Post on 04-Jan-2016
description
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
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w1
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x
Projectionw1
w2
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DdnDnd
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d basic vectors
reduce dimension
Principal Component Analysis (PCA) Motivation: Reduce dimension + minimum
information loss. W = ?
w
w
w
O
Principal Component Analysis
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ix
whi
hi
constant
i
Tiix
xT
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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
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matrix mixing estimatedˆ
sources original estimatedˆ
SVD) ed(Generaliz ),(~ˆ,ˆ
)1()()(
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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
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)(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