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Feature Generation of EEG Data Using Wavelet Analysis
by
Catherine Chesnutt, B.S.
A Thesis
In
ELECTRICAL ENGINEERING
Submitted to the Graduate Faculty
of Texas Tech University in
Partial Fulfillment of
the Requirements for
the Degree of
MASTER OF SCIENCE
IN
ELECTRICAL ENGINEERING
Approved
Dr. Mary C. Baker
Chair of Committee
Dr. Michael W. O'Boyle
Dr. Brian Nutter
Peggy Miller
Dean of the Graduate School
May, 2012
Texas Tech University, Catherine Chesnutt, May 2012
ii
ACKNOWLEDGEMENTS
I would like to extend my personal gratitude to Dr. Mary Baker, a fabulous
advisor and mentor. Thank you for believing in me and inviting me to be a part of the
Autumn's Dawn NICE Lab. Thank you also for your patience and encouragement along
the way, and for helping me complete this thesis.
I would also like to thank Dr. Brian Nutter and Dr. Michael O'Boyle for being on
my committee and challenging me to strive for excellence and a deeper understanding of
signal processing.
Thank you, Lee Burnside, for providing the resources needed for the Matlab
coding and computations.
Thanks to the National Science Foundation's GK-12 Program for providing the
funding for this research.
I deeply appreciate all the members of the Autumn's Dawn NICE Lab for their
general support and friendship.
Thanks to my mother and father, Charles and Carolyn Chesnutt.
Finally, thank you, God: it's a miracle that it is finished.
Texas Tech University, Catherine Chesnutt, May 2012
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS .................................................................................................. ii ABSTRACT ....................................................................................................................... v LIST OF TABLES ............................................................................................................ vi LIST OF FIGURES ......................................................................................................... vii I. INTRODUCTION............................................................................................................ 1
Electroencephalography (EEG) .................................................................................. 2
Wavelet Analysis ........................................................................................................ 4 Wavelet Analysis in EEG Studies............................................................................... 7
Autism Research ......................................................................................................... 8
EEG Analysis Tools .................................................................................................... 9
Purpose ...................................................................................................................... 10
II. FEATURE GENERATION METHODS ......................................................................... 11 Feature Generation Methods ..................................................................................... 11
Average Power ................................................................................................................. 11 Coherence ......................................................................................................................... 12 Generalized Magnitude Squared Coherence (GMSC) ....................................................... 13 Wavelet Power .................................................................................................................. 14 Wavelet Coherence ........................................................................................................... 15 Generalized Magnitude Squared Wavelet Coherence (GMSWC) ..................................... 16 Statistical Moment Measures ........................................................................................... 16 Activity .............................................................................................................................. 17 Mobility ............................................................................................................................. 17 Complexity ........................................................................................................................ 18
Time-Segmented Wavelet Features .......................................................................... 19
Statistical Analysis Using a T-test ............................................................................ 19
III. FEATUREGENGINE ................................................................................................ 21 FeatureGENgine Interface ........................................................................................ 21
Importing to FeatureGENgine ........................................................................................... 21 Feature Generation Methods ........................................................................................... 22 Feature Averaging, Viewing and Exporting ....................................................................... 23 Plotting Wavelet Transforms and Time-Segmented Features .......................................... 25 Test of Significance Using T-Test ....................................................................................... 25
Flexibility of FeatureGENgine ................................................................................. 26
IV. WAVELET ANALYSIS .............................................................................................. 27 A Brief Overview of the Wavelet Transform ........................................................... 27 Wavelet Transforms and Scales ................................................................................ 29
Wavelet Transforms and the Short-Time Fourier Transform....................................31 Wavelet Features ....................................................................................................... 32 Time-Segmented Wavelet Features .......................................................................... 34 Windowing the Time-Segmented Wavelet Features ................................................ 37 Wavelet Test Data ..................................................................................................... 38
Choice of Wavelets: Harmonics and Frequency Detection ..................................... 38 Types of Wavelet Features ........................................................................................ 42
Averages ............................................................................................................................ 42
Texas Tech University, Catherine Chesnutt, May 2012
iv
Power ................................................................................................................................ 43 Complexity and Mobility ................................................................................................... 43 Peaks ................................................................................................................................. 43
Conclusions ............................................................................................................... 43
V. EXAMPLE STUDY: ATTENTION NETWORKS OF AUTISTIC INDIVIDUALS ............... 45 Background ............................................................................................................... 45 Stimulus Materials and Procedure ............................................................................ 46
Subjects ............................................................................................................................. 46 Attention Test ................................................................................................................... 47
Recording and Preprocessing the EEG Data ............................................................ 47 Exporting .......................................................................................................................... 47 Independent Component Analysis ................................................................................... 47 Epoching ........................................................................................................................... 49 Exporting to Matlab .......................................................................................................... 49
Results ...................................................................................................................... 50
ASD Congruent vs. ASD Incongruent ...................................................................... 51
Controls Congruent vs. Controls Incongruent .......................................................... 56
ASD Congruent vs. Controls Congruent .................................................................. 59
ASD Incongruent vs. Controls Incongruent.............................................................. 62
Conclusions .............................................................................................................. 65 Results ............................................................................................................................... 65 Comparisons Between Groups ......................................................................................... 66
VI. CODE CONCLUSIONS AND SUGGESTIONS .............................................................. 69
Wavelet Choice ........................................................................................................ 69
Discrete Wavelet Transform .................................................................................... 70
Multiple Comparisons .............................................................................................. 70
Vectorization ............................................................................................................ 71
REFERENCES ................................................................................................................ 72
Texas Tech University, Catherine Chesnutt, May 2012
v
ABSTRACT
Wavelet analysis is a modern method of time-frequency analysis that can be used
to analyze EEG signals. There are several popular methods of generating wavelet-based
features for the purposes of classification and brain modeling. These methods generate
one feature per wavelet decomposition level, effectively averaging out the temporal
information contained in the wavelet transform. This thesis proposes a method of
generating features based on segments of the continuous wavelet transform and provides
a Matlab software tool capable of generating features of EEG data using this and a
number of other methods. The methods are then tested in an example study on attention
networks in individuals with autism spectrum disorder (ASD). There is evidence of a
selective attention abnormality in autism that is identified by the attention network task
(ANT). The primary area of activation in the brain related to selective attention is the
prefrontal cortex and anterior cingulate. The ANT task was given to a group of five
participants diagnosed with ASD and a control group of five neuro-typical participants.
The EEGs were recorded using a 64-channel EGI system and preprocessed using
EEGLab. The Matlab software tool proposed herein was used to generate features of the
data using coherence, conventional average power, wavelet-power, and time-segmented
wavelet power. The results are examined by comparing the number of features that pass a
t-test for each method. The time-averaged wavelet power method produced more
significant features than conventional average power, and the time-segmented wavelet
power method produced more features than the time-averaged wavelet-power method. As
hypothesized, the prefrontal cortex and anterior cingulate were the most significant area
of activation for the wavelet-based methods. The average values of the power features
were larger in the autistic group, while the average values of coherence were larger in the
controls group. The occipital lobe was also an area of significant difference between the
autistic and controls groups but not within the groups, supporting evidence of
hypersensitivity to visual stimuli in autistic individuals. While the time-averaged wavelet
method produced a small number of significant features, the time-segmented wavelet
method produced a much larger number of significant features that create a model of the
unfolding nature of the processes of the brain.
Texas Tech University, Catherine Chesnutt, May 2012
vi
LIST OF TABLES
2.1 Cognitive states related to EEG frequency bands ................................................... 11
4.1 EEG bands: corresponding scales and frequencies ................................................. 30
5.1 Time-averaged wavelet power features .................................................................. 52
5.2 Time-segmented wavelet power features between ASD Congruent and
ASD incongruent .............................................................................................. 53
5.3 Far coherence between ASD congruent and ASD incongruent .............................. 55
5.4 Local posterior coherence between ASD congruent and ASD
incongruent ........................................................................................... 55
5.5 Far wavelet coherence between ASD congruent and ASD incongruent ................ 56
5.6 Local posterior wavelet coherence between ASD congruent and ASD
incongruent ....................................................................................................... 56
5.7 Time-averaged wavelet power features between controls congruent
and controls incongruent ................................................................................... 57
5.8 Time-segmented wavelet power features between controls congruent
and controls incongruent ................................................................................... 57
5.9 Average power features between ASD congruent and controls
congruent............................................................................................... 59
5.10 Time-averaged wavelet power features between ASD congruent and
controls congruent ............................................................................................. 59
5.11 Time-segmented wavelet power features between ASD congruent
and controls congruent ...................................................................................... 61
5.12 Average power features between ASD incongruent and controls
incongruent ........................................................................................... 62
5.13 Time-averaged wavelet power features between ASD congruent and
controls congruent ............................................................................................. 63
5.14 Time-segmented wavelet power features between ASD incongruent
and controls incongruent in Alpha and Beta bands .......................................... 63
5.15 Summary of Results .............................................................................................. 67
6.1 Time-segmented wavelet power features which passed the t-test
between ASD congruent and ASD incongruent using Coif5 and
Db5 mother wavelets ........................................................................................ 69
Texas Tech University, Catherine Chesnutt, May 2012
vii
LIST OF FIGURES
1.1 Signal with 44, 90, and 140 Hz and its Fourier transform ........................................ 4
1.2 Signal with 44, 90 and 140 Hz time-localized consecutively and its
Fourier transform ............................................................................................... 5
1.3 Daubechie (Db5) mother wavelet and time signal convolution................................ 5
1.4 Signal with 44, 90, and 140 Hz and its continuous wavelet transform ..................... 6
1.5 Time-frequency resolution plots ............................................................................... 6
3.1 Loading datasets into FeatureGENgine ................................................................. 21
3.2 Feature generation panel ......................................................................................... 22
3.3 Coherence selection ................................................................................................ 23
3.4 Plotting feature values............................................................................................. 23
3.5 Plotting wavelet transforms and time-segmented features ..................................... 24
3.6 Plotting wavelet transforms .................................................................................... 25
3.7 Plotting binary matrices and values of features that passed a t-test ........................ 26
4.1 Daubechie (Db5) mother wavelet and time signal convolution.............................. 27
4.2 Spectrogram and wavelet transform of chirp signal of 1-110 Hz ........................... 33
4.3 Time-segmented wavelet power features using different widow sizes .................. 36
4.4 Wavelet transforms of Db5 wavelet signals ........................................................... 39
4.5 Wavelets of Haar, Db5, Coif5, Gaus4, Morl, and Dmey tested with
chirp signal ........................................................................................................ 40
4.6 Scalograms of Db5, Haar, Coif5, Gaus4, Morl, Dmey wavelet
coefficients of 14 Hz sine wave ........................................................................ 41
4.7 Frequency spectra of Haar, Db5, Coif5, and Dmey wavelets ................................. 42
5.1 Examples of congruent and incongruent trials........................................................ 46
5.2 Scalp maps of ICA components using EEGLab ..................................................... 48
5.3 Time-segmented wavelet power features that pass the t-test in alpha
and Beta Bands between ASD Congruent and ASD Incongruent .................... 52
5.4 Time-segmented wavelet power features that pass the t-test in all
bands between ASD congruent and ASD incongruent ..................................... 52
5.5 Time-segmented wavelet features between ASD congruent and ASD
incongruent ......................................................................................................... 54
5.6 Time-segmented wavelet power features that pass the t-test in alpha
and Beta Bands between controls congruent and controls
Texas Tech University, Catherine Chesnutt, May 2012
viii
incongruent ....................................................................................................... 58
5.7 Time-segmented wavelet power features that pass the t-test in all
bands between controls congruent and controls incongruent ........................... 58
5.8 Time-segmented wavelet power features that pass the t-test in alpha
and Beta Bands between ASD congruent and controls congruent ................... 60
5.9 Time-segmented wavelet power features that pass the t-test in all
bands between ASD congruent and controls congruent ................................... 60
5.10 Time-segmented wavelet power features that pass the t-test in all
bands between ASD incongruent and controls incongruent ............................. 65
5.11 Head diagrams of time-segmented wavelet power features that passed
a t-test ................................................................................................................ 68
Texas Tech University, Catherine Chesnutt, May 2012
1
CHAPTER I
INTRODUCTION
Wavelet analysis has been used in recent years to analyze time-domain signals.
