The paper contains a theory and methods of optimal feature selection while testing one weakly stationary Gaussian process against another with similar mean vectors and different covariance matrices. A process of feature selection is realized by a linear transformation T which applied to the original N-dimensional feature vector reduces it to the n- dimensional one, namely, \(y=Tx\), and its essence relies on an optimal (in a specified sense) choice of the matrix T.
The proposed algorithms combine classical methods and distribution theory, especially making use of empirical distributions of the covariance matrices in the original space as well as in the transformed one.
They offer an accurate finite dimensional information-theoretic strategy to feature selection. The provided examples underline their superiority to approaches employing statistical distance measures.