  The Gaussian mixture model (GMM) provides a simple 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 simple as the classical GMM,
but can generate a more informative evidential partition for the considered
dataset. The synthetic and real dataset experiments show that the proposed EGMM
performs better than other representative clustering algorithms. Besides, its
superiority is also demonstrated by an application to multi-modal brain image
segmentation.
