Title: A Nonlinear Kernel Support Matrix Machine for Matrix Learning,
Abstract: In many problems of supervised tensor learning (STL), real world data such as
face images or MRI scans are naturally represented as matrices, which are also
called as second order tensors. Most existing classifiers based on tensor
representation, such as support tensor machine (STM) need to solve iteratively
which occupy much time and may suffer from local minima. In this paper, we
present a kernel support matrix machine (KSMM) to perform supervised learning
when data are represented as matrices. KSMM is a general framework for the
construction of matrix-based hyperplane to exploit structural information. We
analyze a unifying optimization problem for which we propose an asymptotically
convergent algorithm. Theoretical analysis for the generalization bounds is
derived based on Rademacher complexity with respect to a probability
distribution. We demonstrate the merits of the proposed method by exhaustive
experiments on both simulation study and a number of real-word datasets from a
variety of application domains.