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EEG Classification Using Maximum Noise Fractions and spectral classification

EEG Classification Using Maximum Noise Fractions and spectral classification. Steve Grikschart and Hugo Shi EECS 559 Fall 2005. Roadmap . Motivations and background Available DATA MNF Noise covariance estimation Quadratic Discriminant Analysis Spectral Discriminant Analysis Results.

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EEG Classification Using Maximum Noise Fractions and spectral classification

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  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

  3. 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 @ 250 Hz, 6 channels • 6 electrodes on electrically linked mastoids • Denote data as 6x2500 matrix, X = (x1x2 ... x6) *Source: www.cs.colostate.edu/eeg/?Summary

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

  6. Maximum Noise Transform (MNF) • Assume signal in additive noise model: X = S + N • Seek a linear combination of data, Xα, that maximizes signal to noise ratio • Express as an optimization problem:

  7. MNF (continued) • When signal and noise components are orthogonal, STN=NTS=0, equivalently we have: • Generalized Eigenvalue Problem

  8. MNF (continued) • Component with maximum SNR given by top eigenvector • Restrict α's by enforcing orthogonality of each solution • SNR of component Xαj given by λj • Requires estimation of noise covariance NTN • Introduce time correlation by augmenting X matrix

  9. Noise Covariance Estimation • Two basic methods: • Differencing: Data – Time-shifted Data • AR fitting: Fit AR to each channel, take residuals

  10. Estimation by Differencing • dX = X - Xδ, where Xδ is a time-shifted version of X • RN = dXTdX = (S+N-Sδ-Nδ)T(S+N-Sδ-Nδ) • Assuming STN = 0, E[NNδT] = 0, S-Sδ ≈ 0 then RN = (N-Nδ)T(N-Nδ) ≈ 2NTN = 2ΣN

  11. Estimation by AR fitting • Scalar series vs. vector series • Xi(t) = φ1 Xi(t-1) + ... + φq Xi(t-q) + εi(t) • Noise covariance estimated using residuals • Non-linear least squares fit by Gauss-Newton algorithm • Order estimated by AIC • (Typical order around 6*)

  12. QDA But the condition number of the covariance matrix is….. 2.8195e+19

  13. 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.

  14. Mean estimation

  15. Same day results

  16. Next day results

  17. Cross person results

  18. 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

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