore, a total of 9502
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Yeddula 90 trials, of which 6093 were alcoholic and 3409 were controls, were considered. Based on the visual stimuli explained earlier, the remaining trials were classified and their number is shown in the Table 7.1. These were considered as raw VEP signals.
Table 7.1: Alcoholic and Control VEP signal count for analysis based on stimuli S1 ALCOHOLIC 3066 1788 CONTROL
S2 Match 1536 827
S2 No Match 1491 794
Total 6093 3409
. Energy and Power estimations were performed directly on the raw VEP signals for comparing alcoholics and controls. The three additional non-EEG channels were discarded and only 61 channels were considered for the analysis and comparison using 2dimensional interpolated brain plots. DC removal was performed for raw VEP EEG signals as explained in section (2.2.5). The need of CAR filter was identified and the filter was applied, such that Cz was the reference satisfying CAR constraint. The resulting output signals were regarded as CAR applied no-DC VEP signals. The HHT method implemented in the present project as specified in section 3.2 was applied to raw VEP, to no-DC VEP, and to CAR applied no-DC VEP signals considering average or extrema boundary condition with SD=.05 and MAXSIFT=1000 as the stopping criteria. The instantaneous frequency was estimated using the process described in section (3.3) to obtain time-frequency data. Power-related features for the complete decomposed signal and for the first or individual IMFs were estimated using the time-frequency data as explained in section (3.3). Under power-related features, the marginal band powers for various bands, such as δ (.5-4Hz), θ (4-8Hz), α1 (8-10Hz), α2
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Yeddula 91 (10-12Hz), β1 (12-20Hz), β2 (20-30Hz) and γ1 (30-40Hz), were estimated apart from the Total average power. These features were used in comparing the signals. Kruskal-Wallis test based on repetition and random sampling as specified in section (4.1) was implemented with the repetition rate of 1000 to verify the validity of various features that were extracted. To calculate intra-group Hstats, 2000 trials were randomly selected and divided into two groups with 1000 trials for the Control and Alcoholic groups. Similarly, 1000 trials from the Controls and another 1000 from the Alcoholics were randomly selected to evaluate inter-group Hstats. Since two classes/groups were considered in the present testing, similar Hstats assumptions as in section 5.2 can be used here also. k-Nearest Neighbor of order 5 based on Manhattan distance was for classification purposes. The obtained classification results were cross validated with leave-one-out cross validation scheme. For example, when Total average power was considered as the classification feature, then each signal (61 channels) was represented by a 61 dimensional vector, i.e. the total average power for each of 61 channels. Raw VEP signals with 64 channels, Raw VEP signals with 61 channels and CAR applied no-DC VEP signals were decomposed by the HHT implemented in present project and the Total average power and various band powers for the decomposed signal and for the first IMF were used as the parameters for classification. The obtained confusion matrices for various classification problems are included in Appendix C. Based on these confusion matrices, various standard terms such as accuracy (AC), recall or true positive rate (TP), false positive rate (FP), true negative rate (TN), false negative rate (FN), precision (P) and etc., for a 2-class classifier could also be derived as specified in Appendix C. Various features
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Yeddula 92 used in classification were compared utilizing the accuracy results. Also, the classification results based on power-related features evaluated using HHT decomposition were compared for various stimuli groups. The classification results were also obtained using the verified procedures and algorithms, such as the ones specified in Palaniappan (2003) work. Raw VEP signals with 64 channels, Raw VEP signals with 61 channels and CAR applied no-DC VEP signals were filtered using the zero phase distortion Gamma band FIR filter described in Palaniappan (2003) work. Using Root music algorithm, the power vector of the dominant frequency in various channels was implemented as classification feature for k-Nearest Neighbor classification algorithm using Manhattan distance and order 5. These results were compared to the results obtained using the HHT implemented in the present project. 7.3
Results and Discussions Mean of Averaged EEG Power for Alcoholics and Controls were estimated using
the raw VEP signals from 61 scalp electrodes and are presented in Figure 7.1.
Figure 7.1: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using raw VEP signals
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Yeddula 93 It is seen in Figure 7.1 that, the reference Cz electrode (right in the middle) is dominant in the power compared to other electrodes because it might have carried the common mode signal of all the electrodes. The reference electrode Cz was ignored and only the other 60 electrodes were used in obtaining the interpolated plot for Mean of Averaged EEG Power that is shown in Figure 7.2.
Figure 7.2: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using raw VEP signals with Cz ignored Mean of Averaged EEG Power for Alcoholics and Controls were calculated using the no-DC VEP signals from 60 scalp electrodes by ignoring the Cz and were compared in Figure 7.3.
