Alternating direction method of multipliers for regularized multiclass support vector machines

TL;DR

This paper extends the ADMM algorithm to solve regularized multiclass SVMs efficiently, providing a scalable and accurate approach for complex classification problems.

Contribution

It introduces an ADMM-based method for regularized MSVMs, enabling efficient solutions for problems previously difficult to formulate and solve.

Findings

High efficiency demonstrated on synthetic and real data

Global convergence guarantees for the proposed algorithms

Accurate solutions for complex multiclass classification tasks

Abstract

The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to these MSVMs. Using a splitting technique, all considered MSVMs are written as two-block convex programs, for which the ADMM has global convergence guarantees. Numerical experiments on synthetic and real data demonstrate the high efficiency and accuracy of our algorithms.