Independent component analysis applied to biophysical time series and EEG. Arnaud Delorme CERCO, CNRS, France & SCCN, UCSD, La Jolla, USA

Transcription

1 Independent component analysis applied to biophysical time series and EEG Arnad Delorme CERCO, CNRS, France & SCCN, UCSD, La Jolla, USA

2 Independent component analysis Cocktail Party Mixtre of Brain sorce activity

3 A - B.7 Y=[A;B] -0. Linear Combination X=YW ICA Y=W ~ - X ~ ICA is a method to recover a version, of the original sorces by mltiplying the data by a nmixing matrix A B

4 ) ( 4 0 ) ( ) ( ) ( 0 * * * Weight matrix W Data X ICA activity U U = WX Data ICA activity Channel Channel Channel Comp. Comp. Comp.

5 ) ( 4 0 ) ( ) ( ) ( 0 * * * Inverse eight matrix W - ICA activity U Data X X=W - U Data Chan Chan Chan Comp. Comp. Comp.

6 Historical Remarks Heralt & Jtten ("Space or time adaptive signal processing by neral netork models, Neral Nets for Compting Meeting, Snobird, Utah, 986): Seminal paper, neral netork Bell & Sejnoski (99): Information Maximization Amari et al. (996): Natral Gradient Learning Cardoso (996): JADE Applications of ICA to biomedical signals EEG/ERP analysis (Makeig, Bell, Jng & Sejnoski, 996). fmri analysis (McKeon et al. 998) Cortesy of TP Jng

7 ICA Theory Cost Fnctions Family of BSS algorithms Information theory (Infomax) Bayesian probability theory (Maximm likelihood estimation) Negentropy maximization Nonlinear PCA Statistical signal processing (cmlant maximization, JADE) A nifying Information-theoretic frameork for ICA Pearlmtter & Parra shoed that InfoMax, ML estimation are eqivalent. Lee et al. (999) shoed negentropy has the eqivalent property to InfoMax. Girolami & Fyfe shoed nonlinear PCA can be vieed from information-theoretic principle. Cortesy of TP Jng

8 ICA and PCA Principal component analysis Independent component analysis

9 Central limit theorem Brain sorce A Scalp channels = linear mixtre of A and B (more gassian) binning Scalp channel time Brain sorce B Scalp channel

10 ICA Training Process Central limit theorem Remove the mean x = x - <x> Sphere the data by diagonalizing its covariance matrix, x = <xx T > -/ (x-<x>). Update W according to

11 S X Y Maximization of information transfer I(X,Y) Non-linearity - Pick p higher moment in inpt distribtion - Perform tre redndancy redction in the otpt - Perform independent sorce separation From Bell & Sejnoski, Neral Comptation, 99

12 Entropy Mtal Information H(Y) is the entropy of the otpt H(Y X) is hatever entropy the otpt has that did not come from the inpt

13 Entropy Dice: /6 /6 4 6 H = 6 log = Fake dice (make a 6 half of the time): entropy.6 (base ) /0 H = log log =

14 Contingency table for stress and emotionality STRE 4 6 Total EMOT= Total From

15 Contingency freqencies for stress and emotionality STRE 4 6 EMOT= Joint entropy.46; exercise: compte mtal information

16 ICA learning rle Entropy extremm Natral gradient (Amari)

17 Krtosis, Sper- and Sb-Gassian Krtosis: a measre of ho peaked or flat of a probability distribtion is. - Gassian Dist. Krtosis = 0 Sper-Gassian: krtosis > 0 Sb-Gassian: krtosis < 0

18 Moments, Cmlants Moments Central moments Cmlants mean variance skeness krtosis

19 Sb-gassian Sper-gassian Sphering ICA

20 ICA/EEG Assmptions Mixing is linear at electrodes Propagation delays are negligible Component time corses are independent Nmber of components less than the nmber of channels. OK OK ~ Contribtion to EEG ICA limit Nmber of independent components

21 Characteristics of Independent Component of the EEG Concrrent Activity Maximally Temporally Independent Overlapping Maps and Spectra Dipolar Scalp Maps Fnctionally Independent Beteen-Sbject Reglarity

22 Otline Independent component analysis Theory Examples and localization ICA reliability ICA repetitions Different ICA algorithms Data redction

23 Largest 0 Independent Components (single sbject) Onton, Delorme and Makeig, 00

24 From Jng et al., Clinical Nerophysiology, 000

25 Adapted from Jng et al., Clinical Nerophysiology, 000

26 * * * X=W - U Data ICA activity U Comp. Comp. Comp ( ) ( ) ( ) ( ) Data X Chan Chan Chan Inverse eight matrix W -

27 Artifact removal sing ICA Adapted from Delorme et al., sbmitted

28 Adapted from Delorme et al., sbmitted

29 From Makeig, Delorme, et al., PLOS biology, 004

30

31 From Makeig, Delorme, et al., PLOS biology, 004

32 From Makeig, Delorme, et al., PLOS biology, 004

33 From Makeig, Delorme, et al., PLOS biology, 004

34 Localization ICA Electrodes Components ICA component scalp maps 0 - Localization Time (ms)

35 From Delorme, et al., sbmitted

36 Localization of activity From Delorme, et al., sbmitted

37 Sbject MRI MNI model (Loreta) Sbject scanned Sbject components electrode positions scalp map Head mesh Normalization of sbject MRI to MNI brain EEGLAB BRAINVISA SPM Front EEGLAB & FILEDTRIP EEGLAB Coregistration EEGLAB LORETA EEGLAB

38 * * *...,4,,4,,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,... * * * Inverse eight matrix W - ICA activity U Data X (EEG/MEG time series) X=W - U Chan Chan Chan Comp. Comp. Comp....,4,,4,,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,... Inverse eight matrix W - ICA activity U Data X (EEG/MEG voxel activities) Time Time Time Comp. Comp. Comp. Temporal ICA X=W - U Spatial ICA