Matrix Metric Adaptation for Improved Linear Discriminant Analysis of Biomedical Data

A structurally simple, yet powerful, formalism is presented for adapting attribute combinations in high-dimensional data, given categorical data class labels. The rank-1 Mahalanobis distance is optimized in a way that maximizes between-class variability while minimizing within-class variability. This optimization target has resemblance to Fisher’s linear discriminant analysis (LDA), but the proposed formulation is more general and yields improved class separation, which is demonstrated for spectrum data and gene expression data