Wavelet analysis is a type of time-frequency analysis, providing information about both
frequency and time within signals. Since brain activity is highly time-dependent, the use
of the wavelet transform to generate characteristics, or features, of
Electroencephalography (EEG) signals has provided researchers a new tool for
investigating the time-frequency characteristics of the signal. Wavelet analysis generally
reveals characteristics in the data that are missed by traditional frequency analysis.
However, current methods of generating wavelet-based features do not take full
advantage of the wavelet's unique ability to provide time resolution. Most methods
involve generating features from wavelet transforms of the data in such a way as to
average out the temporal information, for the purpose of producing higher classification
rates. While helpful in classifying data, these kinds of features have an ambiguous
physical interpretation. To create brain models using data from EEG studies, it is
important to be able to interpret the data in a meaningful way, not just to be able to
classify it.
The first goal of this thesis is to examine the considerations involved in
generating wavelet features and show their applicability in analyzing EEG signals in
contrast to conventional frequency analysis. The second goal is to formulate a new
method of generating wavelet features through time which makes better use of the
wavelet's time-resolution than current methods but also retains its physically interpretable
meaning. The third goal is to write a software tool in Matlab which is able to accomplish
these first two goals; to generate features of EEG data by a number of different methods
including conventional, wavelet-based, and the time-segmented wavelet method
described in this thesis. The fourth goal is to use the software tool to test the strength of
each method using data from an EEG study on the attentional networks of individuals
with Autism Spectrum Disorder and those who are considered neuro-typical.
Texas Tech University, Catherine Chesnutt, May 2012
2
Electroencephalography (EEG)
Electroencephalography (EEG) is the study of the electrical activity of the brain.
The first attempt at measuring this activity was made in 1875 by a British physician
named Richard Caton. Afterward, advancements in neurophysiology were made
throughout all of Europe, but slowed to a crawl during both World Wars. After the
second World War, the United States took the lead in Electroencephalography (EEG)
research, and the American EEG Society was founded in 1947. In the decades that
followed, EEG research in both Europe and America flourished, and every major
university hospital had an EEG machine by the 1950s [1]. Although today there are other
methods to measure brain activity such as functional magnetic resonance imaging
(fMRI), magnetoencephalography (MEG), positron emission tomography (PET), and
Diffusion Tensor Imaging (DTI), EEG remains one of the most widely used, primarily
due to its relatively low cost and wide availability.
The human brain contains around 100 billion nerve cells [17]. These nerve cells,
or neurons, carry out the functions of the brain and make thought possible. They operate
by sending electrical signals to one another. This exchange involves the passing of anions
and cations through the membranes of the neurons, causing a change in electric potential
that can be measured [1]. Although the electrical activity of a single neuron can be
measured with a microelectrode, it is currently impossible to do so without the use of
invasive procedures that involve insertion of electrodes into the brain. Alternatively, the
measurement of EEG signals can be done using electrodes on the scalp, making a non-
invasive measurement of large groups of neurons. The signals which are produced and
picked up by the electrodes represent the behavior of large numbers of neurons located
just beneath the skull where the electrode was placed. This does not take into account the
activity located deeper inside the brain. The information gained from electrodes has led to
the development of connectivity theory. Connectivity in the human brain refers to
patterns of connections between groups of neurons or regions of the brain. The functions
of the brain rely on the synchronization of these neurons, meaning that they perform
similar operations within a period of time. Research in connectivity shows that the brain's
normal function depends on the synchronization of activity inside distributed networks
Texas Tech University, Catherine Chesnutt, May 2012
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[5]. The collapse of this synchronicity has been shown to result in schizophrenic
behavior, attention and memory deficits, and speech disorders [6] [7] [8] [9]. Increased
synchronization has also been found during neuro-feedback training in subjects with
autism [10]. The use of EEG to measure connectivity has advantages over other
techniques because of its high temporal resolution, frequency specification, multiple-
source measuring, and the ease of elimination of correlated sources using statistics [4]
[11] [12].
EEG signals are primarily analyzed by their frequency content. That is, the
interpretation of the EEG signal is based on the power of the frequencies that it contains.
The primary range of interest for EEGs is from one to 100 Hz. Five main frequency
ranges are normally included in all EEG studies: Delta (0.5-4 Hz), Alpha (4-8 Hz), Beta
(8-12 Hz), Theta (12-30 Hz), and Gamma (30-100 Hz).
There are a number of conditions under which EEG may be acquired – two
common ones are resting state and task oriented. Resting EEG signals are recorded while
a person is sitting still and not engaged in any concentrated mental activity. This type of
signal is used for the detection of seizures, abnormal brain states, diseases, and cognitive
disabilities. Often, resting state EEG is acquired under an “eyes-closed” condition. Task-
oriented EEG signals are recorded while a person is performing a mental task such as
reasoning through a math problem or counting the number of objects on a screen. These
signals are used to better our understanding of cognitive states and brain responses to
cognitive or perceptual stimuli. Both types of signals make use of frequency analysis, but
the nature of task-oriented EEG signals is such that the signal may contain temporal
characteristics that may be lost or averaged out. The task-oriented EEG signals often
contain abrupt changes in frequency due to the changing mental activity during a task. In
order to gain information about these frequencies, the time-structure of the signal must be
preserved. One method used in recent decades to accomplish this is wavelet analysis. One
of the first instances of its use with EEG signals was for the detection of EEG spikes and
seizures in 1993 [32]. Electroencephalographic spikes in EEG signals are points of
sudden brain activity which contain certain frequencies. Whereas their presence alone
within the EEG signal might be detected by a Fourier transform, they are revealed by a
Texas Tech University, Catherine Chesnutt, May 2012
4
wavelet transform to be at a specific place in that signal. Due to the highly temporal
nature of brain activity, wavelets are proposed as an ideal avenue for EEG analysis.
Wavelet Analysis
Fourier Analysis, the oldest form of frequency analysis, began in 1807 with
Joseph Fourier in his work Treatise on the propagation of heat in solid bodies. Fourier
solved the heat equation by combining sine and cosine waves into a superposition, or a
combination, called a Fourier Series. These sine and cosine waves each have a different
frequency, and when combined, produce a time domain signal. The signal can then be
said to be composed of these frequencies. A time domain signal can be decomposed into
its frequencies through a Fourier transform. Figure 1.1 shows a signal composed of three
frequencies and a Fourier transform that reveals these frequencies.
While the Fourier transform reveals the frequency content of the time domain
signal, it gives no information about where in the signal the frequencies were located. In
this case of the signal above, none of the frequencies were localized in time, so the
Fourier transform succeeds at revealing all of the information that is contained in the
signal. If however, the signal's three frequencies were localized at different points in the
signal, as in Figure 1.2, the Fourier transform would not reveal this information. It looks
almost exactly like it did when they were not localized in Figure 1.1.
Figure 1.1 Signal with 44, 90, and 140 Hz and its Fourier transform
Texas Tech University, Catherine Chesnutt, May 2012
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Figure 1.2 Signal with 44, 90 and 140 Hz time-localized and its Fourier transform
Wavelet functions: stretched and compressed versions of "Mother" wavelet
EEG time domain signal convolved with wavelet
Figure 1.3 Daubechie (Db5) Mother wavelet and time signal convolution
To know the locations of the frequencies, a time-frequency analysis must be
implemented. Wavelet and Short-Time Fourier transforms are both types of time-
frequency analysis, and will be explained in further detail in Chapter IV. Wavelet
analysis begins with a set of functions that are stretched and compressed versions of one
main function called a mother wavelet. In the continuous wavelet transform (CWT), the
correlation between each of these wavelet functions and the time signal is calculated
throughout the signal by convolving the wavelet function with the time signal. This
process is shown conceptually in Figure 1.3.
Each wavelet function has its own frequency spectrum, that when correlated with
a signal, reveal whether those frequencies contained in the wavelet function were also
contained in the signal. In using many wavelet functions with different spectra, we
receive information about many different frequencies in the signal throughout time.
Texas Tech University, Catherine Chesnutt, May 2012
6
Figure 1.4 Signal with 44, 90, and 140 Hz and its continuous wavelet transform
Figure 1.4 shows the same signal with the three localized frequencies 44, 90, and 140 Hz
with its wavelet transform.
The wavelet transform in Figure 1.4 has two axes: time and scales. Scales are
inversely proportional to frequency, so that the low scales represent high frequencies. The
plot steps down as it moves through the time axis, since the highest frequency, 140 Hz, is
located at the end. The shading of the plot indicates the amount of correlation. For the
140 Hz part of the signal, we see the highest level of correlation (the lightest color) at
scale 5, and we would scale 5 to correspond closely to 140 Hz. This can be checked using
Matlab's scal2freq function, which tells us that scale 5 corresponds approximately to
133.33 Hz. Thus, each scale represents a decomposition level of the wavelet transform.
These decompositions show how much the time-signal correlated to that particular
Figure 1.5 Time-frequency resolution plots
Fourier Transform Short-Time Fourier Transform Wavelet Transform Frequency
Time
Texas Tech University, Catherine Chesnutt, May 2012
7
wavelet associated with that scale, and since that wavelet has specific frequency
spectrum, we are essentially gaining frequency information throughout time. One or
multiple scales may be calculated.
A keen observer might notice that on the plot of the cwt in Figure 1.4, the
resolution (the size of the blocks) is different for the first frequency (44 Hz) than for the
last (140 Hz). This varying resolution is only possible with multi-resolution analysis,
which is what makes wavelet analysis different than other time-frequency methods such
as the short-time Fourier transform. The frequency resolution is higher for the lower
frequency and decreases as the frequency increases. On the other hand, the time
resolution for the lower frequency in the signal is poor, and then increases for the higher
frequency. The time-frequency resolution plots for the Fourier transform (no time
resolution), short-time Fourier transform, and wavelet transform are shown in Figure 1.5.
Only the wavelet transform is considered a method of multi-resolution analysis (MRA)
that provides varying resolution at different times and frequencies. According to Figure
1.5, the wavelet transform offers the best frequency resolution in the low frequency
range, and conversely its time-resolution is best when looking at higher frequencies.
Since EEG signals primarily contain their most interesting frequencies in the range of 1-
60 Hz, and have five main bandwidths, wavelet transforms are ideal for revealing these
lower frequencies and their approximate locations in time.
Wavelet Analysis in EEG Studies
Classifying EEG data is an important part of brain research, and creates a basis
for understanding causes and treatments of disorders. In order to classify groups or
classes of EEG data, for example, between EEG data taken from neuro-typical subjects
and EEG data from a group of subjects with a disorder, features must be generated from
the data. A feature is a quantity which represents uniqueness between classes; it is a
numerical value which characterizes the data or provides some information about it.
Typically, several features from a dataset are generated using one or more mathematical
methods. The features are then examined to see if we can learn something about the data,
then they might be fed into a pattern classification algorithm in an attempt to correctly
Texas Tech University, Catherine Chesnutt, May 2012
8
classify the data as being from a particular class. In addition to their usefulness in
classification algorithms, many features may also be useful in providing physical insight
into a system. In the case of the EEG, signal features can provide different ways of
viewing and modeling the response of the brain to various inputs and conditions. Several
studies have made use of the wavelet transform to generate features.
One study in 2006 performed an EEG analysis of a learning study using wavelet
transforms and revealed features that were missed by a traditional Fourier analysis of the
same data [15]. Other studies have found similar results, including one performed on
EEG data from subjects engaged in mathematical tasks vs. resting state EEG [46].
Research conducted in 2011 shows that using wavelet coherence to generate features for
EEG data from patients with Alzheimer's Disease (AD) provided better results than
conventional coherence, with more statistically significant differences between AD and
control groups [2]. Although wavelet coherence proved to give better results between AD
and control groups in the individual frequency bands, the conventional coherence gave
better results in the case of the mixed band, possibly due to limited variability of wavelet
features between bands. Another study used conventional power and coherence features
which showed a significant decrease in functional connectivity in children with autism in
contrast to controls. The study further examined the wavelet power of the EEGs and
found additional differences; the autistic subjects responded faster to stimulation but
recovered slower, and there was higher modulation at longer latencies of the test stimuli
[14].
Autism Research
The application of EEG analysis in the area of autism research has increased in
recent years. Autism Spectrum Disorder (ASD) affects 1 out of every 110 children in the
United States and is three times more likely to affect males than females [33]. Many
studies have attempted to discover differences between ASD and neuro-typical brains.