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Yeddula 94
Figure 7.3: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using no-DC VEP signals with Cz ignored Comparing Figures 7.2 and 7.3, it is seen that the maximum power has decreased after DC removal. Apart from this, Figures 7.3 follow similar patterns as that of Figures 7.2 respectively and henceforth similar inferences can be made here too as observed in Figures 7.1 and 7.2 such as higher average EEG power in the occipital region of Controls compared to Alcoholics. Also, similar observation may be made for the frontal portion too. As observed in Figures 7.1, Cz had dominated other electrodes. This could be addressed by re-referencing the EEG signals to Cz electrode considering Common Average Reference condition. A Common Average Reference spatial filter with Cz as the reference was applied to the no-DC VEP signal. Thus obtained 61 electrode EEG signals were used to compute the Mean of Averaged EEG Power for Alcoholics and Controls and were compared using the 2-dimensional interpolated plot with Cz as shown in Figure 7.4 and without Cz as shown in Figure 7.5.
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Yeddula 95
Figure 7.4: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using CAR applied and no-DC VEP signals
Figure 7.5: Mean of Averaged EEG Power for (a) Alcoholics (b) Controls using CAR applied and no-DC VEP signals with Cz ignored Figures 7.4 and 7.5 indicate a very minor difference, irrespective of the consideration of Cz reference electrode, since CAR application had clearly removed the unwanted common mode signal from the reference electrode Cz. We also observe that these signals exhibit a reduced maximum power compared to earlier results illustrated in Figures 7.1, 7.2 and 7.3.
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Yeddula 96 Based on the visual stimulus, the CAR applied no- DC VEP signals were grouped into three groups as S1 (Stimulus 1), S2M (Stimulus 2 – Match) and S2N (Stimulus 2 – No Match). Averaged EEG power for each group was estimated for both Alcoholics and Controls and is shown in Figure 7.6.
Figure 7.6: Mean of Averaged EEG Power of Alcoholics and Controls for different Visual Stimuli evaluated for CAR applied no-DC VEP signals We observe in Figure 7.6 that Stimulus 2 (both Match and No Match) elicit higher frontal activity compared to Stimulus 1 in both Alcoholics and Controls. Perhaps, this observation could be attributed to the fact that the subjects were involved in a higherlevel activity where they were trying to correlate the Stimulus 2 with Stimulus 1 to check for a match or a mismatch. The total 579622 signals (obtained from 9502 trials, with 61 channel for each trial) of CAR applied no- DC VEP signals were decomposed into IMFs and residue using
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Yeddula 97 the HHT algorithm implemented in the present project. Based on the number of IMFs in the signal decomposition, a histogram plot was obtained and is shown in Figure 7.7
Figure 7.7: Histogram Plot showing Number of Input Signals (CAR no-DC VEP) It is evident from Figure 7.7 that all the signals had atleast 2 IMFs and a residue in their decomposition. Total Average power of the decomposed signal using HHT was estimated for all EEG signals and their mean for Alcoholic and Control groups are shown in Figure 7.8
Figure 7.8: Mean of HHT-based Total Average power for (a) Alcoholic (b) Controls
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Yeddula 98 A scaling factor, as explained in section 3.3, was used to make the features shown in Figure 7.8 to be comparable with the original signal power for CAR applied no- DC signals shown in Figure 7.4. The mean of HHT-based Total average power for alcoholics and controls with the scaling factor for CAR applied no-DC signals is illustrated in Figure 7.9.
Figure 7.9: Mean of HHT based Total Average power for (a) Alcoholic (b) Controls using scaling factor The maximum power computed from HHT decompositions decreased for CAR applied no-DC VEP signals compared to Figure 7.8. Also, the Figure 7.9 look similar to the results obtained from direct computation of energy and power for CAR applied noDC VEP signals as shown in Figures 7.4 and 7.5. Apart from Total average power of the decomposed signal, band powers for δ (0.5-4Hz), θ (4-8Hz), α1 (8-10Hz), α2 (10-12Hz), β1 (12-20Hz), β2 (20-30Hz), and γ1 (3040Hz) were estimated for CAR applied no-DC VEP signals as shown in Figure 7.10 comparing alcoholics and controls. These results were scaled with a scaling factor as explained in section (3.3) to convert them into original signal power levels and were shown in Figure 7.11 where alcoholics and controls were compared.
