A Multi-class Support Vector Machine Based on Geometric Margin Maximization

• Published in: Integrated Uncertainty in Knowledge Modelling and Decision Making pp. 101 - 113
• Main Authors: Kusunoki, Yoshifumi, Tatsumi, Keiji
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Class Pairs; Geometric Margin Maximization; Multi-class SVM; Sample Example; Support Vector Machine (SVM)
• ISBN: 9783319754284; 3319754289
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-75429-1_9

Support vector machines (SVMs) are popular supervised learning methods. The original SVM was developed for binary classification. It selects a linear classifier by maximizing the geometric margin between the boundary hyperplane and sample examples. There are several extensions of the SVM for multi-class classification problems. However, they do not maximize geometric margins exactly. Recently, Tatsumi and Tanino have proposed multi-objective multi-class SVM, which simultaneously maximizes the margins for all class pairs. In this paper, we propose another multi-class SVM based on the geometric margin maximization. The SVM is formulated as minimization of the sum of inverse-squared margins for all class pairs. Since this is a nonconvex optimization problem, we propose an approximate solution. By numerical experiments, we show that the propose SVM has better performance in generalization capability than one of the conventional multi-class SVMs.