Physical differences between autistic and neuro-typical brains began to reveal themselves
as early as 1968 with postmortem biopsies [34]. In the following decades research
revealed many more physical differences, located in the limbic system, cerebellum and
Texas Tech University, Catherine Chesnutt, May 2012
9
related inferior olive [35]. These differences include smaller and more densely packed
cells in the hippocampus, amygdala and entorhinal cortex (limbic system), a reduced
number of Purkinje cells in the cerebellar hemispheres, and abnormally large neurons in
the broca, cerebellar nuclei and inferior olive of young autistic subjects [35]. While these
postmortem physical abnormalities reveal differences in the structure of the autistic brain,
they do little to examine how it performs and approaches certain mental tasks or to show
differences in resting-state brain waves. Using EEG to measure this activity on live
participants has revealed many of these differences, including differences in resting-state
EEG coherence in individuals with autism [36], epileptic EEG abnormities in autistic
subjects [37], and evidence of mirror neuron dysfunction in ASD disorders [38] [39].
Many similar studies have used MRI and fMRI to explore these same issues, but EEG
provides a lower cost option and is usually more readily available than MRI machines. In
addition, EEG tends to be more easily tolerable than MRI studies on a large group of
autistic participants. EEG scans are also much preferred when time-dependent
information is desired. Data from MRI scans has good spatial resolution but poor time
resolution due to the nature of the blood-oxygen level dependency (BOLD) response,
while EEG provides poor spatial resolution and excellent time resolution. For measuring
time-dependent brain activity of mental task performance, EEG is a good choice, and
time-structured wavelet transforms seem a promising method of analyzing this activity.
EEG Analysis Tools
A popular tool for EEG analysis is the Matlab program EEGLab. It is open-source
software that has had the benefit of hundreds of contributions from different
programmers. One of its main attributes is its ability to import EEG files from many
different kinds of EEG hardware systems like Neuroscan or EGI. It is often used to pre-
process the raw data using a number of different methods to filter it, remove artifacts
caused by eye blinks or facial movements, and remove bad channels or bad sections of
data. It is highly suited for pre-processing data, but does not provide a statistical analysis
between classes of data. The Matlab program written for this thesis, FeatureGENgine,
Texas Tech University, Catherine Chesnutt, May 2012
10
provides a tool for the generation and examination of features from two groups of EEG
data. EEGLab is used to pre-process the data.
Purpose
The goals of this thesis include four main objectives. The first goal is to examine
the current methods and considerations of generating wavelet features and to show why
wavelet analysis is more applicable for EEG than other time-frequency analysis methods.
The mathematical origins of these methods are given in Chapter II, and a comparison
between wavelet analysis and the short-time Fourier Transform is made in Chapter IV.
The second goal is to implement a new method of generating wavelet features which is
better able to make use of the wavelet's time-resolution than current methods while
retaining a physical meaning, described in Chapter IV. The third goal is to develop a
software tool to facilitate the first two goals. A program for the Matlab environment is
provided to generate and examine features of EEG data using conventional methods,
current wavelet-based methods, and time-segmented wavelet-based methods. The
program's interface and functions are outlined in Chapter III. The fourth and last goal of
this thesis is to determine the strength of each method, using the Matlab software tool, in
being able to discriminate attentional network differences between individuals with
autism and those who are neuro-typical. The results of this are described in Chapter V.
Texas Tech University, Catherine Chesnutt, May 2012
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CHAPTER II
FEATURE GENERATION METHODS
A major goal of this thesis is to provide a Matlab software tool that performs
wavelet analysis of EEG data. The mathematical background for the feature generation
methods in FeatureGENgine, as well as its plotting and classification methods are
discussed, including the functions and methods used in the code implementation. The
meaning of the features and the considerations of their application to EEG signals are
discussed.
Feature Generation Methods
Average Power
A common method of feature generation is to use the average power of the EEG
signals across several different frequency bands of interest. For instance, one feature
might be the value for the average power in the delta band (0.5-4 Hz), a second feature
the average power for the theta band (4-7 Hz), and so forth, for the remaining alpha, beta,
and gamma bands which are common in brain activity. This produces features for each
channel of the EEG in each band.
Several cognitive states generally correspond to the power in each of frequency
bands of interest in any typical EEG scan. These cognitive states are given in Table 2.1.
Table 2.1 Cognitive states related to EEG frequency bands
Band Frequency Range (Hz) Brain Activity
Delta 0.5-4 non-REM sleep, not attentive
Theta 4-8 idling, distracted
Alpha 8-12 relaxed but focused, eyes closed
Beta 12-30 alert and busy, focus
Gamma 30-100 precept formation
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The average power is calculated by taking the root mean square (RMS) of the data,
shown in equation 2.1, where represents the data and is the number of data points.
(2.1)
The data are first filtered with an FIR filter of order 128 into bands common to EEG
frequencies of interest, and then the average power for each of these bands is calculated.
The bands are defined as they appear in the table: Delta:0.5-4 Hz, Theta: 4-7 Hz, Alpha:
8-12 Hz, Beta, 12-30 Hz, and Gamma: 30-100 Hz.
Coherence
Coherence between EEG channels is a standard method of measuring the
synchronicity between two signals. This is often interpreted to represent the strength of
connectivity between regions within the brain.
The coherence between two signals and is defined as [21]:
(2.2)
where the quantity defines the cross spectral density, which is the Fourier
Transform of the cross-correlation function between the two signals:
(2.3)
(2.4)
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The expression is the expectation operator, the average value of the signal over a
period of time. The values for coherence are bounded between 0 and 1. This is due
to the Schwarz inequality, which makes the numerator of the coherence equation always
less than or equal to the denominator, since is a scalar product:
(2.5)
Coherence can be thought of as the correlation coefficient between the components of
two signals at any given frequency [21]. The code uses Matlab's mscohere function to
determine the coherence between a set of channels provided by the user. These sets of
channels are predefined to work with EGI's 64 Channel HGSN Net.They include Far,
Anterior, Local Posterior, Posterior to Anterior, Anterior to Posterior, and User-Specified
sets of channels.
Generalized Magnitude Squared Coherence (GMSC)
When working with EEG signals, calculating coherence features based on pairs of
channels provides information about the connectivity between different parts or regions
of the brain. The generalized magnitude squared coherence spectrum (GMSC)
calculates a measure of overall coherence between all channels [22]. The GMSC is
defined as
(2.6)
where is the largest eigenvalue of , an matrix containing all the
coherence values between all of the channels:
(2.7)
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The values of the GMSC are bounded between 0 and 1, and physically represent the
correlation of all channels at a given frequency; its maximum value of 1 represents a
perfect correlation between all channels at that frequency.
Wavelet Power
Whereas Fourier analysis only provides information about frequency content,
using wavelet transforms to spectrally analyze a signal produces both time and frequency
information about the signal. In Fourier analysis, the signal can be written as a linear
combination of different frequencies with different weights or coefficients. With
wavelets, the signal is written as a linear combination of a set of functions obtained by
shifting, expanding, and contracting a mother function called a mother wavelet.
Decomposing the signal into these components yields its wavelet coefficients. The
wavelet transform is given by the formula
(2.8)
Wavelet power is calculated in a method similar to average power. The same equation is
used, except that it is applied to each scale or decomposition level.
(2.9)
where is the length of the wavelet transform and are the elements of the transform.
In the case of average power, this equation is applied to the data after it has been filtered
for the Delta, Theta, Alpha, Beta, and Gamma bands. In the case of wavelet power, it is
applied to each individual decomposition level. Each decomposition level has a
corresponding pseudo-frequency, or the frequency that corresponds to the scale used in
calculating that decomposition. The pseudo-frequencies are calculated using Matlab's
built in function scal2frq. This function gives the frequencies corresponding to each
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decomposition level based on inputs of scales, wavelet type, and the sampling period
used in the data.
Wavelet Coherence
Wavelet coherence is similar in structure to that of conventional coherence and is
described by [13]:
(2.10)
It is a function of time as well as frequency. Much like the quantity represents the
cross spectral density in the case of conventional coherence, represents the
wavelet cross-spectrum of the two signals, using their wavelet transforms in place of
Fourier transforms, and is defined as [13]
(2.11)
where is the wavelet transform of a signal decomposed along the wavelet
family defined by [13]:
(2.12)
The wavelet family used by default in FeatureGENgine is the Debauchie
wavelet, db5. The wavelet function is approximated using 10 iterations, the default
number of iterations used by the cwt function. The code uses Matlab's wcoher function in
the Wavelet toolbox to compute the wavelet coherence between time signals from two
channels.
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Generalized Magnitude Squared Wavelet Coherence (GMSWC)
A GMSC can also be defined for wavelet coherence and is done so here. The
values of matrix above are replaced by values of wavelet coherence. Since wavelet
coherence is a function of time as well as frequency, the dimension of time must be
added to the GMSC:
(2.13)
(2.14)
Statistical Moment Measures
The time-domain EEG measurements of activity, mobility and complexity are less
commonly used features of EEG signals. These were defined by Hjorth in 1970 [20].
Hjorth proposed that the conventional Fourier analysis of EEGs, which converts the
amplitude/time information to a frequency distribution, led to a pattern of reduced
complexity since it omitted the phase information, and he defined these quantities in
hopes of providing a descriptive system based on time instead of frequency. To
accomplish this, the moments in the frequency domain are translated to the time-domain,
and each correspond to a form of variance. With regard to statistical mathematics, a
moment is a quantity that describes the shape of a set of points. A moment of order is
described by the following, where c is usually zero:
(2.15)
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The quantity refers to a probability density function, and in the case of the
frequency domain it refers to the power spectrum of a time-domain signal, calculated by
multiplying the Fourier transform of the signal by its complex conjugate:
(2.16)
The Fourier transform is defined as:
(2.17)
where is a time domain signal.
The zeroth, second, and fourth moments given by the equation above when
can be used to describe the time-domain EEG measurements of activity, mobility and
complexity.
Activity
The zeroth moment in the frequency domain can be related to its zeroth moment
in the time domain by using the energy equality theorem, which states that the total
energy in the frequency domain is equal to the average power in the time domain, as in
(2.18)
where is the total time of the signal. The average power in the time domain is also
equal to the variance, or . This quantity defines activity, and is simply the variance or
mean power of the signal.
Mobility
If a function of frequency is multiplied by its frequency, , the result in the
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time domain is the first derivative of the corresponding time function. Since we already
have the corresponding time function for the zeroth order moment, the time function for
the second order moment is the second derivative of this.
(2.19)
The quantity
is the standard deviation of the slope. The mobility of a time domain
signal is the ratio of the second order moment to the zeroth order as in
(2.20)
This translates to the measure of the standard deviation of the slope in reference to the
standard deviation of the amplitude. It is in units of a ratio per time, and describes the
mean frequency of the signal.
Complexity
Complexity is a third measure of variance. The fourth order moment is defined as
(2.21)
The complexity is defined as the ratio
(2.22)
This measure of variance describes the deviation of the signal from its 'softest' possible
shape, a simple sine wave, which corresponds to unity. It relates the number of standard
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slopes which are generated during the same amount of time it takes to generate one
standard amplitude that is described by the mobility.
Each of these measures of variance is suitable for measuring either spontaneous
(ongoing) EEG or event related (evoked) response EEG. Another quantity, called string
length, is a measure of the actual length of a signal if a string were outlined over it and
stretched out, and is measured from the beginning of a response following an event
related potential (evoked) EEG. Research shows that the measure of complexity is
strongly related to the string length. This would mean that a complexity measure can be
used in the same way to represent a quality of the EEG similar to that of the string length,
and can be used to describe spontaneous (ongoing) EEG without recording an event
stimulated response, provided the data were taken under similar conditions [18]. String
length is also thought to be related with intelligence [19].
Time-Segmented Wavelet Features
In order to generate time-segmented features, wavelet transforms are calculated
normally and then segments of these are taken, and features are generated from these
instead of the entire transform. The code uses Matlab's blockproc function to accomplish
this with a specified step size in seconds. The length of the block is equal to the sampling
frequency multiplied by this time step. The code also implements a Hamming window on
each segment to reduce the effects of using a rectangular window. This is discussed more
in Chapter IV under Windowing the Time-Segmented Wavelet Features.
