On the linear discriminant analysis for large number of classes

Abstract

We study the challenging problem to classify samples into a large number of classes, and propose the idea of using different Dimensionality-Reduction (DR) projections for different classes of samples. Based on this intuitive idea, the traditional Linear Discriminant Analysis (LDA) and the trace-ratio LDA are formulated to their corresponding new multi-subspace objectives. We justify that certain effects of class-adaptive feature selection are naturally achieved via our multi-subspace DR methods. Experiments on seven datasets show that, our multi-subspace trace-ratio LDA outperform its ratio-trace and single-subspace counterparts, and its advantage is more apparent when the number of classes to be classified is large.