Proximal Support Matrix Machine

In this paper, we have proposed a novel model called proximal support matrix machine (PSMM), which is mainly based on the models of proximal support vector machine (PSVM) and low rank support matrix machine (LRSMM). In design, the PSMM model has comprehensively considered both the relationship between samples of the same class and the structure of rows or columns of matrix data. To a certain extent, our novel model can be regarded as a synthesis of the PSVM model and the LRSMM model. Since the PSMM model is an unconstrained convex problem in essence, we have established an alternating direction method of multipliers algorithm to deal with the proposed model. Finally, since a great deal of experiments on the minst digital database show that the PSMM classifier has a good ability to distinguish two digits with little difference, it encourages us to conduct more complex experiments on MIT face database, INRIA person database, the students face database and Japan female facial expression database. Meanwhile, the final experimental results show that PSMM performs better than PSVM, twin support vector machine, LRSMM and linear twin multiple rank support matrix machine in the demanding image classification tasks.