Statistical Analysis using a T-Test
The code in FeatureGENgine uses Matlab's ttest2 function to compute a t-test
between two sets of data with two unknown means. The function is called in the
following way: h = ttest2(x,y,alpha,tail). The function tests the null hypothesis that the
values in the groups of data in x and y are independent random samples from normal
distributions that have equal means and equal but unknown variances, against the
hypothesis that the means are not equal. The x and y variables can be either vectors or
matrices, and in the case of EEG data, x and y are 3-dimensional matrices. Each one
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describes the features for each subject which have been averaged across epochs, or trials
within the EEG data. The t-test then performs its operation on each set of features for one
class against the other. In the example study in Chapter V, there are five subjects in each
class. The t-test performed on these tests the values of the features for each group, so that
one group of five values is tested against another group of five values. The t-test returns h
= 1 if the null hypothesis is rejected and the means of the two groups are found to be
significantly different at a 5% significance level. This significance level, alpha, is set to
0.05 (5%) as a default in FeatureGENgine, but can be changed by the user in the
interface. The "tail" parameter of the function refers to the type of test to be performed
against the alternative, and can be 'both', 'right' or 'left'. These correspond to a two-tailed
test, where the means are not equal, and to a right or left-tail test, where the mean of one
is higher than the other. The default setting in Matlab is set to 'both' to perform a two-
tailed test.
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CHAPTER III
FEATUREGENGINE
This chapter provides an overview of the FeatureGENgine interface. The overall
process of importing data, generating features, and viewing a statistical analysis using a t-
test is outlined, and the main functions of the FeatureGENgine GUI are highlighted.
FeatureGENgine Interface
The FeatureGENgine program was written in Matlab for the purpose of
generating features from two classes or groups of preprocessed EEG data using a number
of different methods, to allow the user to examine these features easily, and to produce
the results of a simple t-test of the features between the two classes. A t-test is a
preliminary way of knowing whether there are significant differences between the two
groups that should be further examined. The actual values of all the features generated for
each class and each subject can be viewed in a table in the GUI, and if applicable, some
of the features such as wavelet transforms, STFTs, and time-segmented wavelet features
may be plotted.
Importing to FeatureGENgine
EEG data are loaded directly into
FeatureGENgine in the form of a .mat file. The EEG
data is preprocessed in EEGLab and then accessed
directly from the Matlab command line while EEGLab
is running. The data from each subject is stored inside
EEGLab within a structure, and the Matlab command
line can access this structure and resave the data into
arrays corresponding to different classes within a .mat
file. The .mat file contains two arrays, one per class,
and each of these contains as many matrices as there are
subjects, containing the preprocessed EEG data. For the
Figure 3.1 Loading datasets
into FeatureGENgine
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Figure 3.2 Feature generation panel
FeatureGENgine code to run correctly, there must be the same number of subjects in each
class, and each matrix must be the same size. The matrices can be 1, 2, or 3 dimensional.
The user clicks the "Load Data" button and enters names for each class. The user also
enters the sampling frequency at which the EEG data was sampled. The default is 500
Hz, the sampling frequency used by the EGI system used to gather data for the Example
Study in Chapter V. The user can also load features that were previously generated by
FeatureGENgine for the purpose of viewing and plotting them without having to generate
them again.
Feature Generation Methods
The feature methods available in FeatureGENgine described in Chapter II are: (1)
Wavelet Transforms with options to enter wavelet type, decomposition level (2) Average
Power (3) Coherence, with options of Far, Anterior to Posterior, Local Posterior,
Posterior to Anterior, or user-defined channel pairs (4) Wavelet Coherence, with options
to enter wavelet type, decomposition level, Far, Anterior to Posterior, Local Posterior,
Posterior to Anterior, or user-defined channel pairs (5) Statistical Moment Measures (6)
Generalized Magnitude Squared Coherence (7) Generalize Magnitude Squared Wavelet
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Figure 3.3 Coherence selection
Coherence with options to enter the wavelet type and decomposition level (8) Phase
Synchrony and (9) Power Spectral Density Features.
The generations methods (1), (4), and (9) provide the options to generate five
different features: (1) Averages (2) Power, (3) Complexity, (4), Peaks, and (5) Mobility.
These methods (1), (4), and (9) have the option of generating time-segmented features
that can be plotted.
Feature Averaging, Viewing and Exporting
Due to the large amount of data that is generated when producing features and in
order to create sets of data on which to perform a t-test, the features must be averaged
Figure 3.4 Plotting feature values
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Figure 3.5 Plotting wavelet transforms and time-segmented features
across epochs. FeatureGENgine averages the features across epochs for each subject.
Once the features are averaged, they can be viewed in the Feature Table in the GUI
window, Figure 3.4. All averaged features for each subject and for each
class can be viewed, as well as the averages across all subjects, which appears at the
bottom of the scroll list for each class.
Excel files can be created to export the features. These excel files are saved in the
current Matlab directory. One file is created per class, saving the features into sheets
labeled as the Subject Number, and the last sheet contains the features generated from
averaging across all subjects. When the "Create Excel Files" Button is pressed, the user
can rename the excel files being created, which have default names for each class based
on the class names entered when the user first loads the data.
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Figure 3.6 Plotting wavelet transforms
Plotting Wavelet Transforms and Time-Segmented Features
Wavelet transforms, STFTs, and time-segmented features generated by methods
(1), (4) and (9) can be plotted for each class and for each channel. The plotting options
include Line, Image, and Stem Plots. An example of plotting wavelet transforms using
stem plots and image plots are shown in Figure 3.5 and Figure 3.6. The wavelet used to
calculate the CWT is plotted in the bottom right-hand corner of the panel.
Test of Significance using T-Test
Options for classifying the features from the two classes include a simple t-test
based on an alpha value. The binary matrix created by the t-test function is plotted that
highlights the features that passed the t-test. This plot opens in a new GUI window and
plots the average values of these features for each class and for each frequency band in
tables.
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Figure 3.7 Plotting binary matrices and values of features that passed a t-test
Flexibility of FeatureGENgine
FeatureGENgine is a research tool that allows users to analyze EEG data inside
Matlab using a number of different methods. Specifically, it offers both current and new
methods of wavelet based features, and provides a way to extensively examine these
features. The program is structured in such a way as to be flexible enough to add other
functions as desired. The program's main code loads the data from arrays and stores it in
arrays within the handles structure, and performs the various functions related to the
components in the user window. The function that generates the features is separate from
the main code, and each of the feature generation methods inside this function is itself a
separate function. Other generation methods may be added by writing a new function that
handles the data in the same way as the current ones, and then by calling the new function
in the feature generation function. The main code and all the auxiliary functions it calls
are provided in the Code section.
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Wavelet functions: stretched and compressed versions of "Mother" wavelet
EEG time domain signal convolved with wavelet
Figure 4.1 Daubechie (Db5) mother wavelet and time signal convolution
CHAPTER IV
WAVELET ANALYSIS
This chapter addresses the first two goals of this thesis. First it will be shown that
wavelet analysis is more applicable for EEG than other time-frequency analysis methods,
and some signal processing considerations of generating wavelet features will be
examined. Second, after considering currently used methods, a method of feature
generation will be described that takes advantage of the wavelet's time resolution: time-
segmented features. The choice of wavelets is examined by comparing three different
wavelets, db5, coif5, and haar, in an effort to discover which is appropriate for EEG
signals.
A Brief Overview of the Wavelet Transform
As explained in Chapter I, the wavelet transform is a newer method of time-
frequency analysis which, in contrast to Fourier analysis, provides time-dependent
frequency information of a given time signal. In Chapter I it was also shown that wavelet
transforms are a type of multi-resolution analysis that provide good resolution in the
lower frequency range, making them especially applicable for EEG signals, that have a
primary interest range of 1-100 Hz. In particular, the bands labeled Alpha (8-12 Hz) and
Beta (13-30 Hz), that describe attentive, focused thought, are of common interest. EEG
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signals are time-dependent signals that have sudden changes in frequencies due to
changing mental processes.
A wavelet transform is calculated by taking a function, called a mother wavelet,
stretching and compressing it into different versions, and then convolving those versions
with a time signal. The wavelet transform of a signal decomposed along the
wavelet family defined by is [13]:
(4.1)
A time-signal of length will produce a number of time-domain signals, called
decompositions, each of length . The number of these decompositions equals the
number of scales, or the number of versions of the mother wavelet. Each of these
decompositions represents the original signal's correlation to that particular wavelet
throughout time. The stretched and compressed wavelets can be thought of as band-pass
filters which are applied to the signal, each having its own range of frequencies, such that
each signal it produces is limited to the range of frequencies contained in the wavelet.
Thus, a wavelet transform can be calculated on one or many scales that correspond to
decomposition levels, each having a bandwidth. Figure 4.1 repeats Figure 1.4, showing
the conceptual process of convolving a wavelet with a time signal.
The frequency and time resolution abilities of the Fourier transforms, the short-
time Fourier transform, and the wavelet transform were explained in Chapter I. This
tradeoff between time and frequency resolution in time-frequency analysis results from
the uncertainty principle. The uncertainty principle dictates that there must be a limit to
the resolution of position, and momentum :
(4.2)
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In this equation, is equal to
, where , or
Planck's constant. In the area of special relativity, energy is related to time as position is
related to space, and the energy-time version of the uncertainty principle describes this:
(4.3)
It takes a certain amount of time to describe any amount of energy, since energy is
defined by the frequency of the state of something, whether it be a particle or a wave (or
both!). It is because of this principle that all methods of frequency or time-frequency
analysis are limited in their capabilities to provide resolution. Fourier analysis provides
all frequency, and no time resolution, Short-Time Fourier Transforms provide constant
resolution at all time and frequencies, and wavelet analysis, a type of multi-resolution
analysis, provides varying resolution across frequencies. These differences were
explained in more detail in Chapter I and are shown in Figure 1.5. Since EEG frequency
bands of interest are typically in the lower ranges, and those bands tend to be very close
together, the multi-resolution attribute of the wavelet transform makes it a good choice
for EEG signals.
Wavelet Transforms and Scales
Matlab's cwt function calculates the continuous wavelet transform of a time-
domain signal. It is called in the following way: coefs = cwt(S,scales,wavelet_type)
where S is a vector containing a time domain signal, scales is a vector containing the
levels of decomposition that the wavelet transforms are calculated upon, and the wavelet
type specifies which mother wavelet function to use. Throughout this code, the fifth
Daubechies wavelet, Db5, is used. The algorithm inside the cwt function uses the
function intwave to approximate and integrate the wavelet function. As mentioned in
Chapter II, the function is approximated using a default number of ten iterations. The
number of iterations determines the actual number of points inside this approximated
wavelet vector. Then, depending on the scale being calculated, it selects indices from the
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approximated wavelet vector and convolves it with the time signal. It then uses the
function diff, which effectively integrates this convolution, and uses the function wkeep1
to withhold only the central part of this convolution such that the result is the same length
as the original signal.
The scales used in the FetaureGENgine code were specifically chosen to
correspond with the EEG frequency bands of interest and do not increase linearly. They
were chosen so that most of the scales would be calculated for the Delta, Theta, Alpha
and Beta bands. These scales and their corresponding frequencies are as follows:
Scales: [3,5,10,11,14,18,20,24,28,32,40,45,50,60,70,80,90,110,150,200]
Frequencies (Hz): [111.11 66.67 33.33 30.30 23.81 18.52 16.67 13.89 11.90 10.42 8.33
7.41 6.67 5.56 4.76 4.17 3.70 3.03 2.22 1.67]
The first scale, 3, corresponds to 111.11 Hz, and so forth. These vectors of scales
and their corresponding frequencies are used consistently to generate features throughout
the code, but can be changed by the user in the FeatureGENgine GUI. The scales and
their corresponding frequencies are shown for all EEG frequency bands in Table 4.1.
