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Tools to monitor brain state. Alain de Cheveigné, CNRS / ENS / UCL. overview. • Two motivations - importance of brain state - data mining • Algorithms - segmentation - clustering. a definition of state. "something that is true at some time and not at another"

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Tools to monitor brain state

Alain de Cheveigné, CNRS / ENS / UCL


overview

• Two motivations

- importance of brain state

- data mining

• Algorithms

- segmentation

- clustering


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



importance of brain state

 essential to have tools to monitor/characterize brain state


brain data mining

brain data mining


brain data mining

brain data mining

component analysis exploits correlation structure to improve SNR

lots of methods: PCA, ICA, beamforming, CSD, DSS, CSP, etc.


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


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)


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


brain data mining

signal state descriptors

Standard statistics:

- mean

- variance

- covariance

- autocorrelation (including multichannel)


brain data mining

algorithms

Two approaches:

- segmentation

- clustering


brain data mining

segmentation

find step in mean


segmentation

find step in mean

algorithm 1


segmentation

find step in variance

algorithm 1 applied to xt2


segmentation

multichannel case: step in variance

data: 10 channels,

2-fold amplitude increase

sum of V statistics over channels: algorithm 2


segmentation

multichannel case: step in variance

data: 10 channels,

2-fold amplitude

increase/decrease

sum of V statistics over channels: algorithm 2


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)


segmentation

None of these algorithms addresses our initial task:

Find:


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


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)


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


clustering

- similar algorithms, similar results (on these example data)

- segmentation or clustering? depends on data, depends on question


examples

monkey ECoG (NeuroTycho data)

injection of anaesthetic




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