1. Tools to monitor brain state Alain de Cheveigné, CNRS / ENS / UCL

2. overview Two motivations - importance of brain state - data mining Algorithms - segmentation - clustering

3. a definition of state "something that is true at some time and not at another" - statistical distribution of values - validity of a predictive model - parameters of a predictive model

4. importance of brain state

5.  essential to have tools to monitor/characterize brain state

6. brain data mining

7. lots of methods: PCA, ICA, beamforming, CSD, DSS, CSP, etc. component analysis exploits correlation structure to improve SNR

8. brain data mining component analysis can be extremely powerful: simulated data: 10 channels, 1 target, 9 noise sources, random mix matrix, SNR=10 -8 sources sensors noise target works if 9 noise sources, fails miserably if 10:  dimensionality of noise subspace is critical result of component analysis (DSS algorithm)

9. brain data mining Dimensionality = (roughly) number of independent noise sources within data If dim(noise) < n(channels) then there exists a projection of the data (= weighted sum of the channels) such that: (a) all noise sources are canceled, (b) target activity is not (unless we're unlucky) The aim of component analysis (ICA, beamforming, DSS, etc.) is to find such useful projections. If dim(noise)=n(channels) they cannot succeed. We need: dim(noise) < n(channels)

10. brain data mining Hypothesis: There exists a partition of the time axis into subsets A n such that the data are of rank < n(channels) over each subset. Our task: Find this partition: --> related to manifold learning

11. brain data miningsignal state descriptors Standard statistics: - mean - variance - covariance - autocorrelation (including multichannel)

12. brain data miningalgorithms Two approaches: - segmentation - clustering

13. brain data miningsegmentation find step in mean

14. algorithm 1 segmentation

15. find step in variance algorithm 1 applied to x t 2 segmentation

16. multichannel case: step in variance data: 10 channels, 2-fold amplitude increase sum of V statistics over channels: algorithm 2 segmentation

17. multichannel case: step in variance data: 10 channels, 2-fold amplitude increase/decrease sum of V statistics over channels: algorithm 2 segmentation

18. brain data miningalgorithms multichannel case: step in covariance data: 10 channels, 5 sources active in first half (rank=5), 5 sources active in second half (rank=5), rank of full data=10 algorithm 2 applied to x j (t) x j' (t)

19. None of these algorithms addresses our initial task: Find: segmentation

20. Segmentation by joint diagonalization (algorithm 3): Rationale: - assume data X of rank J=n(channels) over entire segment A = A 1 U A 2, and of rank < J over both A 1 and A 2 - there exists a projection of data that is zero over A 1 and non-zero over A 2 - there exists a projection of data that is zero over A 2 and non-zero over A 1 - both can be found by joint diagonalization of covariance matrices of X over A 1 and A: - the first channel of Y=XP is zero over A 1 and last channel zero over A 2 segmentation

21. Segmentation by joint diagonalization (algorithm 3): Algorithm: (a) choose initial arbitrary segmentation A = A 1 U A 2 (b) diagonalize covariance matrices of A and A 1 (c) apply transform Y=XP (d) apply algorithm 2 to first and last columns of X  new partition (e) go to (b) until no change in partition (or max iterations) segmentation

22. multichannel case: step in covariance data: 10 channels, 5 sources active in first half (rank=5), 5 sources active in second half (rank=5), rank of full data=10 algorithm 3 segmentation

23. clustering - similar algorithms, similar results (on these example data) - segmentation or clustering? depends on data, depends on question

24. examples monkey ECoG (NeuroTycho data) injection of anaesthetic

25. examples