Table 4.1 EEG bands: corresponding scales and frequencies
EEG Frequency Band Scales Frequencies (Hz)
Delta 80,90,110,150,200 4.17, 3.70, 3.03, 2.22, 1.67
Theta 45, 50, 60, 70 7.41, 6.67, 5.56, 4.76
Alpha 28, 32, 40 11.90, 10.42, 8.33
Beta 11, 14, 18, 20, 24 30.30, 23.81, 18.52, 16.67,
13.89
Gamma 3,5,10 111.11, 66.67, 33.33
The scale of a wavelet transform does not correspond directly to a certain
frequency. Rather, these frequencies are approximations that are translated from the scale
corresponding to the maximum value of the CWT coefficients. Matlab performs this
using the function scal2freq to calculate these frequencies. To accomplish this, the
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function scale2freq calls another function, centfrq, to calculate the center frequency by
numerically centering the wavelet and taking the maximum value of the modulus of its
Fourier spectrum. It adjusts this to different scales of the wavelet using the following
equation:
(4.4)
where is the center frequency of the spectrum of the wavelet calculated by centfrq, is
the scale of the wavelet, and is the sampling period of the data being used to calculate
the wavelet transform. Each wavelet type has different frequencies that correspond to its
scales, and some wavelets perform better than others at locating these frequencies. Thus,
some wavelets have better accuracy in representing the frequencies in the signal with
which they are convolved, depending on how well the scale of the wavelet corresponds
with the maximum value of the CWT coefficients. To explain this in greater detail,
comparisons are made between the Haar, Db5, Coif5, Gaus4, Morl, and Dmey wavelets
in the Choice of Wavelets Section of this chapter.
Wavelet Transforms and the Short-Time Fourier Transform
As mentioned previously, wavelet analysis is not the only time-frequency analysis
method used for non-stationary signals such as EEG. The Short-Time Fourier Transform
(STFT) is still used to gain time-dependent frequency information. The STFT works by
taking segments of the time-domain signal and performing a Fourier Transform on each
one. It has been used successfully in many Bio-medical applications, but has two main
limitations: (1) It is difficult to select a window length appropriate for a range of features
that vary throughout the time segments, (2) The shortening of the time-segment length to
increase time resolution will decrease frequency resolution given by [40]
(4.5)
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where is the number of points in the time segment and is the sampling period. These
limitations make the STFT more applicable in areas where higher frequencies are of
interest and where frequency resolution is not important. Figure 4.2 (A) shows an image
and a stem plot of a spectrogram of a chirp signal ranging from 1-110 Hz that is 2
seconds long and sampled at 1000 Hz, calculated with FeatureGENgine using Matlab's
spectrogram function, which computes the STFT at a given vector of frequencies using
the Geotzel algorithm and a Hamming window [41]. Figure 4.2 (B) shows the same
signal's wavelet transform calculated with the scales corresponding to the same vector of
frequencies used in the STFT. It should be noted that the scales in Figure 4.2 (B) range
from 1 to 20, but actually correspond to the 20 scales defined above. The STFT and the
wavelet transform give similar results in Figure 4.2. As will be explained in the Time-
Segmented Wavelet Features section, generating time-segmented features based on either
the STFT or the wavelet transform requires shortening the time-segment window,
affecting the frequency resolution of both.
Wavelet Features
In general, there are two reasons to generate features from EEG data. The first is
for the purpose of classification. In this case, the features themselves, or their values, are
not examined. Using different feature extraction techniques, computer algorithms choose
the features that generate the highest classification rates. The second purpose of
generating features is to create brain models. In this case, the values of the features reveal
information about the cognitive states of the participants who were part of the EEG study,
showing not only that two brains are different, but how they are different.
A wavelet transform of a time-domain signal produces a signal of a length equal
to the original signal. A method must therefore be chosen to generate features from these
transforms. In research, these features have been generated a number of ways. One study
used energy, entropy and standard deviation of the Daubechies series (Db2 mother
wavelet) as the features generated from a five-level decomposition, and were able to
classify Epileptic EEGs at a 91.2% classification rate [23]. Another study used statistical
measures of a five-level wavelet decomposition of the data: the mean of absolute values
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of the coefficients in each sub-band, the average power of the wavelet coefficients in
each sub-band, standard deviation of the coefficients in each sub-band, and the ratio of
the absolute mean values of adjacent sub-bands. This study found these features were
useful in classifying seizure EEGs in conjunction with a Mixture of experts (ME), a
neural network structure [24]. Although many studies use the Daubechies wavelets, one
study showed that the first of the Coiflet wavelets resulted in the most accurate
classification of EEG of both abnormal and neuro-typical signals [25]. Another study
(A) Spectrogram of chirp signal with
window size of 0.1 seconds
(B) Wavelet Transforms of chirp signal
and window size of 0.1 seconds and
overlap of 95 points
Figure 4.2 Spectrogram and wavelet transform of chirp signal of 1-110 Hz
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examining EEG artifacts generated wavelet features using the power spectrum, variance
and mean of the Haar mother wavelet [26]. Another study used an Amplitude
Modulation method to extract features from the wavelet decompositions of EEG data,
that defines changes in the time-signal's envelope at its sampling frequency, and produces
high classification rates using SVM neural networks [42].
These studies generated wavelet features of different methods with the purpose of
producing improved classification rates between groups using different algorithms. Some
of these algorithms involve data reduction techniques to extract features that produce the
highest classification rates. While high classification rates are beneficial in algorithms
that attempt to separate EEG data into groups, it can sometimes be difficult to interpret
physical meaning from these features, for the purposes of understanding neural processes
within the brain. Classifying EEG data is useful, but when there is a need to create brain
models to understand the processes of the brain, such as with autistic subjects, the
physical meaning behind the features must be retained. One study separates the WT into
segments to find an optimal active time segment and then extracted fractal feature vectors
for a classification using a linear classifier [45], which does make use of the WT's time
resolution, but is for classification purposes, not brain models. Many times, the feature
extraction and data reduction techniques remove this attribute of the data, especially
where nonlinear transformations are involved. For EEG data to remain physically
interpretable, it is helpful to stay close to the established meaning of power in the five
EEG frequency bands introduced in Chapter II: Delta, Theta, Alpha, Beta, and Gamma,
all corresponding to different general cognitive states. To accomplish this, time-
segmented wavelet features are generated based on the wavelet power in the EEG bands.
Time-Segmented Wavelet Features
The current methods mentioned above, while using wavelet transforms to
generate features, are generating one value or feature per transform. This inevitably
averages out the time-dependent information. Regardless of which method of generation
described thus far is used on the wavelet transforms, although they might describe the
shape or overall nature of the time-domain signal, the temporal information is still
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35
averaged out. Being able only to describe the shape of the signal, such as several of the
aforementioned studies did by using means and standard deviations of the transforms,
provide an ambiguous interpretation of the physical meaning of the data, with the
possible exception of string length (Complexity) being linked to intelligence. A possible
solution to this is to generate these features in segments of time, in a manner similar to
the STFT. To create these time-segmented features, FeatureGENgine first computes the
wavelet transforms as it normally would using Matlab's cwt function. The user specifies a
window size for the features such that each wavelet transform, a function of time itself, is
divided into n of these segments. Features are then generated on each one of these n
segments. This produces one feature per time segment per scale of decomposition, per
channel, per epoch. EEG data epochs can range from seconds to minutes. This makes the
amount of data generated by these time-segmented features quite large. In the case of the
example study, 64 channels, 15 epochs of length 1.4 seconds, a sampling rate of 500 Hz,
a window size of 0.1 seconds, and a wavelet decomposition of 20 scales produces an
entire feature matrix of size 20x14x15x64. One of these is calculated per subject. In our
example study there are two classes, each containing five subjects. The computational
time required for time-segmented wavelet power features is 153.14 seconds per subject.
The time required to calculate time-segmented features from the STFT of all the data per
subject is 24.35 seconds.
The time segment window size of the time-segmented wavelet transforms
determines the frequency resolution of the features. If the window size is too large, the
features generated at the smaller scales, or higher frequencies, are almost undetected.
This shows the ineffectiveness of generating features based on the entire wavelet
transform (a very large window) without breaking it up into segments; the temporal
information is simply averaged out. Basically, it is using a function specifically to
produce some information and then discarding that information. To demonstrate the
importance of the window size, wavelet power features of 20 decomposition levels are
generated from a chirp signal ranging from 1-110 Hz that is 2 seconds long and sampled
at 1000 Hz. Figure 4.3 shows a stem plot of the features computed with a 0.01 second
window (200 time blocks) and a 0.001 second window (2000 time blocks).The smaller
Texas Tech University, Catherine Chesnutt, May 2012
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wavelet scales should be able to reveal the higher frequencies of the signal. The smaller
window size of 0.001 makes the number of features equal to the original length of the
signal, 2000, and should therefore be able to show the entire frequency range of the
signal, which it does in the red portion of the time axis. The plot (A) with the larger
window, however, does not show the higher frequencies located toward the end of the
chirp signal. It should be noted that the scales shown in Figure 4.3 correspond to the
(A) STFT of chirp signal with
window size of 0.01 seconds
(B) Wavelet features of chirp signal with
window size of 0.01 seconds
Figure 4.3 Time-segmented wavelet power features using different widow sizes
Texas Tech University, Catherine Chesnutt, May 2012
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vector of 20 scales defined earlier, and are labeled as being from 1 to 20 in an effort to
make the plots clearer.
In contrast, when the same window size is used in the STFT to generate features,
the decrease in frequency resolution in these lower frequencies is clear in Figure 4.3 (A)
and (B). Both the time-segmented wavelet features and the STFTs were calculated with
the same window size of 0.01 seconds. The decrease in frequency resolution due to Eq.
4.2 is evident in the STFTs, while the wavelet transforms retain their lower frequency
resolution.
Note the purpose of examining the method that retains the greatest amount of time-based
frequency information when generating features from wavelet transforms and STFTs.
Whether taking wavelet transforms or STFTs of EEG data, a large amount of data is
produced. We need to produce characteristic features of this data that will help us identify
two groups as different, and be able to interpret those characteristics in a physically
meaningful way. Since there has been well-established physical meaning in the various
EEG frequency bands we have described, the goal is to retain as much information about
these bands as possible. It is clear that wavelet transforms, although less computationally
efficient in this implementation, are able to generate more features of the original signal.
Windowing the Time-Segmented Wavelet Features
Windowing is an essential part of analyzing signals. It is necessary to truncate a
segment of an aperiodic time signal, such as EEG, for representation in a computer, since
an infinite time signal like this is larger than the computer's memory storage [40]. The
type of window used can affect the resulting frequency spectrum, since the windows
themselves contain their own frequency content. In using the blocproc function to
generate time-segmented features of the wavelet transforms, segments are cut out of the
time-signal (wavelet transform), effectively applying a rectangular window. The resulting
features contain information about the rectangle's frequencies as well as the original
signal. In order to minimize these effects, a Hamming window function is multiplied with
the wavelet transforms before they are processed inside the blocproc function. An overlap
value may also be specified.
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Wavelet Test Data
The Db5 wavelet was scaled to all of the 20 scales defined above and used as
input signals. The transform, computed on the same 20 scales, is shown in Figure 4.4 for
the first and last scales, 3 and 200, corresponding to 111.11 Hz and 1.67 Hz, respectively.
It is interesting to note that while the highest scale in (B) (lowest frequency) was not at
all detected on the lower scaled wavelet transforms, the lowest scale (A) wavelet signal
(highest frequency) was still detected on the highest scaled (lowest frequency) transform.
This is due to the fact that the continuous wavelet transform contains overlap between
scales.
Choice of Wavelets: Harmonics and Frequency Detection
One study found that the Coif wavelet family produced high classification rates
for EEG data [25]. When testing a 2-second chirp signal of 1-110 Hz with the Haar, Db5,
Coif5, Gaus4, Morl, and Dmey wavelets, the coif5 shows the least amount of harmonic
interference, shown in Figure 4.5. This lack of interference is a possible explanation for
the study's findings. The reason for the harmonic interference is due to the frequency
spectra of the wavelets, shown in Figure 4.7 for the Haar, Db5, Coif5, and Dmey
wavelets. Of these four, the frequency spectrum of the Coif5 wavelet shows the least
amount of harmonic frequencies.
The frequency corresponding to a certain scale of a wavelet transform is based on
its center frequency - the maximum of the modulus, or absolute value of its Fourier
spectrum after it is numerically centered. Each type of wavelet has different frequencies
that correspond to its scales, and some wavelets perform better in detecting the
frequencies of the signal with which they are convolved. In using wavelets to generate
EEG features, it is very important that the wavelet perform well. One of the main
objectives in this thesis is to create time-segmented wavelet features that have a physical
meaning in order to develop models of the brain. This physical meaning is attached to the
EEG frequency bands, so that the wavelet used must have its scales match up well with
the frequencies they represent. If they do not match up well, there is less certainty that
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Figure 4.4 Wavelet transforms of Db5 wavelet signals
the wavelet power features generated represent the correct frequency bands. For instance,
some features found to be significant (with a t-test or other test of significance) in the
Alpha band might actually have been in one of the bands beneath or above it, in the Theta
or Beta bands. In order to test the performance of different wavelets in detecting these
frequencies, Matlab's scalogram function is used with wavelet coefficients generated
from a plain 14 Hz sine wave of 1 second [43]. To be more precise, a wavelet transform
is calculated for a 14 Hz sine wave and the energy of each wavelet coefficient is plotted.