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Yeddula 99
Figure 7.10: Various band powers for CAR applied no-DC VEP signals based on HHT decomposition
Figure 7.11: Various scaled band powers for CAR applied – no DC VEP signals based on HHT decomposition As seen in Figures 7.10 ad 7.11, the band powers were reduced after applying the scaling factor. This decrease was similar to the results observed in Figures 7.8 and 7.9. From the results prior Figure 7.10, it is quite evident that controls exhibit higher activity in Frontal and Occipital regions compared to the alcoholics. Though similar inference could be made from Figures 7.10 and 7.11, there are few exceptions. Especially, we observe in Figures 7.10 and 7.11 that Occipital region in controls shows a higher power in δ (.5-4Hz), θ (4-8Hz), α1 (8-10Hz), α2 (10-12Hz), and β1 (12-20Hz)
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Yeddula 100 rhythms than in alcoholics. Band powers in alcoholics for lower rhythms, such as δ, θ, α1, and α2 show symmetrical results across the two hemispheres compared to the high frequency rhythms, such as β1, β2, and γ1. Frontal-Temporal regions in alcoholics indicate higher power, especially in the right hemisphere, for γ1 band compared to their control counterparts. The results shown in Figures 7.10 and 7.11 are in accordance and similar to those reported by Tcheslavski and Gonen (2012). The reduced power in alcoholics evaluated for low frequency bands from δ to β1 rhythms might be deviated from the earlier works, such as Rangaswamy, et al. (2003), Rangaswamy, et al. (2004), Porjesz, et al. (2005) and Porjesz and Begleiter (2003). Perhaps, this discrepancy might be attributed to the fact that the alcoholic subjects considered in the referred works were intoxicated or had the short term alcoholic effects during the study, while the alcoholic subjects considered in the present work had been practicing alcohol abstinence or pre-relapse abstinence (Hall, Havassy and Wasserman 1990; Yuet-wah 2005) for at least 30 days. The results obtained in the present work were supported by other previous works, such as Begleiter and Platz (1972), where observations similar to ours were related to the brain atrophy; Saletu-Zyhlarz, et al. (2004), where the decrease in powers from δ to α2 was related to alcohol relapsing. Also, Bauer (2001) have reported that increased β2 (fast beta activity) could be seen in the subjects, who were more prone to relapse, CoutinChurchman, et al. (2003) reported that δ, θ band power decrease might be attributed to depression and mental disorders caused by subjects’ general medical conditions, alcohol and drug dependence. The powers in various EEG rhythms were evaluated next using the first IMF only and are shown in Figures 7.12 and 7.13.
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Yeddula 101
Figure 7.12: Mean of Averaged EEG power for the first IMF (a) Alcoholics (b) Controls
Figure 7.13: Mean of various band powers for the first IMF It is evident from the power levels in Figure 7.13 that the high frequency activity is more dominant compared to the low frequency rhythms. High frequency γ1 (30-40 Hz) band shows the highest power. These were in accordance to the fact that the first IMF generally had the information regarding the high frequency content and the frequency content range tend to decrease from first IMF towards residue. This feature outlines the advantage of Hilbert Huang Transform’s Empirical Mode Dec Decomposition, omposition, as it acts as an inherent filter bank structure that decomposes the signal into various frequency bands. The Kruskal-Wallis Wallis test was performed next to find the intra intra-group group and interinter group Hstats for various power power-related features and is shown in n Figure 7.14.
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Yeddula 102
Figure 7.14: Hstats (Kruskal-Wallis Test results) evaluated for various HHT based band powers We observe in Figure 7.14 that power-based features obtained from the signal decomposition could be used successfully to distinguish alcoholics and controls. The intra-group Hstats for Alcoholics and intra-group Hstats for Controls, i.e., the first two rows from Figure 7.14, indicate that there are less statistical significant differences within both groups. The inter-group Hstats is more dominant than the intra-group Hstats for Total average Power and band powers for the low frequency EEG rhythms, such as δ to β1. These results are also similar to those reported by Tcheslavski and Gonen (2012). These power-based features were used in further classification of the signals targeted in discrimination between the Alcoholic and Control groups. Though there were specific electrodes having high inter-group Hstats compared to their intra-group Hstats, which should yield a higher accuracy when used for classification, all electrodes were used in classification. The specific electrode selection and classification based on the power
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Yeddula 103 features from those specific electrodes was considered to be beyond the scope of present work and is left to future work/improvements. Considering Alcohol group as Positive and Control group as negative, classification results, such as True Positive rate (TP), False Positive rate (FP), True Negative rate (TN), False Negative rate (FN), Precision Alcoholic (P_Alc), Precision Control (P_Con), Accuracy (AC), obtained using various power-based features by HHT decomposition for CAR applied no-DC VEP signal are presented in Table 7.2 below.
Table 7.2: Classification results based on power based features using HHT decomposition on CAR applied – no DC VEP signal
Total Delta Theta alpha1 alpha2 beta1 beta2 gamma1
TP FP TN FN P_Alc P_Con 0.86575 0.34145 0.65855 0.13425 0.81923 0.73294 0.79944 0.45527 0.54473 0.20056 0.75837 0.60312 0.80355 0.48959 0.51041 0.19645 0.74577 0.59244 0.83325 0.54268 0.45732 0.16675 0.73293 0.60544 0.84343 0.51217 0.48783 0.15657 0.74641 0.63546 0.9309 0.29187 0.70813 0.0691 0.85076 0.8515 0.96439 0.13611 0.86389 0.03561 0.92681 0.93137 0.99065 0.02757 0.97243 0.00935 0.98467 0.9831
AC 0.791412 0.708061 0.698379 0.698379 0.715849 0.850979 0.928331 0.984109
We conclude from Table 7.2 that γ1 band provides the highest classification results with 98.4% accuracy. Also, β2, β1, and Total power lead to fairly good classification results with the accuracy ranging from 92.8% to 79.1%. It should also be noted that, accuracy was not the only metric to compare the classification efficiency. One reason is that there were dominant number of alcoholic points (6093) available compared to control group points (3409). The latter might introduce a bias towards the Alcoholic group. This bias could be observed from the TP and TN columns of the Table 7.2. True Positive rate values (Alcohols) are higher than their corresponding True Negative rate
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Yeddula 104 (Controls) counterparts for all experiments. A classifier is said to be efficient if it classifies the entire positive to positive group and the entire negative to negative group which leads to TP=1,FP=0,TN=1,FP=0. Apart from the accuracy values, various classifiers or classification algorithms could be compared using Receiver Operating Characteristic (ROC) graph based on True Positive rate (TP) and False Positive rate (FP). This is quite advantageous as the complements of TP and FP specify the False Negative (FN) and True Negative (TN) information respectively. ROC graph for the above results is shown in Figure 7.15, where the discrete points correspond to the (FP, TP) pairs for various classification features.
