An EM Algorithm for Mixtures of Hyperspheres

Abstract

This paper studies a new expectation maximization (EM) algorithm to estimate the centers and radii of multiple hyperspheres. The proposed method introduces latent variables indicating to which hypersphere each vector from the dataset belongs to, in addition to random latent vectors having an a priori von Mises-Fisher distribution characterizing the location of each vector on the different hyperspheres. This statistical model allows a complete data likelihood to be derived, whose expected value conditioned on the observed data has a known distribution. This property leads to a simple and efficient EM algorithm whose performance is evaluated for the estimation of hypersphere mixtures yielding promising results.