1. EEG Classification Using 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 = (x 1 x 2... x 6 ) *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, S T N=N T S=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 Xα j given by λ j  Requires estimation of noise covariance N T N  Introduce time correlation by augmenting X matrix

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

10. Estimation by Differencing  dX = X - X δ, where X δ is a time-shifted version of X  R N = dX T dX = (S+N-S δ -N δ ) T (S+N-S δ -N δ )  Assuming S T N = 0, E[NN δ T ] = 0, S-S δ ≈ 0 then R N = (N-N δ ) T (N-N δ ) ≈ 2N T N = 2Σ N

11. Estimation by AR fitting  Scalar series vs. vector series  X i (t) = φ 1 X i (t-1) +... + φ q X i (t-q) + ε i (t)  Noise covariance estimated using residuals  Non-linear least squares fit by Gauss- Newton algorithm  Order estimated by AIC (Typical order around 6 * ) (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 Misclassifications Correct Classifications 2 task classification 19 4 task classification910

16. Next day results Misclassifications Correct Classifications 2 task classification 1111 4 task classification3113

17. Cross person results Misclassifications Correct Classifications 2 task classification 919 4 task classification3523

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