Robust discriminant analysis with feature selective projection and between-classes structural incoherence

Abstract

Our paper proposes a new feature extraction method, named as robust discriminant analysis (RDA), for data classification tasks. Based on linear discriminant analysis (LDA), RDA integrates the feature selection and feature extraction into a unified framework. The transformation matrix with l2,1-norm constraint is introduced to map original data feature into a discriminative low-dimensional subspace, in which the l2,1 sparsity regularizer can endow the feature selection with better interpretability. And, we use two different matrices (i.e., transformation matrix P and reconstruction matrix Q) for better data reconstruction, which can provide more freedom to ensure that the learned data representation holds the main variance and hence improve robustness to noises. To ensure that the learned features are optimal for classification, the structurally incoherent learning is introduced to add additional discriminant ability by minimizing the correlation of different classes. In other hand, the between-classes structural incoherence term is also equivalent to cosine distance metric, which is robust to noises and outliers. An efficient optimization algorithm is designed to solve the proposed optimization model. Extensive experiments conducted on all kinds of benchmark databases confirm the superiority of the proposed method.