analysis of human eeg data pavel stránský supervisor: prof. rndr. petr Šeba, drsc
TRANSCRIPT
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Analysis of Human EEG Data
Pavel Stránský
Supervisor: Prof. RNDr. Petr Šeba, DrSc.
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Content
1. Measurement and structure of EEG signal
2. EEG as a multivariate time series, statistical approach to EEG data processing
3. Small introduction to random matrices theory
4. My present results and outlook
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1
Measurement and Structure of EEG Signal
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1. Measurement and Structure of EEG Signal
Cerebral Electric Activity
EEG = Electro-encephalography, Electro-encephalogram
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1. Measurement and Structure of EEG Signal
Location of the Electrodes(10-20 system, 21 electrodes)
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1. Measurement and Structure of EEG Signal
An Example of EEG
Measurement
•Alpha waves
•Beta, theta, delta waves
•Other graphoelements
•Artefacts
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2.
Statistical Approach to EEG Data
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2. Statistical Approach to EEG Data
Modelling and processing time series
• Vector Autoregression VAR(p)
Stacionarity (Covariance – stacionarity):
for all t and any j
White noise:
for all t, t1, t2
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2. Statistical Approach to EEG Data
Modelling and processing time series (cont.)
• Other ways of treating with time series:Principal component analysis
Independent component analysis
Testing for periodicity (Fisher’s test, Siegel’s test)
mixing
ICA
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3. Small introduction to random matrix theory
(RMT)
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3. Small introduction to RMT
Random matrices
• Study of excitation spectra of compound nuclei• The same behaviour like eigenvalues of random matrices• 3 principal ensembles: GOE, GUE, GSE
Def: Gaussian othogonal ensemble is defined in the space of real symmetric matrices by two requirements:
1. Invariance (O is orthogonal matrix)
2. Elements are statistically independent
which means that , where
(probablity density function)
Hermitian matrices, unitary transformations
Hermitian self-dual matrices, symplectic transformations
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3. Small introduction to RMT
Random matrices (cont.)
• Universality classes:GUE Hamiltonians without time reversal symmetry
GOE Hamiltonians with time reversal symmetry and WITHOUT spin-1/2 interactionsGSE Hamiltonians with time reversal symmetry and WITH spin-1/2 interactions
• Universal law for joint probability density function:
For energies (eigenvalues of H)= 1 GOE
= 2 GUE
= 4 GSE
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3. Little introduction to RMT
Random matrices (cont.)
• Spectral correlations (nearest neighbour spacing distribution):Wigner distribution
Normalization
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p(s)
GOE
GUE
GSE
Poisson
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3. Little introduction to RMT
Random matrices (cont.)
• Other distributions (taking into account correlations for longer distances)statistics (number variance)
3 statistics (spectral rigidity)
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4.Results, outlook
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4. Results, outlook
Correlation analysis of EEG Data
• Dividing EEG signal from M channels x1, ..., xM into cells of constant time length T
• Computing correlation matrix Cm for the mth cell with normalizing mean and variance:
• Finding eigenvalues m of all correlation matrices Cm
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4. Results, outlook
Correlation analysis (cont.)
• Unfolding the spectra:
(after unfolding all eigenvalues are "equally important", the resulting eigenvalue density (x) is constant)
• Finding nearest neighbour distribution p(s) for the unfolded spectra:
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4. Results, outlook
Correlation analysis (cont.)
• Comparing computed spacing distribution with theoretical
Wigner curve
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0 0.5 1 1.5 2 2.5 3 3.5
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p(s)
EEG
Wigner
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4. Results, outlook
Outlook
• Use more subtle method from RMT and time series analysis to analyze the correlations and also autocorrelations (correlations in time)
• Find significant and reproducible variables for standard EEG measured on healthy subjects
• Deviations are expected if there was some neural disease
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4. Results, outlook
Literature
• P. Šeba, Random Matrix Analysis of Human EEG Data, Phys. Rev. Lett. 91, 198104 (2003)
• T. Guhr, A. Müller-Groeling, H. A. Weidenmüller, Random Matrix Theories in Quantum Physics: Common Concepts, Phys. Rep. 299, 189 (1998)
• M. L. Mehta, Random Matrices and the Statistical Theory of Energy Levels, Academic Press (1967)
• H. J. Stöckmann, Quantum Chaos: An Introduction, Cambridge University Press (1999)
• A. F. Siegel, Testing for Periodicity in a Time Series, JASA 75, 345 (1980)• J. D. Hamilton, Time Series Analysis, Princeton University Press (1994)• A. Jung, Statistical Analysis of Biomedical Data, Dissertation, Universität
Regensburg (2003)• J. Faber, Elektroencefalografie a psychofyziologie, ISV nakladatelství Praha
(2001)