A Sparse Representation Model Using the Complete Marginal Fisher Analysis Framework and Its Applications to Visual Recognition

This paper presents an innovative sparse representation model using the complete marginal Fisher analysis (CMFA) framework for different challenging visual recognition tasks. First, a complete marginal Fisher analysis method is presented by extracting the discriminatory features in both the column space of the local samples based within the class scatter matrix and the null space of its transformed matrix. The rationale of extracting features in both spaces is to enhance the discriminatory power by further utilizing the null space, which is not accounted for in the marginal Fisher analysis method. Second, a discriminative sparse representation model is proposed by integrating a representation criterion such as the sparse representation and a discriminative criterion for improving the classification capability. In this model, the largest step size for learning the sparse representation is derived to address the convergence issues in optimization, and a dictionary screening rule is presented to purge the dictionary items with null coefficients for improving the computational efficiency. Experiments on some challenging visual recognition tasks using representative datasets, such as the Painting-91 dataset, the 15 scene categories dataset, the MIT-67 indoor scenes dataset, the Caltech 101 dataset, the Caltech 256 object categories dataset, the AR face dataset, and the extended Yale B dataset, show the feasibility of the proposed method.