Splitting Method for Support Vector Machine with Lower Semi-continuous Loss

TL;DR

This paper introduces a splitting method based on the alternating direction method of multipliers for support vector machines with lower semi-continuous loss functions, proving convergence and demonstrating effectiveness through experiments.

Contribution

The paper develops a novel splitting algorithm for SVMs with lower semi-continuous loss, establishing global convergence using Kurdyka-Lojasiewicz inequality.

Findings

The iterative sequence converges globally to a stationary point.

Numerical experiments confirm the method's effectiveness.

The approach applies to a broad class of loss functions.

Abstract

In this paper, we study the splitting method based on alternating direction method of multipliers for support vector machine in reproducing kernel Hilbert space with lower semi-continuous loss function. If the loss function is lower semi-continuous and subanalytic, we use the Kurdyka-Lojasiewicz inequality to show that the iterative sequence induced by the splitting method globally converges to a stationary point. The numerical experiments also demonstrate the effectiveness of the splitting method.