Analysis of Human EEG Data

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Analysis of Human EEG Data

• Pavel Stránský
• Supervisor
• Prof. RNDr. Petr eba, DrSc.

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Content

• Measurement and structure of EEG signal
• EEG as a multivariate time series, statistical
  approach to EEG data processing
• Small introduction to random matrices theory
• 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-encephalogr
am
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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 (Fishers test,
  Siegels 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

Hermitian self-dual matrices, symplectic
transformations
Hermitian matrices, unitary transformations
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)
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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 interactions
• GSE Hamiltonians with time reversal symmetry and
  WITH spin-1/2 interactions
• Universal law for joint probability density
  function
• For energies x(eigenvalues of H)

b 1 GOE b 2 GUE b 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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3. Little introduction to RMT

• Random matrices (cont.)
• Other distributions (taking into account
  correlations for longer distances)
• S2 statistics (number variance)
• D3 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 xm 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 r(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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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. eba, 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)