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

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

EEG Data *  7 subjects, 5 trials of 4 tasks on 2 days  Hz, 6 channels  6 electrodes on electrically linked mastoids  Denote data as 6x2500 matrix, X = (x 1 x 2... x 6 ) *Source:

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

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:

MNF (continued)  When signal and noise components are orthogonal, S T N=N T S=0, equivalently we have:  Generalized Eigenvalue Problem

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

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

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

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 * )

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

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.

Mean estimation

Same day results Misclassifications Correct Classifications 2 task classification 19 4 task classification910

Next day results Misclassifications Correct Classifications 2 task classification task classification3113

Cross person results Misclassifications Correct Classifications 2 task classification task classification3523

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