Multi-distance Support Matrix Machines

TL;DR

This paper introduces the Multi-distance Support Matrix Machine (MDSMM), a novel classifier that captures intrinsic correlations in matrix data using multi-distance measures, with theoretical analysis and extensive experiments demonstrating its effectiveness.

Contribution

The paper proposes MDSMM, a new matrix classifier leveraging multi-distance measures for correlation capture, along with generalization bounds and empirical validation.

Findings

MDSMM achieves faster learning rates than traditional classifiers.

The method effectively captures intra-matrix correlations.

Experimental results show superior performance on real-world datasets.

Abstract

Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression matrix to be low-rank or sparse. Some other methodologies introduce factorization technique to explore nonlinear relationships of matrix data in kernel space. In this paper, we propose a multi-distance support matrix machine (MDSMM), which provides a principled way of solving matrix classification problems. The multi-distance is introduced to capture the correlation within matrix data, by means of intrinsic information in rows and columns of input data. A complex hyperplane is established upon these values to separate distinct classes. We further study the generalization bounds for i.i.d. processes and non i.i.d. process based on both SVM and SMM classifiers. For typical hypothesis classes where matrix norms are constrained, MDSMM achieves a faster learning rate than traditional classifiers. We also provide a more general approach for samples without prior knowledge. We demonstrate the merits of the proposed method by conducting exhaustive experiments on both simulation study and a number of real-word datasets.