EM algorithm of spherical models for binned data

Abstract

In cluster analysis, dealing with large quantity of data is computational expensive. And binning data can be efficient in solving this problem. In the former study, basing cluster analysis on Gaussian mixture models becomes a classical and powerful approach. EM and CEM algorithm are commonly used in mixture approach and classification approach respectively. According to the parametrization of the variance matrices (allowing some of the features of clusters be the same or different: orientation, shape and volume), 14 Gaussian parsimonious models can be generated. Choosing the right parsimonious model is important in obtaining a good result. According to the existing study, Binned-EM algorithm was performed for the most general and diagonal model. In this paper, we apply binned-EM algorithm on spherical models. Two spherical models are studied and their performances on simulated data are compared. The influence of the size of bins in binned-EM algorithm is analyzed. Practical application is shown by applying on Iris data.