ROC Graph True Positive Rate
1 0.95
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False Positive Rate Figure 7.15: ROC graph for various classification features from Table 7.2 γ1 (Gamma1) power based classification was the (FP, TP) pair i.e. close to (0, 1). Therefore, it should be the most efficient classification scheme as both FP~0, TP~1. Similarly, the ROC graphs were obtained for various classification features, such as the scaled Power-based features for the decomposed signal, power-based features and the
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Yeddula 105 scaled power-based features for the first IMF using the HHT implemented in present project, and were compared as shown in Figure 7.16.
ROC Graph True Positive Rate
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Yeddula 106
ROC Graph True Positive Rate
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False Positive Rate (c) Figure 7.16: ROC graph for (a) Scaled Power based features for decomposed signal (b) Power based features (c) scaled power based features for first IMF using CAR applied no-DC VEP Raw VEP signals (with 64 channels and 61 channels) were used for classification based on Power-related features using HHT decomposition. The corresponding results are shown in Figure 7.17
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Yeddula 107
ROC Graph True Positive Rate
1 0.95
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False Positive Rate (b) Figure 7.17: ROC graph for (a) Power based features for raw VEP (64 channels) (b) Power based features for raw VEP (61 channels) The accuracy of different classification approaches mentioned above is summarized in the Table 7.3.
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Yeddula 108 Table 7.3: Accuracy results for various classification schemes Signal
Description
Method
Accuracy%
CAR applied – no DC signal
γ band power of the signal using Present HHT
kNN order 5 Manhattan
98.4
CAR applied – no DC scaled γ band power of the signal signal using Present HHT
kNN order 5 Manhattan
95.5
CAR applied – no DC signal
γ band power of the first IMF using Present HHT
kNN order 5 Manhattan
98.4
CAR applied – no DC signal
scaled γ band power of the first IMF using Present HHT
kNN order 5 Manhattan
95.7
Raw VEP with 64 channels
γ band power of the signal using Present HHT
kNN order 5 Manhattan
96.8
Raw VEP with 61 channels
γ band power of the signal using Present HHT
kNN order 5 Manhattan
96.0
CAR applied – no DC signal
γ band power Palaniappan (2003) work
kNN order 5 Manhattan
99.2
Raw VEP with 64 channels
γ band power Palaniappan (2003) work
kNN order 5 Manhattan
98.3
Raw VEP with 61 channels
γ band power Palaniappan (2003) work
kNN order 5 Manhattan
98.0
We conclude based on the results in Tables 7.2, 7.3, and Figures 7.15 to 7.17, that CAR applied no-DC signals suit classification problem better than the raw VEP signals. We also conclude that within raw VEP signals, the non-brain surface EEG channels should be included for better classification in comparison, as those channels might contain information regarding common reference signals. From the ROC graphs shown in Figures 7.15, 7.16, and 7.17, it is evident that γ1 band power-based features yield the highest results in various classification problems compared to other band powers and Total average power. It should also be noted that scaling process for the various powerbased features obtained using HHT as explained in section 3.3 had negatively affected the
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Yeddula 109 accuracy. We also conclude from Table 7.3 that the results obtained in the present work are comparable to the results obtained based on Palaniappan (2003) work. The classification results obtained using kNN classifier for Alcoholic and Control VEP based on γ1 band power estimates, evaluated using HHT decomposition of CAR applied no-DC VEP signals were compared next for various stimuli. It should be important to note that the classification was not performed using stimuli as classes. However, the Alcohol and Control group data pertaining to S1, S2M, S2N were considered individually and classified into two groups, such as Positive (Alcohol) and Negative (Control).The results are illustrated in the following Table 7.4.
Table 7.4: Classification results compared for various stimuli Stimuli S1 S2M S2N All
Accuracy 0.97116 0.96107 0.95667 0.98411
TP 0.98467 0.96875 0.97049 0.99065
FP 0.05201 0.0532 0.06927 0.02757
TN 0.94799 0.9468 0.93073 0.97243
FN 0.01533 0.03125 0.02951 0.00935
P_Alc 0.97012 0.97128 0.96338 0.98467
P_Con 0.97302 0.94224 0.94381 0.9831
Of the three stimuli, S1 data show slightly higher classification accuracy than for the other stimuli such as S2M and S2N. When the data pertaining to all stimuli were considered, the classification was even more accurate than the classification using data pertaining to the specific individual stimulus. The reason behind this can be related to the k-Nearest Neighbor classification methodology where large training data is needed for better classification accuracy. Therefore, S1, S2M and S2N are subsets of the complete data giving smaller training datasets and resulting in slightly reduced accuracies compared to overall data.
