Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis

by Nguyen Duc Thang

5/2009

Outline

Part one Introduction Principal Component Analysis (PCA) Signal Fraction Analysis (SFA) EEG signal representation Short time PCA

Part two Classifier Experimental setups, results, and analysis

Introduction

Feature extraction

Classification

PCA, SFA,

Short time PCA

LDA, SVM

Outline

Part one Introduction Principal Component Analysis (PCA) Signal Fraction Analysis (SFA) EEG signal representation Short time PCA

Part two Classifier Experimental setups, results, and analysis

Projection

xwx T1

w1

x

x

Projectionw1

w2

x

)13()32()12(

] [ 21

Wxx

wwW T

DdnDnd

WXX

wwwW Td

...

]... [ 21

d basic vectors

reduce dimension

Principal Component Analysis (PCA) Motivation: Reduce dimension + minimum

information loss. W = ?

w

w

w

O

Principal Component Analysis

iih2min

ix

whi

hi

constant

i

Tiix

xT

ii

T

i

i

xxC

wCwxwx max)(maxmax 22O

Minimize projection errors

Maximize variations

Principal Component Analysis

- wi is the eigenvector of the covariance matrix Cx

- Among D eigenvectors of Cx, choose d<D eigenvectors

- W=[w1,w2,…,wd]T is projection matrix, reduce dimension D → d

w1

w2

Outline

Part one Introduction Principal Component Analysis (PCA) Signal Fraction Analysis (SFA) EEG signal representation Short time PCA

Part two Classifier Experimental setups, results, and analysis

Signal Fraction Analysis (SFA)

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s

vAsx

Signal Fraction Analysis

Assumption: The source signals are uncorrelated

Algorithm

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)](),...,(),([)( 21

tstsE

tstststs

ji

Tn

matrix mixing estimatedˆ

sources original estimatedˆ

SVD) ed(Generaliz ),(~ˆ,ˆ

)1()()(

A

s

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txtxty

Results

Comparison between SFA and ICA

Correlation between estimated sources and ground truths

- SFA: suitable for small sample size, fast computation

- ICA: suitable for large sample size

Extract basic vectors by SFA

SFA of bases are ],...,,[

sources) ted(uncorrela ˆ

ˆ

ˆˆ

21

1

TDwwwW

sWx

AW

sAx

WSFAx

WPCAx

Outline

Part one Introduction Principal Component Analysis (PCA) Signal Fraction Analysis (SFA) EEG signal representation Short time PCA

Part two Classifier Experimental setups, results, and analysis

Feature extraction

Feature extraction

Classification

EEG signal representation (Feature extraction) Raw feature

Time-embedded feature

dimensions

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...)(

)(

)( 2

1

r

tx

tx

tx

tx

r

r EEG channels

r EEG channels

l+1dimensions 1

)(

...

)(...

)(

...

)(

)(1

1

)(lr

ltx

tx

ltx

tx

tx

r

r

More temporal information

Extract PCA features

Training data (embedded space)

D=r(l+1)

N samples

PC

A d basic vectors form projection matrix WPCA

D

WPCA X =

d

PCA features

(d X D)Time-embedded features

Extract SFA features

Training data (embedded space)

D=r(l+1)

N samples

SF

A d basic vectors form projection matrix WSFA

D

WSFA X =

d

SFA features

(d X D)Time-embedded features

Outline

Part one Introduction Principal Component Analysis (PCA) Signal Fraction Analysis (SFA) EEG signal representation Short time PCA

Part two Classifier Experimental setups, results, and analysis

The shortcomings of conventional PCA

projection line

Not good for large number of samples

Short time PCA approach

Apply PCA on short durations

Extract short time PCA features

D

Time-embedded features

h

D

h

window

PC

A n basic vectors

D

n

stack

Short time PCA features

D X n

Next

Part one Introduction Principal Component Analysis (PCA) Signal Fraction Analysis (SFA) EEG signal representation Short time PCA

Part two Classifier Experimental setups, results, and analysis