The maximum of these energy coefficients should correspond to the scale calculated by
scal2frq using 14 Hz as the input frequency. This is done for six different wavelets in
Figures 4.6. For each plot, the horizontal red line represents the scale at which the
wavelet corresponds to 14 Hz, the frequency of the input signal, according to the scal2frq
function. The location of the red line with respect to the maximum energy of the
coefficients and the amount of variation of the energy across scales describes the
performance of the wavelet in locating the 14 Hz frequency. The scales corresponding to
the Haar, Db5, Coif5, Gaus4, Morl, and Dmey wavelets are 71, 48, 49, 36, 58, 47,
respectively.
(A) Wavelet Transforms of Wavelet of
Scale 3
(B) Wavelet Transforms of Wavelet of
Scale 200
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Figure 4.5 Wavelets of Haar, Db5, Coif5, Gaus4, Morl, and Dmey tested
with chirp signal
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Of the six wavelets examined, the Morl and Gaus4 appear to have the best
frequency detection. The red horizontal line representing the scale that corresponds to 14
Hz travels very nearly across the center of the maximum of the energy coefficients, and
these coefficents do not vary quite so much across the scales. While the Coif5 wavelet
shows little harmonic interference in its representation of the chirp signal, its scalogram
shows its frequency detection as less than perfect. While the Morl wavelet does show
Figure 4.6 Scalograms of Haar, Db5, Coif5, Gaus4, Morl, and Dmey wavelet coefficients
of 14 Hz sine wave (scale corresponding to 14 Hz represented by red horizontal line)
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some interference in its representation of the chirp signal, it provides good frequency
detection.
Figure 4.7 - Frequency Spectra of Haar, Db5, Coif5, and Dmey wavelets
Types of Wavelet Features
Averages
Taking averages of wavelet transforms might defeat the purpose of using them.
The appeal of a wavelet transform is its ability to retain temporal information, so
averaging the various decomposition levels practically erases this information. Still,
taking averages of the wavelet transforms has yielded features which have passed a
significance test.
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Power
Calculating the average power of the wavelet transforms yields more significant
features in the sample data than averaging the entire wavelet transform. It is similar to
calculating regular power in designated frequency bands, except that instead of having
the five bands of Delta, Theta, Alpha, Beta and Gamma, there are as many bands as there
are decomposition levels, since each decomposition is effectively a band pass filter of the
time-signal. These average power features have a meaning similar to conventional
average power in the EEG bands, only they have higher frequency resolution. This makes
it easier to divide the EEG bands into sub-bands which also have meaning according to
research: low-Beta, high-Beta, etc.
Complexity and Mobility
Using complexity and mobility to calculate wavelet features has yielded many
significant features in the sample data, particularly complexity. When complexity is used
on test data that contains wavelets as input signals, the features are clearly different for
each decomposition level. They increase from very small to very large values from the
lower to the higher scales, respectively.
Peaks
Features can be generated by calculating the number of peaks in the wavelet
transform that cross a certain threshold. The FeatureGENgine code uses a threshold of
90% or 0.9 times the highest point in the signal.
Conclusions
To generate wavelet features in a fashion that retains the physical meaning of the
features, wavelet power features are generated in segments of time. The response of the
STFT and the wavelet transform to the windowing required for generating time-
segmented features makes the wavelet transform more appropriate, since it provides more
frequency resolution in the EEG ranges of interest. The choice of mother wavelet used to
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generate these features should reflect the wavelet's level of harmonic interference and its
ability to detect frequencies that align with its scales. The Coif5 wavelet provides good
frequency detection while having little harmonic interference. Results from using wavelet
power features and time-segmented wavelet power features are compared with an
example EEG study in the next chapter.
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CHAPTER V
EXAMPLE STUDY: ATTENTION NETWORKS OF AUTISTIC INDIVIDUALS
Participants were recruited for a study that examined the differences in attention
between neuro-typical children and those diagnosed with Autism Spectrum Disorder
(ASD). The goal of the study was to inspect the differences in areas and activations of
the brain that occur as a result of a mental task involving a 'distracting' stimulus. It is
thought that individuals with ASD have a tendency to hyper-focus on aspects of their
environment, to their detriment.
Background
Attention refers to the cognitive process of focusing on a certain aspect of one's
environment while ignoring other aspects of it. Cognitive psychology suggests that there
are several types of attention. In particular, selective attention is a type of executive
control, and describes the extent to which the other aspects of an environment are
ignored. A study in 2005 established a technique to assess selective attention, called the
Attentional Network Task (ANT) [47]. The task involves two different stimuli. The first
is a picture of five fish that all face the same direction (congruent), and the second is the
same set of fish with the middle one facing the opposite direction from the others
(incongruent). The study discovered an association between selective attention and
activation in the anterior cingulate and frontal cortex. There is an abnormality in the
selective attention processes of autistic individuals when compared with neuro-typical;
autistics tend to hyper-focus on a specific aspect of their environment, and sometimes
those aspects are irrelevent. The study in this chapter was conducted to examine whether
the activation regions for each type of ANT stimulus were different for autistic and
neuro-typical subjects. It is thought that when presented with the ANT stimuli, autistic
individuals process both congruent and incongruent types of stimuli in a similar manner,
while neuro-typical individuals process the two differently. The neuro-typical brain
should be more distracted by the presence of opposite-facing fish in the incongruent
stimulus, while the autistic brain fails to process the surrounding fish. Thus, the
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hypothesis for this study is that there will be a large number of differences between
autistic and neuro-typical brain patterns in response to the incongruent fish, more
differences within the autistic group than neuro-typical between types of stimuli, and that
these differences will occur in the area linked to selective attention: the prefrontal cortex
and the anterior cingulate.
Stimulus Materials and Procedure
Each participant was given a handedness questionnaire upon arriving at the
location of the study. The study was then explained to them briefly and they were shown
examples of the stimuli they would be seeing on the computer screen during the EEG
recording. After these instructions were given, head measurements were made and an
EGI 64-Channel EEG net was placed on their heads after the proper preparation of the
net. The participant was then placed in a sound-proof room with or without his or her
legal guardian and performed the test on the computer screen.
Subjects
Participants were between the ages of 13 and 18. Those in the ASD group had
been previously diagnosed with a form of ASD. Those in the controls group were
selected from a typically developing individuals of the same age group.
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Attention Test
The test itself consists of a series of pictures of fish in the middle of the screen. In
each picture, the middle fish is facing either the same direction or the opposite direction
of the fish on either side of it, show in Fig.5.1. Figure 5.1 (A) shows a congruent trial, all
the fish are facing the same direction. Figure 5.1 (B) shows an incongruent trial, the
middle fish is facing opposite to the ones on its left and right. Each trial presented to a
subject contains either a picture of congruent-facing fish or incongruent-facing fish. The
subject then pressed a button to signify which direction the middle fish was facing.
assumed that the cognitive responses that distinguish between groups occurs primarily in
this initial time period.
The purpose of the study was to identify neuronal differences in the attentional
networks of neurotypical children and those diagnosed with Autism Spectrum Disorder.
These differences are possibly due to the ASD child's tendency to hyper-focus, meaning
they are less affected by the opposite-facing directions of the surrounding fish than a
neurotypical child would be.
Recording and Preprocessing EEG Data
Exporting
The EEG data were recorded using EGI's Net-Station software and a 64-Channel
net. The test was created in E-prime, which is configured to communicate with EGI
during recording. The EEG files were filtered with a 60 Hz notch filter, a 0.1 Hz low pass
filter, and re-montaged to a 10-10 montage format before exporting from Net-Station.
They were then imported into EEGLab. The data segments removed included data
recorded between stimulus trials and before and after the trials begin and end.
Independent Component Analysis
Independent Component Analysis (ICA) is a standard technique for removing
artifacts from EEG data. It isolates components that are embedded within the data so that
they can be removed. Components due to heart rate, eye-blinks, and muscle movement
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Figure 5.2 Scalp maps of ICA components using EEGLab
can be detected by ICA. EEGLab offers an ICA tool to remove such artifacts. To remove
eye-blink artifacts, ICA was performed on the data in EEGLab. These are chosen at the
discretion of the user, but are usually identifiable and are described in the EEGLab
manual [27]. The criteria for recognizing eye blinks, described in the EEGLab manual
and applied to this data are the following: (1) The smoothly decreasing EEG spectrum
(2) The scalp map shows a strong far-frontal projection (3) It is possible to see individual
eye movements in the component activity graph [28]. Likewise, the criteria for
determining relevant brain artifacts that should remain in the data are: (1) Dipole-like
scalp maps (2) Spectral peaks at typical EEG frequencies (i.e., 'EEG-like' spectra) (3)
Regular ERP-image plots (meaning that the component does not account for activity
occurring in only a few trials). There are two ICA algorithms available in EEGLab: one
calls the runica.m file and one calls the jader.m file. The runica algorithm is
recommended in the manual and was used in this instance. According to the manual, any
physiological significance to the results of using these different algorithms has not been
determined. They return nearly equivalent results when used with low dimensional data
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which fulfill the assumptions of the algorithm [29]. The runica algorithm is proposed to
be suitable for EEG data and is an implementation of the ICA algorithm written by Bell
and Sejnowski in 1995 [30]. It is thought to be suitable because the nature of the spatial
ambiguity of the EEG data, which the algorithm is able to take into account as it
separates source identification from source localization using blind source separation
[31]. Figure 5.2 shows the first twelve ICA component scalp maps for a typical EEG
scan. The first and second components, shown by the arrows, most likely contain eye-
blink artifacts. Components like these are removed in the example study.
Epoching
The data are then segmented into epochs using EEGLab. The parameters for the
epochs begin with the stimulus flag (the point at which the participant is shown the
pictures of the fish) and end 1.4 seconds after the stimulus flag. The sampling rate is 500
Hz, making each epoch 700 data points long. The time length of the epoch was chosen
according to the average response time, that occurred within 1.4 milliseconds.
Exporting to Matlab
The files were then exported from EEGLab into .mat files. Each dataset in
EEGLab contains a structure with information fields. The data field contains the
processed data. Each data field of each dataset that is part of the study is then called in
the matlab command line and placed in an array using the following command:
EEG_array_1{i} = ALLEEG(i).data
Two separate arrays are made, one for each class of data. For each class, i represents the
index of the subject. For a class with five subjects, i ranges from 1 to 5. These two arrays
are then saved into a .mat file with the following command:
save EEG_arrays EEG_array_1 EEG_array_2
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This saves EEG_array_1 and EEG_array_2 into EEG_arrays.mat, a file which appears in
the current Matlab directory folder.
Results
A t-test is a test of significance designed to show whether two groups of data are
statistically significantly different. The t-test used in FeatureGENgine is a two-tailed test,
meaning that it tests the null hypothesis against the alternative that the means of the two
groups are different. A t-test is a simple way to tell whether the features generated are
able to distinguish the two groups of EEG data. Not only is it important to see whether
these features from the two groups are significantly different, but it is also of great
interest to examine the values of those features. The values have physically meaningful
interpretations. The results of the t-tests performed on the time-segmented features can be
viewed as a binary matrix. Since each t-test returns either a one (for passing) or a zero
(not passing), a matrix of ones and zeros of size Channel x Time Segments, or 64x14, is
produced for each scale. The FeatureGENgine GUI plots these matrices as images
according to each scale or corresponding frequency, such that ones are represented with a
white square and zeros remain black. It also plots an overlay of all the binary matrices
that fall under a specific EEG bandwidth. Since more than one feature can pass the t-test
in the same time-segment (there are multiple scales per band), these overlaid images are
gray-scaled. The highest number of features that passed are represented by the whitest
square, while the lowest number that passed for a time-segment, which would be one, are
represented by a darker shade of gray. These matrices illustrate the advantage of using
time-segmented wavelet features. Some features that pass the t-test are localized in time
segments. Physically, this means that significantly different activity between groups
occurred at specific times. Also, some of the features which passed the t-test have higher
or lower average values between groups in certain time segments, while different
features which passed at a different place in time have opposite average values between
groups. This will become apparent in the first results category, ASD Congruent vs. ASD
Incongruent.
