combined classification and channel/basis selection with l1-l2 regularization with application to...
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![Page 1: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/1.jpg)
Combined classification and channel/basis selection withL1-L2 regularization with application to P300 speller
system
Ryota Tomioka & Stefan HaufeTokyo Tech / TU Berlin / Fraunhofer FIRST
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P300 speller system
EvokedResponse
Farwell & Donchin 1988
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P300 speller systemA B C D E FG H I J K LM N O P Q RS T U V W XY Z 1 2 3 45 6 7 8 9 _
A B C D E FG H I J K LM N O P Q RS T U V W XY Z 1 2 3 45 6 7 8 9 _
ER detected!
ER detected!
The character must be “P”
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Common approach
Feature extraction
P300 detection
Decoding
e.g., ICA or channel selection
e.g., Binary SVM classifier
e.g., Compare the detector outputs
EEG signal
Feature vector
Detector outpus(6 cols& 6rows)
Decoded character(36 class)
?
?
Lots of intemediate goals!!
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Our approach
e.g., ICA or channel selection
e.g., Binary SVM classifier
Compare the detector outputs
Decoding
EEG signal
Decoded character(36 class)
P300 detection
Feature extraction
Define a “detector” fW(X)
![Page 6: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/6.jpg)
Our approach
minimize L(W) + lW(W)
Data-fit Regularization
Regularized empirical risk minimization:
Decoding
EEG signal
Decoded character(36 class)
P300 detection
Feature extraction
Detect P300
Extract structure
![Page 7: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/7.jpg)
Learning the decoding model
• Suppose that we have a detector fw(X) that detects the P300 response in signal X.
f1 f2 f3 f4 f5 f6
f7
f8
f9
f10
f11
f12
This is nothing but learning 2 x 6-class classifier
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How we do this
12 2 8 1 3 4 11 9 5 6 10 7 …
Multinomial likelihood f. Multinomial likelihood f.
-log PW(col | Xi) -log PW(row | Xi)+Si=1
nL(w) =
…
( )
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Detector
fW(X) =<W, X>
X#samples
#cha
nnel
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W#samples
#cha
nnel
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L1-L2 regularization
2 4 6 8 10 12 14 16
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W#samples
#cha
nnel
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2 4 6 8 10 12 14 16
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2 4 6 8 10 12 14 16
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(1) Channel selection (linear sum of row norms)
(2) Time sample selection(linear sum of col norms)
(3) Component selection(linear sum of component norms)
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The method
minimize L(W) + lW(W)
2 x 6-class multinomial loss L1-L2 regularization
Nonlinear convex optimization with second order cone constraint
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Results - BCI competition III dataset II [Albany](1) Channel selection regularizer
l=5.46Subject A:99% (97%)72% (72%)
Subject B:93% (96%)80% (75%)
(Rakotomamonjy & Gigue)
15 repetitions5 repetitions
![Page 13: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/13.jpg)
Results- BCI competition III dataset II [Albany](2) Time sample selection regularizer
l=5.46Subject A:98% (97%) 70% (72%)
Subject B:94% (96%)81% (75%)
(Rakotomamonjy & Gigue)
15 repetitions5 repetitions
![Page 14: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/14.jpg)
Results- BCI competition III dataset II [Albany](3) Component selection regularizer
15 repetitions5 repetitions
l=100Subject A:98% (97%) 70% (72%)
Subject B:94% (96%)82% (75%)
(Rakotomamonjy & Gigue)
![Page 15: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/15.jpg)
Filters(1) Channel selection regularizer
(2) Time sample selection regularizer
(3) Component selection regularizer
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Summary
• Unified feature extraction and classifier learning– L1-L2 regularization
• Use decoding model to learn the classifier– 2x 6-class multinomial model
• Solve the problem in a convex regularized empirical risk minimization problem– Nonlinear second-order cone problem(efficient subgradient based optimization routine will
be made available soon!)
![Page 17: Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo](https://reader030.vdocuments.site/reader030/viewer/2022032701/56649c785503460f9492db11/html5/thumbnails/17.jpg)