Bayes classification based on minimum bounding spheres

Abstract

The minimum bounding sphere of a set of data, defined as the smallest sphere enclosing the data, was first used by Schölkopf et al. to estimate the VC-dimension of support vector classifiers and later applied by Tax and Duin to data domain description. Given a set of data, the minimum bounding sphere of each class can be computed by solving a quadratic programming problem. Since the spheres are constructed for each class separately, they can be used to deal with the multi-class classification problem easily, as proposed by Zhu et al. In this paper, we show that the decision rule proposed by Zhu et al. is generally insufficient to achieve the state-of-the-art classification performance. We, therefore, propose a new decision rule based on the Bayes decision theory. This new decision rule significantly improves the performance of the resulting sphere-based classifier. In addition to its low computational complexity and easy expandability to multi-class problems, the new classifier achieves comparable performance to the standard support vector machines on most of the real-world data sets being tested.