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The binary matrices produced by the features passing the t-test at alpha = 0.05 are
shown for each of the four categories: ASD Congruent vs. ASD Incongruent, ASD
Incongruent vs. Controls Incongruent, Controls Congruent vs. Controls Incongruent, and
ASD Congruent vs. Controls Congruent. It is not only of interest to find distinctions
between ASD and neuro-typical subjects, but also to find differences within the ASD and
Control groups.
A table showing the channels, frequency, and number of features that passed the
t-test is given for each category and for each type of feature. The actual values for
average power and wavelet power are listed, and the tables with the time-segmented
wavelet features show only the features that passed in the Alpha and Beta bands and
whether the average value for a feature that passed the t-test was higher in the first group
or the second group.
ASD Congruent vs. ASD Incongruent
There were no features that passed the t-test for conventional average power
between the ASD congruent and ASD incongruent classes. For time-averaged wavelet
power features, 6 features passed the t-test, shown in Table 5.1. For time-segmented
wavelet power features, 91 features passed the t-test. The channels and time locations of
those which passed in the alpha and beta bands and for all bands are shown in Figures 5.3
and 5.4, respectively. The details of these features are given in Table 5.2. Note that of all
the significant channels in time-averaged wavelet power features, the same channels
arose in the time-segmented wavelet features except for Channel 9 (F1) and 48 (TP8),
although Channels similar to these, F10 and T10, did pass.
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Figure 5.3 Time-segmented wavelet power features that pass the t-
test in Alpha and Beta bands for ASD congruent vs. ASD
incongruent
Figure 5.4 Time-segmented wavelet power features that pass the t-
test in all bands between ASD congruent and ASD incongruent
Table 5.1 - Time-Averaged Wavelet Power Features
Frequency
Band
Channel Class 1 Average Class 2 Average
Delta 1 - F10 125.8844
84.8390
Theta 48- TP8 4.8296
6.3251
Alpha 48-TP8 3.7821
5.0799
Beta 0 0 0
Gamma 9 -F1, 52-T8, 55-T10 0.0202
0.0143
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Table 5.2 Time-segmented wavelet power features for ASD congruent vs. ASD
incongruent
Frequency Total
Number
of
Features
Channels and
Segment
Locations ( ) of
Total Features
Number of
Features
With Larger
Average
Value
Channels
of Higher
Features
Class
Alpha 8.33 6 AF3(3), F3(3),
P1(4), P2(3),
T8(10), FT8(7)
5 AF3, F3,
P2, T8,
FT8
2
10.42 7 AF3(3), P5(4),
P3(4), P7(6),
P1(4), P9(6),
PO3(1)
6 P5, P3,
P7, P1,
P9, PO3
1
11.90 5 P7(6), P1(4),
P9(6), PO3(1),
FC2(9)
4 P7, P1,
P9, PO3
1
Beta 13.89 3 P7(6), PO3(1),
FC2(9)
2 P7, PO3 1
16.67 2 Fz(3), PO3(1) 1 PO3 1
18.52 1 Fz(3) 1 Fz 2
23.81 1 AFz(5) 1 AFz 2
30.33 3 Fz(10) AFz(5),
C2(10)
3 Fz, AFz,
C2
2
As an example of how to interpret the data in Table 5.2, six total features passed
the t-test using time-segmented wavelet features with a frequency of 8.33 Hz. The
channels that contained these features were AF3, F3, P1, P2, T8, and FT8, and the time
segments in which they passed were 3, 3, 4, 3, 10, and 7, respectively. Five of these
features had higher average values in Class 2, the trials corresponding to the incongruent
stimulus.
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(A) Time-segmented wavelet power features of 3.70 Hz (Delta Band)
(B) Time-segmented wavelet power features of the Beta band
Figure 5.5 Time-segmented wavelet features between ASD congruent
and ASD incongruent
An interesting part of the results for this group was made visible only by both the
time resolution and the superior low-frequency resolution provided by the wavelet
features. For many of the frequencies listed in Table 5.1, the number of higher features
would show up time segments located in the middle of the epoch, and then switch in the
later time segments toward the end. For instance, for the 3.70 Hz features, six out of ten
features were higher in Class 1, but all of those features were located in the same time
segment, which was near the end at 1.2 seconds. The other four features, which were
higher in Class 2, were located clustered together over two time segments in the center of
the epoch. This is shown in Figure 5.5 (A) for 3.70 Hz, where all of the features in time
segment number 12, or 1.2 seconds, were higher in Class 1, Congruent, and the three
features in the middle in segments 6, 7, and 10 were higher in Class 2. Similarly, in the
Beta band in Figure 5.5 (B), 3 out of the 10 features which passed were higher in Class 1,
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and all 3 of these segments were located toward the beginning of the epoch, at segments
1 and 6. The rest of the features at segments 3, 5, 9, and 10 were higher in Class 2. These
discrepancies between features across time may provide an explanation as to the
differences between time-averaged wavelet power features and time-segmented ones.
There are some time-segmented features which reflect the time-averaged features
throughout all bands, and some that do not agree with them, depending on the time
segments in which they are located. This shows that time-segmented features may reveal
a much more dynamic picture of brain activity.
Features that passed the t-test at alpha = 0.05 were found using Far and Local
Posterior frequency coherence.
Table 5.3 Far coherence between ASD congruent and ASD incongruent trials
Table 5.4 Local Posterior coherence between ASD congruent and incongruent trials
Similar channels passed the significance test for the same coherence categories as
in the regular coherence features, Far and Local Posterior, but many of them passed in
different bands, shown in Tables 5.5 and 5.6. The O1-F7 channel pair passed for both the
frequency and the wavelet coherence types, but in the Theta band for the frequency
coherence and in the Delta band for wavelet coherence. For both types however, the
average was higher in Class 2, incongruent trials.
Channel Pair Frequency Band Class 1 Average Class 2 Average
O1-F7
Theta 0.180217 0.212842
P4-F4
Delta 0.263669
0.211623
Channel Pair Frequency Band Class 1 Average Class 2 Average
O2-C4
Delta 0.248966 0.18383
Gamma 0.242735
0.216649
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Table 5.5 Far wavelet coherence between ASD congruent and ASD incongruent trials
Table 5.6 Local posterior wavelet coherence between ASD congruent and
ASD incongruent trials
Controls Congruent vs. Controls Incongruent
In the comparison between controls congruent trials and controls incongruent
trials, no features passed the t-test for average power, 2 features passed for time-averaged
wavelet power, and 54 features passed the t-test for the time-segmented wavelet features,
shown in Tables 5.7 and 5.8. There were no features that passed the t-test for either
frequency coherence or wavelet coherence. Figure 5.6 shows the features for the Alpha
and Beta bands, and Figure 5.7 shows all of the features that passed the t-test (in all
bands). Overall, in this category, most of the significant features were higher in the ASD
congruent group. However, the time features reveal some important differences. In the
Delta band, many of the significant features are higher in the controls congruent class in
the early time segments, and are higher for other features in the controls incongruent
class in the later time segments.
Channel Pair Frequency Band Class 1 Average Class 2 Average
P4-F8 23.81(Beta) 3.5551 2.6035
30.30 Hz (Beta) 3.2774 2.4946
O1-F7 1.67 (Delta) 9.2611 11.868
P8-F8 30.30 Hz (Beta) 3.0060 2.4097
Channel Pair Frequency Band Class 1 Average Class 2 Average
P8-C4 Gamma 3.2025 3.8487
O2-C4 Gamma 6.9675 5.3305
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Table 5.7 Time-averaged wavelet power features between controls congruent and
controls incongruent
Table 5.8 Time-segmented wavelet power features between controls congruent
and controls incongruent
Frequency Band Channel Class 1 Average Class 2 Average
Gamma
TP10 0.1354 0.1140
CP1 0.0170 0.0120
Frequency Total
Number
of
Features
Channels
and Segment
Locations( )
of Total
Features
Number
of
Features
With
Larger
Average
Value
Channels of
Higher
Features
Class
Alpha 8.33 4 Fz(4), F1(8),
AF3(8), F3(8)
4 Fz, F1, AF3,
F3
1
10.42 6 F1(5,8),
AF3(5,8),
PO4(7), P6(5)
5 F1,AF3, P6 1
11.90 3 F1(5),
AF3(5),F3(5)
3 F1, AF3, F3 1
Beta 16.67 1 61(9) 1 61 2
18.52 2 T10(9), 61(9) 2 T10, 61 2
23.81 3 F7(6),
CP1(6), 61(9)
3 F7, CP1, 61 2
30.33 4 AF3(1),
F9(6),
CP1(4),
T10(9)
2 F9, T10 2
Texas Tech University, Catherine Chesnutt, May 2012
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Figure 5.6 Time-segmented wavelet power features that pass the t-test in Alpha and Beta
bands between controls congruent and controls incongruent
Time Segments (seconds)
Figure 5.7 Time-segmented wavelet power features that pass the t-test in all bands between
controls congruent and controls incongruent
Time Segments (seconds)
Texas Tech University, Catherine Chesnutt, May 2012
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ASD Congruent vs. Controls Congruent
For the comparison between ASD congruent and controls congruent, one feature
passed for average power, 7 features passed for plain wavelet power, and 278 features
passed for time-segmented wavelet power features, shown in Tables 5.9, 5.10 and 5.11,
respectively. The two channels with the most time-segmented wavelet features that
passed were 23 and 17, or T9 and F9. Some significant features were higher for one class
in during certain segments, and other features are higher for the other class at other
segments. The time-segmented wavelet power features are shown in Figures 5.8 and 5.9
for Alpha and Beta bands and for all bands, respectively.
Table 5.9 Average power features between ASD congruent and controls congruent
Table 5.10 Time-averaged wavelet power features between ASD congruent and controls
congruent
Frequency
Band
Channel Class 1 Average Class 2 Average
Gamma O1 3.5178
1.9923
Frequency
Band
Channel Class 1 Average Class 2 Average
Theta TP8 - 48 6.3251 4.2719
Alpha 61 6.9294 4.5638
Gamma CP1 - 21 0.0130 0.0160
P7 - 30 0.1787 0.0945
F6 - 59 0.0779 0.1031
61 0.1434 0.1048
O1 - 35 0.9332 0.6816
Texas Tech University, Catherine Chesnutt, May 2012
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Figure 5.9 Time-segmented wavelet power features that pass the t-test in all bands
between ASD congruent and controls congruent
Time Segments
(seconds)
Figure 5.8 Time-segmented wavelet power features that pass the t-test in Alpha and
Beta bands between ASD congruent and controls congruent
Time Segments (seconds)
Texas Tech University, Catherine Chesnutt, May 2012
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Table 5.11 Time-segmented wavelet power features between ASD congruent and
controls congruent
Frequency Total
Number
of
Features
Channels and
Segment
Locations( ) of
Total Features
Number of
Features
With
Larger
Average
Value
Channels
of Higher
Features
Class
Alpha 8.33 14 F2(20), FC1(1),
F9(11),F7(4),
C3(6,11),
T9(11), P1(3,4),
Poz(11),
PO4(11), O2(5),
CP2(13), 62(3)
6 FC1, F9,
F7,C3,T9,
CP2
1
10.42 8 F2(7),
CP1(7),T9(4),
P1(4), Pz(3),
Poz(3), O2(5),
P2(4)
5 P1, Pz,
Poz, O2,
P2
2
11.90 6 F2(7), F9(12),
T9(4), P1(4),
Pz(3), Poz(3),
3 P1, Pz,
Poz,
2
Beta 13.89 12 FC1(2), FC3(2),
C1(2), F9(12),
F7(4), T9(4,10),
P1(4),
T10(5,10),
61(5,10)
8 FC1, FC3,
C1, F9,
F7,T9,
T10(10),
61(10)
1
16.67 17 F10(10), Fz(7),
FC1(2), F1(7),
AF3(7), C1(2),
F7(9),CP1(7),
T9(4,9,10),
T10(8,10),
61(5,8,10),
64(10)
17 F10,
Fz,FC1,
F1, AF3,
C1, F7,
CP1,
T9,T10,
61, 64
1
Texas Tech University, Catherine Chesnutt, May 2012
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ASD Incongruent vs. Controls Incongruent
There were 7 features that passed the t-test for average power,19 for time-
averaged wavelet power, and 324 for time-segmented wavelet power features. The values
of these features are given in Tables 5.12, 5.13, and 5.14. The locations of the features in
the Alpha and Beta bands are shown in Figure 5.10 and in the head diagrams in Figure
5.11.
