A Theoretical Framework for Multi-sphere Support Vector Data Description

Abstract

In support vector data description (SVDD) a spherically shaped boundary around a normal data set is used to separate this set from abnormal data. The volume of this data description is minimized to reduce the chance of accepting abnormal data. However the SVDD does not guarantee that the single spherically shaped boundary can best describe the normal data set if there are some distinctive data distributions in this set. A better description is the use of multiple spheres, however there is currently no investigation available. In this paper, we propose a theoretical framework to multi-sphere SVDD in which an optimisation problem and an iterative algorithm are proposed to determine model parameters for multi-sphere SVDD to provide a better data description to the normal data set. We prove that the classification error will be reduced after each iteration in this learning process. Experimental results on 28 well-known data sets show that the proposed multisphere SVDD provides lower classification error rate comparing with the standard single-sphere SVDD.