EEG Classification Using Maximum Noise Fractions and spectral classification

1
EEG ClassificationUsing Maximum Noise Fractions
and spectral classification

• Steve Grikschart and Hugo Shi
• EECS 559 Fall 2005

2
Roadmap

• Motivations and background
• Available DATA
• MNF
• Noise covariance estimation
• Quadratic Discriminant Analysis
• Spectral Discriminant Analysis
• Results

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Motivations and Background

• New capabilities for differently abled persons
  (i.e. ALS)
• Psychomouse!
• Divide and conquer approach increases capabilities

4
EEG Data

• 7 subjects, 5 trials of 4 tasks on 2 days
• 10 seconds _at_ 250 Hz, 6 channels
• 6 electrodes on electrically linked mastoids
• Denote data as 6x2500 matrix,
• X (x1 x2 ... x6)

Source www.cs.colostate.edu/eeg/?Summary
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Data Transformation

• Seek a data transformation for easier
  classification
• Optimally using all 6 channel's information
• Also exploiting time correlation
• Dimension reduction not needed

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Maximum Noise Transform (MNF)

• Assume signal in additive noise model
• X S N
• Seek a linear combination of data, Xa, that
  maximizes signal to noise ratio
• Express as an optimization problem

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MNF (continued)

• When signal and noise components are orthogonal,
  STNNTS0, equivalently we have
• Generalized Eigenvalue Problem

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MNF (continued)

• Component with maximum SNR given by top
  eigenvector
• Restrict a's by enforcing orthogonality of each
  solution
• SNR of component Xaj given by ?j
• Requires estimation of noise covariance NTN
• Introduce time correlation by augmenting X matrix

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Noise Covariance Estimation

• Two basic methods
• Differencing Data Time-shifted Data
• AR fitting Fit AR to each channel, take residuals

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Estimation by Differencing

• dX X - Xd, where Xd is a time-shifted version
  of X
• RN dXTdX (SN-Sd-Nd)T(SN-Sd-Nd)
• Assuming STN 0, ENNdT 0, S-Sd 0 then
• RN (N-Nd)T(N-Nd) 2NTN 2SN

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Estimation by AR fitting

• Scalar series vs. vector series
• Xi(t) f1 Xi(t-1) ... fq Xi(t-q) ei(t)
• Noise covariance estimated using residuals
• Non-linear least squares fit by Gauss-Newton
  algorithm
• Order estimated by AIC
• (Typical order around 6)

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QDA

• But the condition number of the covariance matrix
  is..
• 2.8195e19

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Frequency Domain Classification

• Mean signal estimated by averaging across all
  training data.
• Spectral Analysis performed for all training data
  using Parzen windows, then averaged across all
  training samples.

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Mean estimation
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Same day results
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Next day results
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Cross person results
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Conclusions

• This EEG method has promising results but still
  needs work for acceptable performance
• Multi-variate analysis may help
• Same day results are good, but not as useful for
  practical applications