Finite mixture models estimation with a credal EM algorithm

This paper is concerned with finite mixture models estimation in the framework of Transferable Belief Model. This model relies on a non probabilistic formalism for representing and manipulating imprecise and uncertain information with belief functions. Within this framework, a credal EM algorithm, a variant of classical EM algorithm based on belief functions, is introduced for finite mixture parameters learning. This algorithm can be applied in several situations where available information on the data generation model is partially known. In the learning problem, this knowledge is represented with belief functions which allow to represent as better as possible the uncertainty on the component from where each observation has been generated. Several experimentations highlight situations where the algorithm is applied when available information on the learning set is imprecise (partially supervised learning where the actual component of each sample is only known as belonging to a subset of components), and/or uncertain (unsupervised learning where the knowledge about the actual sample is represented by a belief function), Synthetic data sets allow us to demonstrate the good performance of the proposed approach based on estimated parameters analysis and learning with gaussian finite mixture models.