eeg classification using maximum noise fractions and spectral classification
DESCRIPTION
EEG Classification Using Maximum Noise Fractions and spectral classification. Steve Grikschart and Hugo Shi EECS 559 Fall 2005. Roadmap. Motivations and background Available DATA MNF Noise covariance estimation Quadratic Discriminant Analysis Spectral Discriminant Analysis Results. - PowerPoint PPT PresentationTRANSCRIPT
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
T
TT
)(max
))((maxmax
1,
1,1,
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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k kg
kgkQ F
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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