Bayesian estimation of Kernel bandwidth for nonparametric modelling

Abstract

Kernel density estimation (KDE) has been used in many computational intelligence and computer vision applications. In this paper we propose a Bayesian estimation method for finding the bandwidth in KDE applications. A Gamma density function is fitted to distributions of variances of K-nearest neighbours data populations while uniform distribution priors are assumed for K. A maximum log-likelihood approach is used to estimate the parameters of the Gamma distribution when fitted to the local data variance. The proposed methodology is applied in three different KDE approaches: kernel sum, mean shift and quantum clustering. The third method relies on the Schrödinger partial differential equation and uses the analogy between the potential function that manifests around particles, as defined in quantum physics, and the probability density function corresponding to data. The proposed algorithm is applied to artificial data and to segment terrain images. © 2009 Springer Berlin Heidelberg.