Towards optimum linear transformation under zero-mean Gaussian mixtures for detection of motor imagery EEG

Optimum linear transformation under mixture of zero-mean Gaussian conditions is an intriguing problem, especially in learning discriminative spatial components in motor imagery EEG for building brain computer interfaces. However, it is not well addressed in the past. In this paper, we study optimum linear transformation under mixture of zero-mean Gaussian. In particular, we formulate optimum transformation as a Bhattacharyya error bound minimization problem, and derive a numerical solution to estimate the bound from training samples. Based on the solution, we develop an algorithm for selecting optimum linear transformation. The proposed method is evaluated, in comparison with the state-of-the-art methods, using a publicly available data set of motor imagery EEG. The results attest to the superiority of the method for detecting motor imagery.