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Yeddula 110 We may conclude considering the above results that the usage of present HHT method to produce time-frequency data and the following extraction of power-based features from the time-frequency data was justifiable for the Alcoholic and Control VEP analysis
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Yeddula 111 8
Chapter 8 CONCLUSIONS
This work implements a simple HHT algorithm with the novel ‘average or extrema’ boundary condition during envelope interpolation. The present study shows that the proposed HHT method is computationally faster and shows decent results when compared with other HHT implementations. A simple and novel way of extracting timefrequency data and power estimates is proposed and successfully used in the analysis of various real world signals. Our study shows that the time-frequency data obtained using the proposed HHT method is far superior to those obtained using STFT for a nonstationary synthetic signal. The present study has also identified the limitation of using traditional KruskalWallis test in determining the homogeneity of intra-group data based on arbitrary subgroup division. This limitation has been successfully addressed in our work by proposing and implementing a repetitive and random division into subgroups of the modified Kruskal-Wallis test. Various features, such as HWF, total average power, and marginal band power estimates, were extracted with the proposed HHT methods from epileptic EEG signals. Based on the observed results, we conclude that the ictal activity in EEG during seizures can be easily identified and distinguished from non-seizure activity. k – Nearest Neighbor based classification, performed on the features extracted suggest that: (1) Power estimates yield a higher classification accuracy compared to HWF (Oweis and Abdulhay 2011), (2) Marginal band power estimates alone produce better results compared to the combination of total average power and marginal band power estimates. The present work achieved
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Yeddula 112 the accuracy ranging from 80% to 100% for various Epileptic EEG classification problems and while using HHT-based power estimates. We also conducted the analysis of SSVEP BCI EEG signals using the implemented HHT-based methods. The HHT spectral plots of EEG signal obtained from the occipital region confirms the dominant activity around the SSVEP stimuli frequency. The results support the early observation that the occipital region produces the highest response for SSVEP stimuli in the 5Hz - 15Hz band. The present study also confirmed that the marginal band power estimates for the frequency bands centered on the SSVEP stimuli frequency (8Hz, 14Hz, 28Hz) vary with the alterations of the bandwidth (±0.1Hz, ±0.5Hz, ±1.5Hz). The observation that these variations are absolute in nature while preserving the relative trend across various bandwidths make these marginal band power estimates as successful features to classify different SSVEP BCI signals. The 8Hz, 14Hz, 28Hz centered marginal band power estimates were considered as the classification features and were successfully classified with the 70% classification accuracy. When 8Hz and 14Hz centered band powers were considered alone in a two-class classification, the accuracy reached 92%. The results obtained in the present project are comparable to that of those obtained by traditional time-frequency analysis methods applied on highly preprocessed and artifact removed signals (Bakardjian, Tanaka and Cichocki 2010). This highlights the robustness of the proposed HHT method since no complex preprocessing methods or artifact removal techniques were used in the present study. In the present project, simple energy and power estimations from the raw VEP signals justified the application of CAR filter and DC removal techniques while analyzing the “Alcoholics” EEG VEP data. Differences in the frontal lobe activity for
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Yeddula 113 different stimuli were observed in both Alcoholic and Control groups. The differences in asymmetrical hemispherical functions of brain in data processing between alcoholics and controls can be observed from the 2-D interpolated plots of the HHT-based marginal band power estimates and for various EEG rhythms. Statistically significant differences between Alcoholics and Controls were observed for various regions of the brain and for each rhythm analyzed. The marginal band power estimates for various EEG rhythms were used next for classification between Alcoholic and Control groups. γ1 and β2 band power yielded classification accuracy up to 98.2% and 92.3% respectively. We, therefore, conclude that the proposed HHT method and power-related feature estimation based on it are useful in extracting features across various frequency bands without the application of band pass filters. This confirms an early observation that the empirical mode decomposition of HHT acts as an inherent filter bank structure. The latter can be observed in chapters 5, 6, and 7, where we were able to obtain power estimates for several rhythmic bands while implementing the proposed HHT methods. All classification problems in the present project were verified using the LeaveOne-Out cross validation scheme and the results were on par or better than the results reported in literatures for similar classification problems.
