A Nonlinear Kernel Support Matrix Machine for Matrix Learning

TL;DR

This paper introduces a kernel support matrix machine (KSMM) for supervised learning on matrix data, offering a more efficient alternative to existing tensor classifiers by exploiting structural information with a convergent algorithm.

Contribution

The paper proposes a novel KSMM framework with a unifying optimization problem and an asymptotically convergent algorithm, improving efficiency over existing tensor classifiers.

Findings

KSMM outperforms existing methods in experiments.

Theoretical generalization bounds are established.

Efficient convergence demonstrated on real datasets.

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.