Finding the Number of Clusters for Nonparametric Segmentation

Non-parametric data representation can be done by means of a potential function. This paper introduces a methodology for finding modes of the potential function. Two different methods are considered for the potential function representation: by using summations of Gaussian kernels, and by employing quantum clustering. In the second case each data sample is associated with a quantum physics particle that has a radial energy field around its location. Both methods use a scaling parameter (bandwidth) to model the strength of the influence around each data sample. We estimate the scaling parameter as the mean of the Gamma distribution that models the variances of K-nearest data samples to any given data. The local Hessian is used afterwards to find the modes of the resulting potential function. Each mode is associated with a cluster. We apply the proposed algorithm for blind signal separation and for the topographic segmentation of radar images of terrain.