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Yeddula 114 9
Chapter 9 FUTURE SCOPE
The present HHT method still subjects to a few draw backs when compared to the Rato’s HHT. Various stages of HHT implementation such as interpolation, boundary conditions, sifting process, etc. may be further improved. Also, instantaneous frequency estimations and various features’ estimation need to be studied in more detail and verified from mathematical point of view for accurate and proper application of the present methods to clinical systems and various real world signal analysis problems. The present data used for epileptic EEG analysis were selectively collected. Hence, this limitation needs to be addressed by applying and verifying the present methodology to a multi-channel raw epileptic EEG signals. This verification would justify further applications of present methodology in real clinical systems. Also, the present work can be enhanced further to estimate the epileptogenic zone by using Phase Synchrony analysis in conjunction with HHT analysis as Phase Synchrony analysis aids in understanding the internal circuitry of neuronal connections. Various advanced artifact removal algorithms may be implemented for SSVEP BCI EEG signal analysis. The preprocessed signals could be analyzed with the present methodology possibly leading to higher classification accuracy. Perhaps, present methodology could result in building a robust real world BCI system. In the present project, thought the differences in the power of frontal region electrodes for different stimuli were observed, the latter needs statistic verification to draw a more accurate conclusion. Also, asymmetrical behavior of brain hemispheres can
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Yeddula 115 be further analyzed and dependence of the asymmetry on subjects’ drinking habits can be verified using present methodology. Using the present methodology that seems to provide accurate analysis of nonlinear and nonstationary signals, various experiments in different areas can be designed. For instance, effect of various Colors based visual stimuli on EEG, analyzing the EEG, the EDR and the other bio signals in emotion and mood detection, BCI device implementation, etc. would be of interest. As the present implementation was performed completely in the Matlab environment, its realization using an open source scientific languages, such as Python, may be of interest. Such open source implementation may help advancing and improving the present methodology at a much quicker rate.
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Yeddula 116 10
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Yeddula 135 Wikipedia. Kruskal–Wallis one-way analysis of variance. Wikipedia, The Free Encyclopedia. . May 31, 2012. http://en.wikipedia.org/w/index.php?title=Kruskal%E2%80%93Wallis_oneway_analysis_of_variance&oldid=495270653 (accessed July 5, 2012). Wu, Ming-Chya, and Nordan E. Huang. "Biomedical Data Processing Using HHT: A Review." In Advanced Biosignal Processing, edited by A. Nait-Ali, 335-352. Springer, 2009. Wu, Zhaohua, and N.E. Huang. "ENSEMBLE EMPIRICAL MODE DECOMPOSITION:A NOISE-ASSISTED DATA ANALYSIS METHOD." Advances in Adaptive Data Analysis (World Scientific Publishing Company) 1, no. 1 (2009): 1-41. Yan, R., and R.X. Gao. "A Tour of the Tour of the Hilbert-Huang Transform: An Empirical Tool for Signal Analysis." Instrumentation & Measurement Magazine, IEEE (IEEE) 10, no. 5 (2007): 40-45. Yuet-wah, Cheung. "Between abstinence and relapse: the role of “Pre-relapse abstinence” in drug rehabilitation in Hong Kong." International Conference on Tackling Drug Abuse. Hong Kong: Narcotics Division, Security Bureau, the Government of the Hong Kong SAR, 2005. 354-372. Zhang, X.L., H. Begleiter, B. Porjesz, and A. Litke. "Electrophysiological evidence of memory impairment in alcoholic patients." Biological Psychiatry (Elsevier) 42, no. 12 (1997): 1157-1171.
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Yeddula 136 11
APPENDICES APPENDIX - A
A1: Confusion matrices for Epileptic EEG Classification Confusion matrices for various classification problems Problem (a):
Table A1.1: Problem (a) confusion matrices
62
Predicted
C1 C2
C1 97 65
C2 C3 79 24 133 2
C3
28
10
62
Predicted C1 C2 C3 C1 100 97 3 C2 89 100 11
Expected
(5)
C3
5
5
Predicted C1 C2 C3 C1 194 6 0 C2 3 191 6 C3 1 5 94
(7) Expected
90
Expected
2
C3
25
1
74
Predicted
(4) Expected
Expected
(3)
36
C1 C2 C3 C1 113 61 26 C2 74 124 2 C3
32
1
67
Predicted C1 C2 C3 C1 186 13 1 C2 6 188 6
(6) Expected
Expected
C3
Predicted C1 C2 C3 C1 146 28 26 C2 38 159 3
(2)
C3
0
5
95
Predicted C1 C2 C3 C1 182 17 1 C2 35 161 4 C3 12 1 87
(8) Expected
Predicted C1 C2 C3 C1 132 35 33 C2 35 163 2
(1)
C1, C2, C3 were the three classes representing Normal (A, B), InterIctal activity (C, D), Ictal activity (E) respectively. (1) HWF of first IMF based on the present HHT implementation.
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Yeddula 137 (2) HWF of first IMF based on the Rato’s HHT implementation. (3) HWF of first and second IMF based on the present HHT implementation. (4) HWF of first and second IMF based on the Rato’s HHT implementation (5) Total average power of the decomposed signal based on the present HHT implementation. (6) Total average power and various band powers of the decomposed signal based on the present HHT implementation (7) Total various band powers of the decomposed signal based on the present HHT implementation. (8) Average power and various band powers of the first IMF based on the present HHT implementation. Problem (b):
Table A1.2: Problem (b) confusion matrices Predicted C1 C2
C1
393
7
C2
5
95
(2) Expected
Expected
(1)
Predicted C1 C2
C1
394
6
C2
6
94
C1, C2 were the two classes representing Non-Seizure activity (A, B, C, D) and Seizure activity (E) respectively. (1) Total average power and various band powers of the decomposed signal based on the present HHT implementation. (2) Total various band powers of the decomposed signal based on the present HHT implementation.
