Unsupervised fuzzy model-based Gaussian clustering

Abstract

In 1993, Banfield and Raftery first proposed model-based Gaussian (MB-Gauss) clustering, using eigenvalue decomposition of Gaussian covariance matrix to detect different cluster shapes. In this paper, we extend MB-Gauss to a fuzzy model-based Gaussian (F-MB-Gauss) clustering. However, the performance of both MB-Gauss and F-MB-Gauss algorithms depend heavily on initializations and require a number of clusters to be assigned a priori. To solve these problems, an unsupervised learning schema for F-MB-Gauss clustering is proposed. Therefore, an unsupervised fuzzy model-based Gaussian (UF-MB-Gauss) clustering algorithm is constructed where the proposed UF-MB-Gauss algorithm not only solves the initialization problem, but can also automatically obtain an optimal number of clusters. In the literature, MB-Gauss with Bayesian information criterion (BIC) is a common way for determining the number of clusters for Gaussian mixtures. Furthermore, several clustering methods that can automatically determine the number of clusters have been proposed in the literature. Therefore, comparison is made between the proposed UF-MB-Gauss clustering algorithm and these related clustering methods using numerical data and real data sets. Experimental results and comparisons demonstrate the superiority and usefulness of the proposed UF-MB-Gauss clustering algorithm.