Stochastic EM algorithm for mixture estimation on manifolds
This paper presents a novel algorithm for estimating parameters of a mixture of Gaussian laws when data lie in a Riemannian manifold. We consider the stochastic variant of the well-known Expectation-Maximization (EM) algorithm in the case of Riemannian geometry. The Riemannian mixture is devoted, here, to the case of Riemannian manifold of Symmetric Positive Definite (SPD) matrices. With a slight modification, the stochastic EM algorithm developed originally for Euclidean case can also be derived for SPD manifold. We provide some MonteCarlo numerical simulations in order to analyse, in details, the proposed algorithm in comparison with the conventional EM one.