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In many problems of supervised tensor learning (STL), real world data such asface images or MRI scans are naturally represented as matrices, which are alsocalled as second order tensors. Most existing classifiers based on tensorrepresentation, such as support tensor machine (STM) need to solve iterativelywhich occupy much time and may suffer from local minima. In this paper, wepresent a kernel support matrix machine (KSMM) to perform supervised learningwhen data are represented as matrices. KSMM is a general framework for theconstruction of matrix-based hyperplane to exploit structural information. Weanalyze a unifying optimization problem for which we propose an asymptoticallyconvergent algorithm. Theoretical analysis for the generalization bounds isderived based on Rademacher complexity with respect to a probabilitydistribution. We demonstrate the merits of the proposed method by exhaustiveexperiments on both simulation study and a number of real-word datasets from avariety of application domains.

A Nonlinear Kernel Support Matrix Machine for Matrix Learning