Discriminatory Data Mapping by Matrix-Based Supervised Learning Metrics

Supervised attribute relevance detection using cross-comparisons (SARDUX), a recently proposed method for data-driven metric learning, is extended from dimension-weighted Minkowski distances to metrics induced by a data transformation matrix Ω for modeling mutual attribute dependence. Given class labels, parameters of Ω are adapted in such a manner that the inter-class distances are maximized, while the intra-class distances get minimized. This results in an approach similar to Fisher’s linear discriminant analysis (LDA), however, the involved distance matrix gets optimized, and it can be finally utilized for generating discriminatory data mappings that outperform projection pursuit methods with LDA index. The power of matrix-based metric optimization is demonstrated for spectrum data and for cancer gene expression data.