Low‐rank nonnegative sparse representation and local preservation‐based matrix regression for supervised image feature selection

Abstract

Matrix regression has attracted much attention due to directly select some meaningful features from matrix data. However, most existing matrix regressions do not consider the global and local structure of the matrix data simultaneously. To this end, we propose a lowrank nonnegative sparse representation and local preserving matrix regression (LNSRLP-MR) model for image feature selection. Here, the loss function is defined by the left and right regression matrices. To capture the global structure and discriminative information of the training images and reduce the effect of heterogeneous data and noises, we impose the low-rank constraint on the self-representation error matrix and the nonnegative sparse constraint on the coefficient vector. The graph matrix can be learned adaptively through representation coefficients, so that accurate local structure information in samples can be revealed. Feature selection is performed by obtained row sparse transformation matrix. An optimization procedure and its performance are also present. Experimental results on several image datasets show that compared with the-state-of-the-art method, the average classification accuracy of the proposed method is improved by at least 1.2% and up to 3.3%. For images with noise or occlusion, the accuracy is improved significantly, up to 4%, which indicates that this method has strong robustness.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Non‐negative low‐rank adaptive preserving sparse matrix regression model for supervised image feature selection and classification

“…On the other hand, since $$Tr({({{\bf{A}}^{(k)}})^T}{{\bf{X}}_i}{{\bf{B}}^{(k)}}) = Tr({({{\bf{W}}^{(k)}})^T}{{\bf{X}}_i})$$ with $${{\bf{W}}^{(k)}} = {{\bf{A}}^{(k)}}{({{\bf{B}}^{(k)}})^T} \in {R^{m \times n}}$$, the first and fifth terms in ANLRP‐SMR model can degenerate into matrix regression, and replace low‐rank representation with sparse representation, then it can be regarded as the LNSRLP‐MR model in [61]: …”