Avoiding Optimal Mean Robust and Sparse BPCA with L1-norm Maximization

Abstract

Recently, the robust PCA/2DPCA methods have achieved great success in subspace learning. Nevertheless, most of them have a basic premise that the average of samples is zero and the optimal mean is the center of the data. Actually, this premise only applies to PCA/2DPCA methods based on L2-norm. The robust PCA/2DPCA method with L1-norm has an optimal mean deviate from zero, and the estimation of the optimal mean leads to an expensive calculation. Another shortcoming of PCA/2DPCA is that it does not pay enough attention to the instinct correlation within the part of data. To tackle these issues, we introduce the maximum variance of samples’ difference into Block principal component analysis (BPCA) and propose a robust method for avoiding the optimal mean to extract orthonormal features. BPCA, which is generalized from PCA and 2DPCA, is a general PCA/2DPCA framework specialized in part learning, can makes better use of the partial correlation. However, projection features without sparsity not only have higher computational complexity, but also lack semantic properties. We integrate the elastic network into avoiding optimal mean robust BPCA to perform sparse constraints on projection features. These two BPCA methods (non-sparse and sparse) make the presumption of zero-mean data unnecessary and avoid optimal mean calculation. Experiments on reference benchmark databases indicate the usefulness of the proposed two methods in image classification and image reconstruction.