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

摘要

In this paper, we propose a novel Schatten p-norm-based two-dimensional principal component analysis (2DPCA) method, which is named after 2DPCA-Sp, for image feature extraction. Different from the conventional 2DPCA that is based on Frobenius-norm, 2DPCA-Sp learns an optimal projection matrix by maximizing the total scatter criterion based on Schatten p-norm in the low-dimensional feature space. Since p can take different values, 2DPCA-Sp is regarded as a general framework of 2DPCA. We also propose an iterative algorithm to solve the optimization problem of 2DPCA-Sp with 0 < p < 1, which is simple, effective, and easy to implement. Experimental results on several popular image databases show that 2DPCA-Sp with 0 < p < 1 is robust to impact factors (e.g. illuminations, view directions, and expressions) of images. (C) 2015 Elsevier Inc. All rights reserved.