Flexible sparse robust low-rank approximation of matrix for image feature selection and classification

The left/right projection matrix and recovery matrix used for the reconstruction error in the traditional generalized low-rank approximation of matrix models are the same and orthogonal, which makes the model inflexible. To this end, we propose the flexible sparse robust low-rank approximation of matrices model to integrate feature selection into subspace learning and to exclude the redundant features. In the proposed model, two recovery matrices are introduced to together recover the original image data from the subspace spanned by the selected features, resulting in more freedom and flexible to jointly select useful features for low-dimensional representation. Moreover, the L1-norm is imposed on the reconstruction error and L2,1-norm on the Kronecker product of left and right transformation matrices, which can reduce the influence of noise on errors and perform feature selection while learning the optimal transformation matrices and recovery matrices. According to some theoretical analysis, an alternative iterative solution method is designed, and the convergence and time complexity of the algorithm are analyzed. The experimental results on some image datasets show that our method is superior to the existing state-of-the-art methods.