EGMM: an Evidential Version of the Gaussian Mixture Model for Clustering

The Gaussian mixture model (GMM) provides a convenient yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM), in the theoretical framework of belief functions to better characterize cluster-membership uncertainty. With a mass function representing the cluster membership of each object, the evidential Gaussian mixture distribution composed of the components over the powerset of the desired clusters is proposed to model the entire dataset. The parameters in EGMM are estimated by a specially designed Expectation-Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as convenient as the classical GMM, but can generate a more informative evidential partition for the considered dataset. Experiments with synthetic and real datasets demonstrate the good performance of the proposed method as compared with some other prototype-based and model-based clustering techniques.