Pattern Classification via Single Spheres

Previous sphere-based classification algorithms usually need a number of spheres in order to achieve good classification performance. In this paper, inspired by the support vector machines for classification and the support vector data description method, we present a new method for constructing single spheres that separate data with the maximum separation ratio. In contrast to previous methods that construct spheres in the input space, the new method constructs separating spheres in the feature space induced by the kernel. As a consequence, the new method is able to construct a single sphere in the feature space to separate patterns that would otherwise be inseparable when using a sphere in the input space. In addition, by adjusting the ratio of the radius of the sphere to the separation margin, it can provide a series of solutions ranging from spherical to linear decision boundaries, effectively encompassing both the support vector machines for classification and the support vector data description method. Experimental results show that the new method performs well on both artificial and real-world datasets.