Learning the number of gaussian components using hypothesis test

Abstract

This paper addresses the problem of estimating the correct number of components in a Gaussian mixture given a sample data set. In particular, an extension of Gaussianmeans (G-means) and Projected Gaussian-means (PG-means) algorithms is proposed. All these methods are based on onedimensional statistical hypothesis test. G-means and PG-means are wrapper algorithms of the k-means and ExpectationMaximization (EM) algorithms, respectively. Although G-means is a simple and fast algorithm, it does not perform well when clusters overlap since it is based on k-means. PG-means can handle overlapped clusters but requires more computation and sometimes fails to find the right number of clusters.In this paper, we propose an extension, called Extended Projected Gaussian means (XPG-means). XPG-means is a wrapper algorithm of Possibilistic Fuzzy C-means (PFCM) algorithm. XPG-means integrates the advantages of both algorithms while resolving some of the disadvantages involving overlapped clusters, noise, and computational complexity. More specifically, XPG-means handles overlapped clusters better than G-means because of the use of fuzzy clustering, handles noise better than both algorithms because it uses possibilitistic clustering. XPG-means is less computationally expensive than PG-means because it uses local hypothesis testing scheme used by G-means that is specific to Gaussians wherease PG-means uses a more general Kolmogorov-Smirnow test on Gaussian mixtures. In addition, XPG-means demonstrates less variance in estimating the number of components than either of the other algorithms.