Learning Robust Weighted Group Sparse Graph for Discriminant Visual Analysis

Abstract

Recently, sparse representation (SR) based graph has been successfully applied for dimensionality reduction (DR). However, the unsupervised characteristic of SR may cause instable representation results, which is undesired for graph construction. To alleviate the problem, a robust weighted group sparse representation (RWGSR) method is developed by minimizing the combination of l1-norm regularized representation fidelity and the weighted l2,1-norm regularized representation coefficients. RWGSR can find the robust and stable intrinsic intra-class and inter-class adjacent relations of samples. The intra-class and inter-class representations of RWGSR are then utilized to construct corresponding intra-class and inter-class graphs. With the graphs, a novel supervised DR algorithm named robust weighted group sparse graph based embedding (RWGSE) is proposed. Benefitting from RWGSR, RWGSE considers both intra-class and inter-class intrinsic structures of data, and seeks a low-dimensional subspace by simultaneously minimizing the intra-class scatter and maximizing the inter-class scatter. Extensive experiments on public benchmark face and object datasets show the effectiveness of the proposed method.