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Classifying EventRelated Desynchronization in EEG, ECoG, and MEG Signals

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Title: Classifying EventRelated Desynchronization in EEG, ECoG, and MEG Signals


1
Classifying Event-Related Desynchronization in
EEG, ECoG, and MEG Signals
  • Kim Sang-Hyuk

2
Contents
  • Introduction
  • Experimental setup and procedure
  • Preanalysis
  • Data processing
  • Generalization error estimation

3
Introduction
  • Several different technologies exist for
    measuring brain activity
  • They have their own advantages and limitations
  • Spatial and temporal resolution
  • Cost, portability and risk to the user
  • Comparative studies are required in order to
    guide
  • Motor-imagery BCI experiments based on
    Electroencephalography (EEG), electrocorticography
    (ECoG) and magnetoencephalography (MEG)
  • A simple binary synchronous (trial-based)
    paradigm
  • Present quantitative results focusing on
  • The effect of the number of trial
  • The effect of spatial filtering

4
Introduction
  • EEG
  • Electrical signals are measured by passive
    electrodes
  • Very high temporal resolution
  • Low cost, risk, and portability
  • Limitation of spatial resolution
  • ECoG
  • Electrical signals obtained from an array of
    electrodes beneath the skull
  • High SNR
  • A better response at higher frequencies
  • Invasive
  • MEG
  • Measuring the tiny magnetic field fluctuations
    induced by the electrical activity of cerebral
    neurons
  • Expensive and nonportable

5
Experimental Setup and Procedure
  • EEG
  • 8 untrained right handed male subjects
  • 39 silver chloride electrodes
  • Sampling frequency 256Hz
  • The subjects were seat in an armchair at 1-m
    distance in front of a computer screen

Positions of electrodes
6
Experimental Setup and Procedure
  • Each trial started with a blank screen
  • A small fixation cross displayed in the center of
    the screen from second 2 to 9
  • At 2s, a short warning tone (beep)
  • At 3s, the fixation cross was overlaid with an
    arrow at the center of the monitor for 1.5s
  • The direction of arrow point either to the left
    or to the right
  • In order to avoid event related signals in later
    processing stages, only data from seconds 4 to 9
    of each trial was considered

7
Preanalysis
  • In order to identify and exclude subjects that
    did not show significant µ-activity at all
  • Restricted to only the 17 EEG channels that were
    located over or close to the motor cortex
  • Calculate of the µ-band using the Welch method
    (short time Fourier transform) for each subject
  • This feature extraction resulted in one parameter
    per trial and channel
  • The eight data sets consisting of the
    Welch-features were classified with linear
    support vector machines including individual
    model selection for each subject
  • Generalization errors were estimated by 10-fold
    cross validation (CV)
  • For three subjects the preanalysis showed very
    poor error rates close to chance level, their
    data sets were excluded from further analysis

8
Preanalysis
  • Short Time Fourier Transform (STFT)
  • A Fourier-related transformation used to examine
    the frequency and phase content of local sections
    of a signal over time
  • Discrete-time STFT
  • Wn is the window function
  • Window is sliding along time axis

Examples of window overlap
9
Preanalysis
  • Short Time Fourier Transform (STFT)

Examples of STFT
10
Preanalysis
  • Short Time Fourier Transform (STFT)
  • 5 segment for a trial, overlapping 50
  • Averaging the spectra of 5
  • A vector of log amplitudes at different
    frequencies for each sensor

Averaging
A vector
11
Data Preprocessing
  • Autoregressive (AR) Model
  • AR(p) model is defined as
  • Where are the parameters of the model
  • P is order
  • The output is modeled as a linear combination of
    P past values of the output
  • For the remaining five subjects, the recorded 5s
    windows of each trial resulted in a time series
    of 1280 sample points per channel
  • AR model of order 3 is fitted to the time series
    of all 39 channels using forward backward linear
    prediction
  • The three resulting coefficients per channel and
    trial formed the new representation of the data
  • The extraction of the features did not explicitly
    incorporate prior knowlede
  • They are not directly linked to the µ-rhythm

12
Support Vector Machine
  • Linear Support Vector Machine
  • Choose a decision boundary between classes such
    that margin is maximized
  • Margin the distance in feature space between the
    boundary and the nearest data points (support
    vectors)

Linearly separable case
13
Support Vector Machine
  • Linear Support Vector Machine
  • The function of hyperplane
  • weight vector normal to hyperplane
  • threshold
  • The distance of a point from a hyperplane

14
Support Vector Machine
  • Linear Support Vector Machine
  • Scale so that the value of , at the
    support vectors, is equal to 1 for S1 and equal
    to -1 for S2
  • Margin
  • Compute the parameters , of the hyperplane
    so that to
  • Minimize
  • Subject to to
    where corresponding class
    indicator (1 for , -1 for )

15
Support Vector Machine
  • Linear Support Vector Machine
  • The Karush-Kuhn-Tucker (KKT) conditions
  • is the vector of the Lagrange multipliers
  • is the Lagrangian function
    defined as
  • Finally results are

16
Support Vector Machine
  • Soft Margin Support Vector Machine
  • In the case where the classes are not separable,
    soft margin support vector machine is available
  • The training feature vectors categorized into
    three cases
  • Vectors that fall outside the band and are
    correctly classified
  • Vectors falling inside the band and which are
    correctly classified
  • Vectors that are misclassified

17
Support Vector Machine
  • Soft Margin Support Vector Machine
  • All three cases can be treated under a single
    type of constraints
  • The first category of data
  • The second
  • The third
  • The goal is to make the margin as large as
    possible but at the same time to keep the number
    of points with as small as possible
  • Cost function
  • Where is the vector of the parameters

18
Support Vector Machine
  • Soft Margin Support Vector Machine
  • The parameter C is a positive constant that
    controls the relative influence of the two
    competing terms
  • Optimization of the cost function is difficult
    due to a discontinuous function
  • A closely related cost function
  • Minimize
  • Subject to
  • Depending on C, the optimal margin will widen and
    more points will become support vectors
  • Finding a good value for C is part of the model
    selection procedure

19
Generalization Error Estimation
  • K-Fold Cross Validation
  • A statistical method for validating a predictive
    model
  • Whole data is separated into k subsets (folds) of
    equal size
  • Each fold is also divided into k subsets and k
    subsets are categorized into train set and test
    set
  • K-1 subsets are used for training of classifier
  • 1 set is used for validation
  • Model training and evaluation is repeated k times
    with each of the k subsets

An example of 5-fold cross-validation
20
Contents of Next Lecture
  • Feature Selection Method
  • Fisher criterion
  • Zero-norm optimization
  • Recursive feature elimination (RFE)
  • Results in EEG
  • Procedure and results in ECoG
  • Procedure and results in MEG
  • Overview of results in EEG, ECoG and MEG
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