Two-dimensional discriminant analysis based on Schatten p-norm for image feature extraction

Abstract

A Schatten p-norm-based two-dimensional principal component analysis (2DPCA-SP) method was proposed for image feature extraction in our previous work. As an unsupervised method, 2DPCA-SP ignores the label information of training samples, which is essential to classification tasks. In this paper, we propose a novel Schatten p-norm-based two-dimensional discriminant analysis (2DDA-SP) method for image feature extraction, which learns an optimal projection matrix by maximizing the difference of Schatten p-norm-based between-class dispersion and Schatten p-norm-based within-class dispersion in low-dimensional feature space. By using both the Schatten p-norm metric and the label information of training samples, 2DDA-SP not only can efficiently extract discriminative features, but is also robust to outliers. We also propose an efficient iterative algorithm to solve the optimization problem of 2DDA-SP with 0<p<1. Experimental results on several image databases show that 2DDA-SP with 0<p<1 is effective and robust for image feature extraction.