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.

Evidential clustering is an approach to clustering based on the use of Dempster-Shafer mass functions to represent cluster-membership uncertainty. In this paper, we introduce a neural-network based evidential clustering algorithm, called NN-EVCLUS, which learns a mapping from attribute vectors to mass functions, in such a way that more similar inputs are mapped to output mass functions with a lower degree of conflict. The neural network can be paired with a one-class support vector machine to make it robust to outliers and allow for novelty detection. The network is trained to minimize the discrepancy between dissimilarities and degrees of conflict for all or some object pairs. Additional terms can be added to the loss function to account for pairwise constraints or labeled data, which can also be used to adapt the metric. Comparative experiments show the superiority of N-EVCLUS over state-of-the-art evidential clustering algorithms for a range of unsupervised and constrained clustering tasks involving both attribute and dissimilarity data.

Evidential clustering is an approach to clustering in which cluster-membership uncertainty is represented by a collection of Dempster-Shafer mass functions forming an evidential partition. In this paper, we propose to construct these mass functions by bootstrapping finite mixture models. In the first step, we compute bootstrap percentile confidence intervals for all pairwise probabilities (the probabilities for any two objects to belong to the same class). We then construct an evidential partition such that the pairwise belief and plausibility degrees approximate the bounds of the confidence intervals. This evidential partition is calibrated, in the sense that the pairwise belief-plausibility intervals contain the true probabilities "most of the time", i.e., with a probability close to the defined confidence level. This frequentist property is verified by simulation, and the practical applicability of the method is demonstrated using several real datasets.