Feature selection on movement imagery discrimination and attention detection

Abstract

Noninvasive brain–computer interfaces (BCI) translate subject’s electroencephalogram (EEG) features into device commands. Large feature sets should be down-selected for efficient feature translation. This work proposes two different feature down-selection algorithms for BCI: (a) a sequential forward selection; and (b) an across-group variance. Power rar ratios (PRs) were extracted from the EEG data for movement imagery discrimination. Event-related potentials (ERPs) were employed in the discrimination of cue-evoked responses. While center-out arrows, commonly used in calibration sessions, cued the subjects in the first experiment (for both PR and ERP analyses), less stimulating arrows that were centered in the visual field were employed in the second experiment (for ERP analysis). The proposed algorithms outperformed other three popular feature selection algorithms in movement imagery discrimination. In the first experiment, both algorithms achieved classification errors as low as 12.5% reducing the feature set dimensionality by more than 90%. The classification accuracy of ERPs dropped in the second experiment since centered cues reduced the amplitude of cue-evoked ERPs. The two proposed algorithms effectively reduced feature dimensionality while increasing movement imagery discrimination and detected cue-evoked ERPs that reflect subject attention.

Appendix

This appendix describes the calculation of the discrimination coefficients a employed in:

$$ {\mathbf{z}} = {\mathbf{Ya}}.$$

Considering that z is the discrimination function and Y is the feature matrix. Initially, the SVD of the within-group covariance matrix W is calculated as:

$$ {\mathbf{W}} = {\mathbf{USU}}^{\rm T}. $$

S is a diagonal matrix, and U appears twice since covariance matrices are symmetric. B is the between-group covariance matrix. In order to obtain a better coordinate system, the vector a in the following Fisher criterion:

$$ \varvec{\alpha} = {\frac{{{\mathbf{a}}^{\rm T} {\mathbf{Ba}}}}{{{\mathbf{a}}^{\rm T} {\mathbf{Wa}}}}} $$

is replaced by ${\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{v}},$ resulting in:

$$ \varvec{\alpha} = {\frac{{{\mathbf{v}}^{\rm T} {\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{BUS}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{v}}}}{{{\mathbf{v}}^{\rm T} {\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{WUS}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{v}}}}} = {\frac{{{\mathbf{v}}^{\rm T} {\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{BUS}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{v}}}}{{{\mathbf{v}}^{\rm T} {\mathbf{v}}}}} $$

In general, for a symmetric matrix H, the maximum of ${\mathbf{v}}^{\rm T} {\mathbf{Hv}}$ is attained for the first singular vector v = v ₁. Similarly, the maximization of α may be calculated through the following SVD:

$$ {\mathbf{v}}^{\rm T} {\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{BUS}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{v}} = {\mathbf{VHV}}^{T} $$

The maximum of α is ${\mathbf{v}}_{1}^{T} {\mathbf{VHV}}^{T} {\mathbf{v}}_{1} = {\varvec{\lambda}}_{1} ,$ is the highest singular value of H. Converting back to original coordinates a:

$$ {\mathbf{a}} = {\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{v}}_{1}, $$

which is equivalent to the first column of ${\mathbf{US}}^{{ - {1/2}}} {\mathbf{U}}^{\rm T} {\mathbf{V}}.$