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

The sparse matrix regression (SMR) model for the feature selection method has attracted much attention. However, most existing models do not consider the globality and adaptively preserve the local structure of the image data in projection space. To settle such issues, an adaptive non-negative low-rank preserving SMR model for supervised image feature selection is proposed. It first uses the low-rank representation with non-negative constraint to capture the globality and more discriminative information of image data and makes the error matrix in self-representation of training data sparse. Next, the non-negative low-rank representation coefficients are used to establish a graph matrix learning model to reveal the local manifold structure of the image data. Thus, the proposed model enhances the discriminative ability as well as performs feature selection by the obtained transformation matrix. Finally, an alternating iterative algorithm for solving this model is developed and its convergence and complexity are also analyzed. Experimental results on some image data sets show that the proposed algorithm is effective for images and its recognition ability is obviously superior to other existing methods. In addition, the proposed method is also applied to two scene image classifications to further verify its effectiveness.