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Combined classification and channel/basis selection with L1-L2 regularization with application to P300 speller system Ryota Tomioka & Stefan Haufe Tokyo Tech / TU Berlin / Fraunhofer FIRST

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P300 speller system Evoked Response Farwell & Donchin 1988

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P300 speller system 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” f W (X)

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Our approach Data-fitRegularization Regularized empirical risk minimization: Decoding EEG signal Decoded character (36 class) P300 detection Feature extraction Detect P300 Extract structure

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Learning the decoding model Suppose that we have a detector f w (X) that detects the P300 response in signal X. f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 f8f8 f9f9 f10f10 f 11 f 12 This is nothing but learning 2 x 6-class classifier

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How we do this 122813411956107 … Multinomial likelihood f. …

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Detector f W (X) = X X #samples #channels W W #samples #channels

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L1-L2 regularization W W #samples #channels (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 2 x 6-class multinomial lossL1-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 =5.46 Subject A: 99% (97%) 72% (72%) Subject B: 93% (96%) 80% (75%) (Rakotomamonjy & Gigue) 15 repetitions 5 repetitions

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Results- BCI competition III dataset II [Albany] (2) Time sample selection regularizer =5.46 Subject A: 98% (97%) 70% (72%) Subject B: 94% (96%) 81% (75%) (Rakotomamonjy & Gigue) 15 repetitions 5 repetitions

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Results- BCI competition III dataset II [Albany] (3) Component selection regularizer 15 repetitions 5 repetitions =100 Subject A: 98% (97%) 70% (72%) Subject B: 94% (96%) 82% (75%) (Rakotomamonjy & Gigue)

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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!)

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