Asymmetric Principal Component and Discriminant Analyses for Pattern Classification

This paper studies the roles of the principal component and discriminant analyses in the pattern classification and explores their problems with the asymmetric classes and/or the unbalanced training data. An asymmetric principal component analysis (APCA) is proposed to remove the unreliable dimensions more effectively than the conventional PCA. Targeted at the two-class problem, an asymmetric discriminant analysis in the APCA subspace is proposed to regularize the eigenvalue that is, in general, a biased estimate of the variance in the corresponding dimension. These efforts facilitate a reliable and discriminative feature extraction for the asymmetric classes and/or the unbalanced training data. The proposed approach is validated in the experiments by comparing it with the related methods. It consistently achieves the highest classification accuracy among all tested methods in the experiments.