Table 5.12 Average power features between ASD incongruent and controls incongruent
18.52 17 FC1(2), F1(9),
FP1(7), AF3(9),
F9(9), F7(6,9),
C3(8),
CP1(7,8), T9(4,
10), T10(8, 10),
61(8,10), 64(10)
14 FC1, F1,
FP1, AF3,
F9, F7,
C3, CP1,
T9, T10,
1
23.81 15 Fz(8), Afz(8),
F1(8),FP1(6,8),
F5(6), F9(6),
F7(6), FT7(6),
C3(5),
CP1(6,7,8),
T9(6,10)
15 Fz, Afz,
F1, FP1,
F5, F9,
F7,FT7,
C3, CP1,
T9
1
30.33 18 Fz(8), Afz(8),
F1(8), FP1(6),
F9(6), FT7(6),
C3(5), CP1(7),
T9(3,6), P7(12),
Pz(2), CP2(4,6),
P4(8), CP6(6),
C2(12),
FC2(12),
17 Fz, Afz,
F1, FP1,
F9, FT7,
C3, CP1,
T9, P7,
CP2, P4,
CP6, C2,
FC2
1
Frequency
Band
Channel Class 1
Average
Class 2 Average
Delta F9 - 17 11.5974 8.9519
Alpha F9 - 17 6.3426 4.9994
Theta T9 - 23 3.6662 2.5049
Beta T9 - 23 2.9457 1.9083
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Table 5.13 Time-averaged wavelet power features between ASD incongruent and
controls incongruent
Table 5.14 Time-segmented wavelet power features between ASD incongruent and
controls incongruent in Alpha and Beta bands
Frequency
Band
Channel Class 1
Average
Class 2 Average
Alpha T9 - 23 4.9183
3.0949
T9 - 23 6.6380
4.0178
F9 - 17 7.4275
5.1098
Beta T9 - 23 1.1681 0.7002
T9 - 23 2.0770 1.1193
Cp6 - 46 1.6013 1.1448
Frequency Total
Number
of
Features
Channels
and
Segment
Locations ( )
of Total
Features
Number of
Features
With
Larger
Average
Value
Channels
of Higher
Features
Class
Alpha 8.33 19 F10 (3),
AF4(4),
FP2(4),
AF3(8),
F3(1), F9(7),
F9(11),
F7(9),
T9(2,11),
P7(1),
Poz(3),
P2(3),
CP2(11),
TP10(13),
T10(11),
16 AF4, FP2,
AF3, F3,
F9, F7,
T9,P7,
CP2,
TP10,
T10, F4,
64
1
Texas Tech University, Catherine Chesnutt, May 2012
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F4(4), 64(7,
11)
10.42 19 F2(9),
FP2(9),
Fz(9),
AFz(9),
F1(8),
FP1(5,8),
AF3(5,8),
F3(8), C1(9),
F9(5,7),
PO3(1),
Pz(3),
Poz(3),
PO4(3),
CP6(5),
F4(9), 63(5)
16 F2, FP2,
Fz, F1,
FP1, AF3,
F3, C1,
F9, PO3,
CP6, F4,
63
1
11.90 12 FC1(8),
Afz(9),
F1(5,8),
FP1(8),
AF3(5,8),
F9(5),
C3(7,14),
PO3(1),
TP10(13),
12 FC1, AFz,
F1, FP1,
AF3, F9,
C3, PO3,
TP10
1
Beta 13.89 10 FP2(2),
FC1(8),
FP1(8),
AF3(5),
F9(1,5,12),
F7(5),
C3(14),
CP2(2),
10
FP2, FC1,
FP1, AF3,
F9, F7,
C3, CP2
1
16.67 11 Fz(13),
Afz(13),
FP1(13),
F9(1, 12),
C3(14),
T9(7),
CP2(1,2),
T10(14),
63(5)
11 Fz, Afz,
FP1, F9,
C3, T9,
CP2, T10,
63
1
18.52 14 Afz(13), 14 Afz, F1, 1
Table 5.14 Continued
Texas Tech University, Catherine Chesnutt, May 2012
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Conclusions
Results
The study was conducted with the hypothesis that there would be a large number
of differences between the autistic and neuro-typical (control) groups when examining
brain responses to the incongruent fish, reflecting the selective attention abnormality
present in autism and that there would be a more differences within the autistic group
than within controls between the two types of stimuli. It was also hypothesized that these
differences would occur in an area associated with selective attention: the prefrontal
cortex and anterior cingulate. As postulated, the largest number of features that passed a
F1(13),
FP1(13),
AF3(13),
F9(1,2),
C3(14),
T9(7),
CP2(1,2,3),
C2(3),
FC2(12),
T10(12),
63(5)
FP1, AF3,
F9, C3,
T9, CP2,
C2, FC2,
T10,63
Figure 5.10 Time-segmented wavelet power features that pass the t-test in all bands
between ASD incongruent and controls incongruent
Time Segments (seconds)
Table 5.14 Continued
Texas Tech University, Catherine Chesnutt, May 2012
66
t-test were found between the autistic (ASD) group and the neuro-typical (controls) for
the incongruent stimulus for all types of features. While the algorithm found many of
these significant features in the left and right prefrontal areas, as expected, it also found
other significant features in the parietal and occipital lobes. Furthermore, nearly all of the
average values of the power features in this comparison were higher for the autistic
group, while the coherence features were higher for the controls group. One study
employed the ANT to investigate attention networks in subjects with ASD and found that
a decrease in the ability to modulate different levels of alertness was related to socio-
communicative deficits, associating the general attention function to ASD
symtomatology [48]. The higher average power values in the autistic group might reflect
this lack of ability to move between levels of alertness or attention, and confirms these
differences in attention as an ASD symptom. The high number of features found to be
significantly different according to a t-test between ASD and controls, the presence of
more significant features within the ASD group than within controls, and the locations of
these differences in the prefrontal cortex and anterior cingulate all support the original
hypothesis.
Comparisons Between Groups
A summary of the results of all four comparisons is given in Table 5.11. The ASD
incongruent and controls incongruent group had the most features that passed a t-test. The
comparisons between the ASD and controls shows the occipital lobe as a significant area
of difference, while this area was not significant in comparisons made within the ASD
and control groups. Studies have shown that the occipital lobe, the visual processing
center of the brain, processes visual stimuli differently in individuals with autism. One
study found that autistic children are hypersensitive to visual stimulation, a finding that is
consistent with the higher wavelet power values observed in the occipital lobe [14]. The
time-segmented wavelet power features that passed a t-test between the ASD and control
groups and within the two groups are plotted on head diagrams using a 10-10 montage in
Figure 5.15. The red, blue, and purple electrodes represent the features that passed the t-
test in the Alpha, Beta, and both Alpha and Beta bands, respectively.
Texas Tech University, Catherine Chesnutt, May 2012
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Table 5.15 Summary of results
Average
Power
Wavelet
Power
Time-
Segmented
Wavelet
Power
Area of Significance
(Alpha and Beta
bands)
ASD Congruent vs.
ASD Incongruent
0 6 91 Prefrontal left,
parietal left and right
Controls Congruent vs.
Controls Incongruent
0 2 54 Prefrontal left,
parietal right
ASD Congruent vs.
Controls Congruent
1 7 278 Prefrontal left and
right, parietal,
occipital
ASD Incongruent vs.
Controls Incongruent
7 19 324 Prefrontal left and
right, parietal,
occipital
Texas Tech University, Catherine Chesnutt, May 2012
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Figure 5.11 Head diagrams of time-segmented wavelet
power features that passed a t-test
Texas Tech University, Catherine Chesnutt, May 2012
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CHAPTER VI
CODE CONCLUSIONS AND SUGGESTIONS
FeatureGENgine was written as a Matlab tool to explore the possibilities and
considerations of generated wavelet-based features of EEG data. The program has proved
its usefulness in generating time-segmented wavelet features that were found to reveal
significant differences between groups based on a t-test. Its further development has
several possible directions.
Wavelet Choice
As mentioned in Chapter IV, the choice of the mother wavelet can either decrease
or increase the amount of harmonic interference and certainty in frequency
representation. All of the results in Chapter V were calculated using the Db5 wavelet.
The Coif5 wavelet, examined in Chapter IV, produced more significant features than the
Db5 wavelet, shown in Table 5.10 for the comparison between ASD congruent and ASD
incongruent trials. Some of these features were located in the same channel, and those
that were not were located in channels in close proximity, but most are from different
frequency bands. These features are contrasted in Table 5.14. The Coif5 computations,
which took an average time of 17 seconds, took longer than for the Db5, which took an
average of 10 seconds.
Table 6.1 Time-segmented wavelet power features which passed the t-test between ASD
congruent and ASD incongruent using Coif5 and Db5 mother wavelets
Coif5 Wavelet
Db5 Wavelet
Channel Channel
9 - F1 2 (Gamma) 9 - F1 1 (Gamma)
55 - T10 3 (Gamma) 48 - TP8 11 (Alpha)
47 - TP10 5 (Beta) 48 - TP8 12 (Theta)
55 - T10 7 (Beta) 52 - T8 19 (Delta)
55 - T10 8(Beta) 55 - T10 19 (Delta)
36 - Poz 9 (Alpha) 1 - F10 20 (Delta)
55 - T10 9 (Alpha)
30 - P7 10 (Alpha)
55 - T10 10 (Alpha)
53 - FC4 18 (Delta)
Texas Tech University, Catherine Chesnutt, May 2012
70
Discrete Wavelet Transform
The increase in the number of significant features and the discrepancy in the
frequency detection and channels of the features suggests that the choice of the mother
wavelet should be further examined. A mother wavelet function might be written in order
to minimize the amount of harmonic interference and maximize frequency detection. One
study that might prove useful in this endeavor provides an algorithm for the design of a
wavelet filter that is optimized under certain minimum energy constraints [49]. However,
the wavelet filter in that study is designed for the discrete wavelet transform (DWT)
domain, which has not been explored in this thesis. The CWT requires a large amount of
computational time to generate time-segmented wavelet features. This invites the
possibility of generating these features using the DWT instead, because it is a
computationally faster option.
The DWT, however, has an inherent shift variant problem that makes it unsuitable
for many signal analysis applications, especially that of transient signals such as EEG.
The shift variance property essentially means that the DWT of a signal is considerably
different if that signal is shifted in time by even one sample. The nature of time-
segmented wavelet features makes this an important issue. If two electrode channels
produce two similar signals that differ only by a few milliseconds, the features generated
from a DWT of these two signals might be found to be statistically significantly different.
It is then more difficult to say with certainty which features are actually significant. Many
studies have proposed algorithms to make the DWT shift-invariant [50] [51] [52]. One of
these algorithms might be employed to generated time-segmented wavelet features of a
DWT, however, the computational time required by the algorithm might be comparable
to that of the CWT.
Multiple Comparisons
Another consideration of generated time-segmented wavelet features is the
number of comparisons made due to the large number of features generated. In statistics,
the problem of multiple comparisons arises when there are too many features being
Texas Tech University, Catherine Chesnutt, May 2012
71
compared between two groups. The more features compared, the more likely it is for
some of them to appear different. To compensate for this increase in error, the Bonferoni
correction might used to set the significance level, or alpha value. The FeautureGENgine
program allows the user to set the alpha value for the t-test. When the alpha value is set to
0.005, the comparison between ASD incongruent and controls incongruent described in
Chapter V produced 13 time-segmented wavelet power features that passed the t-test, in
contrast to the 324 produced at alpha = 0.05. For this alpha value, the comparison
between ASD congruent and controls congruent produced 8 features that passed, two
features passed within the ASD congruent and incongruent trials, and one feature passed
for the comparison between trials in the controls group. No features generated by time-
averaged wavelet power or conventional average power passed a t-test at alpha = 0.005.
Vectorization
Code vectorization improves the efficiency and required computational time of
programs. The FeatureGENgine code uses mainly for-loops to generate features from the
several matrices that hold the EEG data. Certain feature generation methods might be
modified to process the matrices instead of separating them into one vector signals
corresponding to subject, channel and epoch.
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