tools to monitor brain state
DESCRIPTION
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" - PowerPoint PPT PresentationTRANSCRIPT
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Tools to monitor brain state
Alain de Cheveigné, CNRS / ENS / UCL
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overview
• Two motivations- importance of brain state
- data mining
• Algorithms- segmentation
- clustering
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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
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importance of brain state
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importance of brain state
essential to have tools to monitor/characterize brain state
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brain data miningbrain data mining
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brain data miningbrain data mining
€
yk = w jkj∑ x j
lots of methods: PCA, ICA, beamforming, CSD, DSS, CSP, etc.
component analysis exploits correlation structure to improve SNR
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brain data miningbrain data miningcomponent 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)
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brain data miningbrain 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)
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brain data miningbrain 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.
€
A = Un Andim(An ) < J (number of channels)
Our task:
Find this partition:
--> related to manifold learning
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brain data miningsignal state descriptors
Standard statistics:- mean- variance- covariance- autocorrelation (including multichannel)
€
mA (x) = (1/nA ) x(t)t∈A∑
vA (x) = mA (x 2) −mA (x)2
CA (X) = (1/nA ) x j (t)t∈A∑ xk (t)[ ]
rA ,τ (x) = (1/n) x(t)t∈A∑ x(t −τ )
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brain data miningalgorithms
Two approaches: - segmentation - clustering
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brain data miningsegmentationfind step in mean
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find step in mean
algorithm 1
segmentation
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find step in variance
algorithm 1 applied to xt2
segmentation
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multichannel case: step in variance
data: 10 channels, 2-fold amplitude increase
sum of V statistics over channels: algorithm 2
segmentation
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multichannel case: step in variance
data: 10 channels, 2-fold amplitude increase/decrease
sum of V statistics over channels: algorithm 2
segmentation
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brain data miningalgorithmsmultichannel 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)
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None of these algorithms addresses our initial task:
Find:
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A = Un Andim(An ) < J (number of channels)
segmentation
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Segmentation by joint diagonalization (algorithm 3):
Rationale: - assume data X of rank J=n(channels) over entire segment A = A1 U 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
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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
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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
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clustering
- similar algorithms, similar results (on these example data)- segmentation or clustering? depends on data, depends on question
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examples
monkey ECoG (NeuroTycho data)
injection of anaesthetic
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examples
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examples