Mixture modeling with compact support distributions for unsupervised learning

Abstract

The importance of the q-Gaussian distributions is attributed to their power law nature and the fact that they generalize the Gaussian distributions (q → 1 retrieves the Gaussian distributions). While for q > 1, a q-Gaussian distribution is nothing but a Student's t-distribution, which is a long tailed distribution, for q < 1 it is a distribution with a compact support. Though mixture modeling with t-distributions has been studied, mixture modeling with compact support distributions has not been explored in the literature. The main aim of this paper is to study mixture modeling using q-Gaussian distributions that have a compact support. We study estimation of the parameters of this model using Maximum Likelihood Estimator (MLE) via Expectation Maximization (EM) algorithm. We further study applications of these compact support distributions to clustering and anomaly detection. As far as our knowledge, this is the first work that studies compact support distributions in statistical modeling for unsupervised learning problems.