Robust Discriminant Subspace Learning with α-Divergence for Image Classification.

Abstract

This paper proposes a novel robust Fisher Discriminant Analysis (FDA) for discriminative subspace learning in the presence of outliers. The proposed approach is motivated by the maximum-likelihood perspective on FDA and its connection to Kullback-Leibler (KL) divergence minimization. Within the probabilistic FDA framework, we develop a robust model by adopting the α-divergence as a flexible alternative to the KL divergence. The resulting method induces an adaptive redescending weighting scheme, in which each observation is weighted according to its statistical compatibility with the model, where the robustness level continuously controlled by α. As α decreases from 1, the influence of outliers is progressively suppressed, while classical FDA is recovered at α = 1. Combined with a two-fold iterative optimization procedure, the proposed method mitigates contamination at both the class-modeling stage and the projection-learning stage. We further provide theoretical analysis of the robustness mechanism, convergence, and computational complexity analysis to support the effectiveness and efficiency of the proposed method. Extensive experiments on synthetic data and multiple public image datasets under diverse contamination settings demonstrate that the proposed method consistently outperforms representative robust FDA variants and related approaches.