A Nonlinear Kernel Support Matrix Machine for Matrix Learning
This work addresses efficiency and optimization issues in matrix-based classifiers for applications like image and medical data analysis, but it is incremental as it builds on existing tensor learning methods.
The authors tackled the problem of slow and suboptimal training in supervised tensor learning by proposing a kernel support matrix machine (KSMM) for matrix data, achieving competitive performance on real-world datasets.
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.