A Support Vector Method for Clustering

Abstract

We present a novel method for clustering using the support vector ma(cid:173) chine approach. Data points are mapped to a high dimensional feature space, where support vectors are used to define a sphere enclosing them. The boundary of the sphere forms in data space a set of closed contours containing the data. Data points enclosed by each contour are defined as a cluster. As the width parameter of the Gaussian kernel is decreased, these contours fit the data more tightly and splitting of contours occurs. The algorithm works by separating clusters according to valleys in the un(cid:173) derlying probability distribution, and thus clusters can take on arbitrary geometrical shapes. As in other SV algorithms, outliers can be dealt with by introducing a soft margin constant leading to smoother cluster bound(cid:173) aries. The structure of the data is explored by varying the two parame(cid:173) ters. We investigate the dependence of our method on these parameters and apply it to several data sets.