Matrix Variate Distribution-Induced Sparse Representation for Robust Image Classification

Sparse representation learning has been successfully applied into image classification, which represents a given image as a linear combination of an over-complete dictionary. The classification result depends on the reconstruction residuals. Normally, the images are stretched into vectors for convenience, and the representation residuals are characterized by I₂-norm, which actually assumes that the elements in the residuals are independent and identically distributed variables. However, it is hard to satisfy the hypothesis when it comes to some structural errors, such as illuminations, occlusions, and so on. In this paper, we represent the image data in their intrinsic matrix form rather than concatenated vectors. The representation residual is considered as a matrix variate following the matrix elliptically contoured distribution, which is robust to dependent errors and has long tail regions to fit outliers. Then, we seek the maximum a posteriori probability estimation solution of the matrix-based optimization problem under sparse regularization. An alternating direction method of multipliers (ADMMs) is derived to solve the resulted optimization problem. The convergence of the ADMM is proven theoretically. Experimental results demonstrate that the proposed method is more effective than the state-of-the-art methods when dealing with the structural errors.