chapter 15: classification of time-embedded eeg using short-time principal component analysis
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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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/1.jpg)
Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis
by Nguyen Duc Thang
5/2009
![Page 2: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/2.jpg)
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
![Page 3: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/3.jpg)
Introduction
Feature extraction
Classification
PCA, SFA,
Short time PCA
LDA, SVM
![Page 4: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/4.jpg)
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
![Page 5: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/5.jpg)
Projection
xwx T1
w1
x
x
![Page 6: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/6.jpg)
Projectionw1
w2
x
)13()32()12(
] [ 21
Wxx
wwW T
DdnDnd
WXX
wwwW Td
...
]... [ 21
d basic vectors
reduce dimension
![Page 7: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/7.jpg)
Principal Component Analysis (PCA) Motivation: Reduce dimension + minimum
information loss. W = ?
w
w
w
O
![Page 8: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/8.jpg)
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
![Page 9: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/9.jpg)
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
![Page 10: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/10.jpg)
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
![Page 11: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/11.jpg)
Signal Fraction Analysis (SFA)
?
s
vAsx
![Page 12: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/12.jpg)
Signal Fraction Analysis
Assumption: The source signals are uncorrelated
Algorithm
ji 0)}()({
)](),...,(),([)( 21
tstsE
tstststs
ji
Tn
matrix mixing estimatedˆ
sources original estimatedˆ
SVD) ed(Generaliz ),(~ˆ,ˆ
)1()()(
A
s
yxgsvdAs
txtxty
![Page 13: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/13.jpg)
Results
![Page 14: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/14.jpg)
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
![Page 15: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/15.jpg)
Extract basic vectors by SFA
SFA of bases are ],...,,[
sources) ted(uncorrela ˆ
ˆ
ˆˆ
21
1
TDwwwW
sWx
AW
sAx
WSFAx
WPCAx
![Page 16: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/16.jpg)
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
![Page 17: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/17.jpg)
Feature extraction
Feature extraction
Classification
![Page 18: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/18.jpg)
EEG signal representation (Feature extraction) Raw feature
Time-embedded feature
dimensions
)(
...)(
)(
)( 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
![Page 19: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/19.jpg)
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
![Page 20: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/20.jpg)
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
![Page 21: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/21.jpg)
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
![Page 22: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/22.jpg)
The shortcomings of conventional PCA
projection line
Not good for large number of samples
![Page 23: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/23.jpg)
Short time PCA approach
Apply PCA on short durations
![Page 24: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/24.jpg)
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
![Page 25: Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis](https://reader036.vdocuments.us/reader036/viewer/2022062314/56813a0b550346895da1db46/html5/thumbnails/25.jpg)
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