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Brain State Monitoring Tools for Data Mining Algorithms Overview

Explore the importance of monitoring brain state and data mining algorithms for segmentation, clustering, and component analysis. Learn about various methods like PCA, ICA, and DSS. Discover how to analyze brain data using signal state descriptors and statistical measures. Get insights into segmentation and clustering algorithms for multichannel data. Gain knowledge on joint diagonalization for effective segmentation.

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Brain State Monitoring Tools for Data Mining Algorithms Overview

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  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. importance of brain state  essential to have tools to monitor/characterize brain state

  6. brain data mining brain data mining

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

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

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

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

  12. brain data mining algorithms Two approaches: - segmentation - clustering

  13. brain data mining segmentation find step in mean

  14. segmentation find step in mean algorithm 1

  15. segmentation find step in variance algorithm 1 applied to xt2

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

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

  18. brain data mining algorithms 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 xj(t) xj'(t)

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

  20. segmentation Segmentation by joint diagonalization (algorithm 3): Rationale: - assume data X of rank J=n(channels) over entire segment A = A1U A2, and of rank < J over both A1 and A2 - there exists a projection of data that is zero over A1 and non-zero over A2 - there exists a projection of data that is zero over A2 and non-zero over A1 - both can be found by joint diagonalization of covariance matrices of X over A1 and A: - the first channel of Y=XP is zero over A1 and last channel zero over A2

  21. segmentation Segmentation by joint diagonalization (algorithm 3): Algorithm: (a) choose initial arbitrary segmentation A = A1 U A2 (b) diagonalize covariance matrices of A and A1 (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)

  22. segmentation 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

  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

  26. examples

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