Robust Multicategory Support Vector Machines using Difference Convex Algorithm.

TitleRobust Multicategory Support Vector Machines using Difference Convex Algorithm.
Publication TypeJournal Article
Year of Publication2018
AuthorsZhang, Chong, Minh Pham, Sheng Fu, and Yufeng Liu
JournalMath Program
Volume169
Issue1
Pagination277-305
Date Published2018 May
ISSN0025-5610
Abstract

The Support Vector Machine (SVM) is one of the most popular classification methods in the machine learning literature. Binary SVM methods have been extensively studied, and have achieved many successes in various disciplines. However, generalization to Multicategory SVM (MSVM) methods can be very challenging. Many existing methods estimate functions for classes with an explicit sum-to-zero constraint. It was shown recently that such a formulation can be suboptimal. Moreover, many existing MSVMs are not Fisher consistent, or do not take into account the effect of outliers. In this paper, we focus on classification in the angle-based framework, which is free of the explicit sum-to-zero constraint, hence more efficient, and propose two robust MSVM methods using truncated hinge loss functions. We show that our new classifiers can enjoy Fisher consistency, and simultaneously alleviate the impact of outliers to achieve more stable classification performance. To implement our proposed classifiers, we employ the difference convex algorithm (DCA) for efficient computation. Theoretical and numerical results obtained indicate that for problems with potential outliers, our robust angle-based MSVMs can be very competitive among existing methods.

Alternate JournalMath Program
Original PublicationRobust multicategory support vector machines using difference convex algorithm.
PubMed ID29736090
PubMed Central IDPMC5935468
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 GM126550 / GM / NIGMS NIH HHS / United States
Project: