Optimal margin distribution matrix machine

Abstract

As a proficient matrix classifier, Support Matrix Machine (SMM) utilizes the structural information within matrices to achieve remarkable classification results. Recent theoretical advancements have emphasized the importance of optimizing margin distribution (MD) for improving generalization performance. Regrettably, this crucial aspect has been neglected within the framework of the SMM. Furthermore, SMM inherits the hinge loss function from Support Vector Machine (SVM), which has a detrimental impact on its robustness to noise interference. To address these issues, we propose a novel matrix classification method called Optimal Margin Distribution Matrix Machine (ODMM) by introducing a novel MD-based loss function. Our model not only leverages the structural information of the matrix through the low-rank condition but also enhances the generalization performance of the classifier by optimizing the margin distribution. Specifically, we derive the MD-based loss function based on the first-order and second-order statistics of the margin, replacing the traditional hinge loss function in SMM. Additionally, to solve the optimization problem of ODMM, we developed an algorithm based on the Alternating Direction Method of Multipliers (ADMM) framework. Finally, we demonstrate the superior performance of our proposed ODMM through comprehensive comparative experimental analysis.