EEG ClassificationEEG ClassificationUsing Maximum Noise Fractions Using Maximum Noise Fractions

and spectral classificationand spectral classification

Steve Grikschart and Hugo Steve Grikschart and Hugo ShiShi

EECS 559 Fall 2005EECS 559 Fall 2005

RoadmapRoadmap

Motivations and backgroundMotivations and background Available DATAAvailable DATA MNFMNF Noise covariance estimationNoise covariance estimation Quadratic Discriminant AnalysisQuadratic Discriminant Analysis Spectral Discriminant AnalysisSpectral Discriminant Analysis ResultsResults

Motivations and BackgroundMotivations and Background

New capabilities for New capabilities for differently abled differently abled persons (i.e. ALS)persons (i.e. ALS)

Psychomouse!Psychomouse! Divide and conquer Divide and conquer

approach increases approach increases capabilitiescapabilities

EEG DataEEG Data**

7 subjects, 5 trials of 7 subjects, 5 trials of 4 tasks on 2 days 4 tasks on 2 days

10 seconds @ 250 10 seconds @ 250 Hz, 6 channels Hz, 6 channels

6 electrodes on 6 electrodes on electrically linked electrically linked mastoidsmastoids

Denote data as Denote data as 6x2500 matrix, 6x2500 matrix, XX = ( = (xx11 xx22 ... ... xx66))

*Source: www.cs.colostate.edu/eeg/?Summary

Data TransformationData Transformation

Seek a data transformation for easier Seek a data transformation for easier classificationclassification

Optimally using all 6 channel's informationOptimally using all 6 channel's information Also exploiting time correlationAlso exploiting time correlation Dimension reduction not neededDimension reduction not needed

Maximum Noise Transform (MNF)Maximum Noise Transform (MNF)

Assume signal in additive noise model: Assume signal in additive noise model:

X = S + NX = S + N

Seek a linear combination of data, Seek a linear combination of data, XXαα,, that that maximizes signal to noise ratio maximizes signal to noise ratio

Express as an optimization problem:Express as an optimization problem:

2

, 1 , 12

max maxT T

T T

T T

S S S

N N N

MNF (continued)MNF (continued)

When signal and noise components are When signal and noise components are orthogonal, orthogonal, SSTTN=NN=NTTS=0S=0, equivalently we , equivalently we have:have:

Generalized Eigenvalue ProblemGeneralized Eigenvalue Problem

NN

NNNSSNSS

NN

NSNS

NN

XX

TT

TTTTT

TT

TTT

TT

TT

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TT

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MNF (continued)MNF (continued)

Component with maximum SNR given by Component with maximum SNR given by top eigenvectortop eigenvector

Restrict Restrict αα''ss by enforcing orthogonality of by enforcing orthogonality of each solutioneach solution

SNR of component SNR of component XXααjj given by given by λλjj Requires estimation of noise covariance Requires estimation of noise covariance

NNTTNN Introduce time correlation by augmenting Introduce time correlation by augmenting

XX matrix matrix

Noise Covariance EstimationNoise Covariance Estimation

Two basic methods:Two basic methods: Differencing: Data – Time-shifted DataDifferencing: Data – Time-shifted Data AR fitting: Fit AR to each channel, take AR fitting: Fit AR to each channel, take

residualsresiduals

Estimation by DifferencingEstimation by Differencing

dXdX = = XX - - XXδδ, where , where XXδδ is a time-shifted is a time-shifted

version of version of XX RRNN = = dXdXTTdXdX = ( = (S+N-SS+N-Sδδ-N-Nδδ))TT((S+N-SS+N-Sδδ-N-Nδδ))

Assuming Assuming SSTTN = 0, N = 0, E[E[NNNNδδTT]] = 0, S-S = 0, S-Sδδ ≈ 0 ≈ 0

thenthen

RRNN = (N-N = (N-Nδδ))TT(N-N(N-Nδδ) ≈ 2N) ≈ 2NTTN = 2N = 2ΣΣNN

Estimation by AR fittingEstimation by AR fitting

Scalar series vs. vector seriesScalar series vs. vector series XXii((tt)) = = φφ1 1 XXii((t-1t-1)) + ... + + ... + φφq q XXii((t-qt-q)) + + εεii((tt))

Noise covariance estimated using Noise covariance estimated using residualsresiduals

Non-linear least squares fit by Gauss-Non-linear least squares fit by Gauss-Newton algorithmNewton algorithm

Order estimated by AIC Order estimated by AIC (Typical order around 6(Typical order around 6**))

QDAQDA

But the condition number of the covariance matrix But the condition number of the covariance matrix is…..is…..

2.8195e+192.8195e+19

Frequency Domain ClassificationFrequency Domain Classification

Mean signal estimated by averaging Mean signal estimated by averaging across all training data.across all training data.

Spectral Analysis performed for all training Spectral Analysis performed for all training data using Parzen windows, then data using Parzen windows, then averaged across all training samples.averaged across all training samples.

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Mean estimationMean estimation

Same day resultsSame day resultsMisclassificationsMisclassifications Correct ClassificationsCorrect Classifications

2 task 2 task classificationclassification

11 99

4 task 4 task

classificationclassification

99 1010

Next day resultsNext day resultsMisclassificationsMisclassifications Correct ClassificationsCorrect Classifications

2 task 2 task classificationclassification

1111 1111

4 task 4 task

classificationclassification

3131 1313

Cross person resultsCross person resultsMisclassificationsMisclassifications Correct ClassificationsCorrect Classifications

2 task 2 task classificationclassification

99 1919

4 task 4 task

classificationclassification

3535 2323

ConclusionsConclusions

This EEG method has promising results This EEG method has promising results but still needs work for acceptable but still needs work for acceptable performanceperformance

Multi-variate analysis may helpMulti-variate analysis may help Same day results are good, but not as Same day results are good, but not as

useful for practical applicationsuseful for practical applications