1. 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

2. P300 speller system Evoked Response Farwell & Donchin 1988

3. P300 speller system ER detected! The character must be “P”

4. 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!!

5. 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)

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

7. 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

8. How we do this 122813411956107 … Multinomial likelihood f. …

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

10. 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)

11. The method 2 x 6-class multinomial lossL1-L2 regularization Nonlinear convex optimization with second order cone constraint

12. 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

13. 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

14. 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)

15. Filters (1) Channel selection regularizer (2) Time sample selection regularizer (3) Component selection regularizer

16. 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!)