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Yeddula 138 Problem (c):
Table A1.3: Problem (c) confusion matrices
Expected
Predicted C1 C2 C3 C1 96 4 0 C2 3 92 5 C3 0 5 95
(2) Expected
Predicted C1 C2 C3 C1 92 8 0 C2 7 88 5 C3 0 4 96
(1)
C1, C2, C3 were the three classes representing Normal (A), InterIctal activity (D) and Ictal activity (E) respectively. (1) Total average power and various band powers of the decomposed signal based on the present HHT implementation. (2) Total various band powers of the decomposed signal based on the present HHT implementation. Problem (d):
Table A1.4: Problem (d) confusion matrices
87
Predicted C1 C2
C1
100
0
C2
1
99
C2
(6)
13
Predicted C1 C2
C1 100 C2
87
0
0 100
C1 100 C2
(7)
11
89
predicted C1 C2
C1 100 C2
0
4
0 96
(4) expected
13
0
predicted C1 C2
predicted C1 C2
C1 100 C2
(8) expected
C2
C1 100
(3) Expected
3
Predicted C1 C2
Expected
97
(2) Expected
C1
(5) expected
Predicted C1 C2
Expected
expected
(1)
5
95
predicted C1 C2
C1 100 C2
0
5
0 95
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Yeddula 139 C1, C2 were the two classes representing Non-Seizure activity (A) and Seizure activity (E) respectively. (1) HWF for the first IMF based on the present HHT implementation. (2) HWF for the first and second IMF based on the present HHT implementation (3) HWF for the first, second and third IMF based on the present HHT implementation. (4) HWF for the first, second and third IMF based on the Rato’s HHT implementation. (5) Total average power and various band powers of the decomposed signal based on the present HHT implementation. (6) Total various band powers of the decomposed signal based on the present HHT implementation. (7) Average power and various band powers of the first IMF based on the present HHT implementation. (8) Various band powers for the first IMF based on the present HHT implementation. Problem (e):
Table A1.5: Problem (e) confusion matrices
C1 C2 C3 C4 C5
C1 87 24 3 4 0
Predicted C2 C3 C4 C5 6 3 4 0 74 1 0 1 2 66 28 1 0 48 43 5 0 0 4 96
(2) expected
Expected
(1)
C1 C2 C3 C4 C5
C1 94 11 2 2 0
Predicted C2 C3 C4 C5 1 4 1 0 88 1 0 0 0 77 20 1 0 45 48 5 1 1 4 94
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Yeddula 140 C1, C2, C3, C4, C5 were the five classes representing A, B, C, D, E sets of EEG respectively. (1) Total average power and various band powers of the decomposed signal based on the present HHT implementation (2) Total various band powers of the decomposed signal based on the present HHT implementation.
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Yeddula 141 APPENDIX – B B1: Biosemi layout and Electrodes order The electrode layout used for SSVEP EEG data acquisition
Figure B1.1: Biosemi 128 electrode layout (http://www.biosemi.com/pics/cap_128_layout_medium.jpg)
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Yeddula 142 Table B1.1: Biosemi Electrode # and Name # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Name A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28 A29 A30 A31 A32
# 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Name B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30 B31 B32
# 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96
Name C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32
# 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128
Name D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17 D18 D19 D20 D21 D22 D23 D24 D25 D26 D27 D28 D29 D30 D31 D32
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Yeddula 143 APPENDIX – C C1: Alcoholic and Control VEP classification Confusion matrices for various classification problems were listed here.
