The mixed-nirn orixunal support vector classifier (M-PSVC)

Abstract

Support vector machines (SVMs) have been recognized as one of the most powerful tools for machine learning, pattern classi¯cation, and function estimation. A num- ber of di®erent variations for the SVMs have been pro- posed, such as the º-SVM, least-squares SVM, proxi- mal SVM (PSVM), reduced SVM (RSVM), Lagrangian SVM (LSVM), etc. This paper addresses the issue of generalization of the proximal SVM. We propose a mixed-norm proximal support vector classi¯er (referred to as the m-PSVC) that combines the characteristics of 1-norm and 2-norm classi¯cation errors jointly. Us- ing the method of Lagrange multipliers, we derived a form suitable for e±cient implementation. It is found that the decision boundary of the m-PSVC concides with that of the PSVC exactly, while the classi¯ca- tion margin of the former is proportional to the factor. Some demonstrative examples are given to show the relations among the newly developed m- PSVC, standard PSVC, and conventional LS-SVC.