Expected
Table C1.1: Scaled Power based features for the HHT decomposition of CAR applied – no DC VEP
Total Alc Con
Predicted (KNN order 5) Alc Con Alc delta 5678 415 Alc 5135 813 2596 Con 1327
Con 958 2082
Theta Alc Con
Alc 5160 1931
Con 933 1478
alpha1 Alc Con
Alc 5040 1921
Con 1053 1481
alpha2 Alc Con
Alc 5111 1921
Con 982 1488
beta1 Alc Con
Alc 5525 1365
Con 568 2044
beta2 Alc Con
Alc 5676 820
Con 417 2589
gamma1 Alc Con
Alc 5913 244
Con 180 3165
Expected
Table C1.2: Power based features for the HHT decomposition of CAR applied – no DC VEP
Total Alc Con
Predicted (KNN order 5) Alc Con Alc delta 5275 818 Alc 4871 1164 2245 Con 1552
Con 1222 1857
Theta Alc Con
Alc 4896 1669
Con 1197 1740
alpha1 Alc Con
Alc 5077 1850
Con 1016 1559
alpha2 Alc Con
Alc 5139 1746
Con 954 1663
beta1 Alc Con
Alc 5672 995
Con 421 2414
beta2 Alc Con
Alc 5876 464
Con 217 2945
gamma1 Alc Con
Alc 6036 94
Con 57 3315
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Yeddula 144
Expected
Table C1.3: Power based features for first IMF CAR applied – no DC VEP
Total Alc Con
Predicted (KNN order 5) Alc Con Alc delta 5869 224 Alc 5355 774 2635 Con 2649
Con 738 760
Theta Alc Con
Alc 5201 2417
Con 892 992
alpha1 Alc Con
Alc 5105 2217
Con 988 1192
alpha2 Alc Con
Alc 5046 2121
Con 1047 1288
beta1 Alc Con
Alc 5485 1784
Con 608 1625
beta2 Alc Con
Alc 5831 541
Con 262 2868
gamma1 Alc Con
Alc 6037 94
Con 56 3315
Expected
Table C1.4: Scaled Power based features for first IMF CAR applied – no DC VEP
Total Alc Con
Predicted (KNN order 5) Alc Con Alc delta 5833 260 Alc 5395 999 2410 Con 2661
Con 698 748
Theta Alc Con
Alc 5171 2369
Con 922 1040
alpha1 Alc Con
Alc 5138 2246
Con 955 1163
alpha2 Alc Con
Alc 5064 2170
Con 1029 1239
beta1 Alc Con
Alc 5448 1784
Con 608 1467
beta2 Alc Con
Alc 5639 870
Con 454 2539
gamma1 Alc Con
Alc 5917 237
Con 176 3172
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Yeddula 145
Expected
Table C1.5: Power based features for HHT decomposition of VEP signals (64 channels)
Total Alc Con
Predicted (KNN order 5) Alc Con Alc delta 5016 1077 Alc 4704 1456 1953 Con 1619
Con 1389 1790
Theta Alc Con
Alc 4736 1712
Con 1357 1697
alpha1 Alc Con
Alc 4961 1963
Con 1132 1446
alpha2 Alc Con
Alc 5071 2019
Con 1022 1390
beta1 Alc Con
Alc 5393 1784
Con 608 2075
beta2 Alc Con
Alc 5612 717
Con 481 2692
gamma1 Alc Con
Alc 5970 178
Con 123 3231
Expected
Table C1.6: Power based features for HHT decomposition of VEP signals (61 channels)
Total Alc Con
Alc 4955 1457
Predicted Con delta 1138 Alc 1952 Con
Theta Alc Con
Alc 4712 1716
Con 1381 1693
alpha1 Alc Con
Alc 4901 2003
Con 1192 1406
alpha2 Alc Con
Alc 5016 2061
Con 1077 1348
beta1 Alc Con
Alc 5340 1784
Con 608 2019
beta2 Alc Con
Alc 5551 838
Con 542 2571
gamma1 Alc Con
Alc 5943 234
Con 150 3175
Alc 4683 1605
Con 1410 1804
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Yeddula 146 Table C1.7: Palaniappan’s Gamma Power based features used in kNN classification
Expected
Predicted (KNN order 5) (1) Alc Con Alc 6059 34 Con 41 3368 (2) Alc Con
Alc 6007 79
Con 86 3330
(3) Alc Con
Alc 6007 101
Con 86 3308
(1) CAR applied – DC removed VEP signals (61 channel) used in classification (2) VEP signals (64 channels) used in classification (3) VEP signals (61 channels) used in classification
C2: Standard term calculation for a 2-class classifier Consider a confusion matrix obtained from a 2-class classifier
Table C2.1: Sample 2-class classifier Confusion matrix
Expected
Predicted Negative Positive Negative
A
b
Positive
C
d
a and d are the number of correct predictions that an instance is negative or positive respectively. b and c are the number of incorrect predictions that an instance is positive and negative respectively. \TTSMT-
aT
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Yeddula 147 qMS# OUN'w# M'#
T
a a
EPN# OUN'w# M'#
a
qMS# #Q'w# M'# EPN# #Q'w# M'# ZM#TNU ZUN'w#
T T
a
These can be used to compare various classification algorithms.
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Yeddula 148 APPENDIX – D D1: Matlab Code for Synthetic Signal Fs=400; T=[0:1/Fs:5-1/Fs 5:1/Fs:10-1/Fs 10:1/Fs:15-1/Fs 15:1/Fs:20-1/Fs]; x=[20*cos(2*pi*10*T(1:2000)) 10*cos(2*pi*25*T(2001:4000)) 40*cos(2*pi*50*T(4001:6000)) 20*cos(2*pi*100*T(6001:8000))]; D2: Links for HHT implementations Present Implementation: Dropbox link: http://dl.dropbox.com/u/14473554/EMD.zip
Flandrin (using mirrored boundary conditions): http://perso.ens-lyon.fr/patrick.flandrin/emd.html
Rato’s HHT : http://www.mathworks.com/matlabcentral/fileexchange/21409-empirical-modedecomposition
Miscellaneous codes available: http://www.mathworks.com/matlabcentral/fileexchange/19681-hilbert-huang-transform http://www.clear.rice.edu/elec301/Projects02/adaptiveFilters/project/parsing/emd.m
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Author's copy - produced at Lamar University
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