Robust clustering by deterministic agglomeration EM of mixtures of multivariate t-distributions

摘要

This paper presents new robust clustering algorithms, which significantly improve upon the noise and initialization sensitivity of traditional mixture decomposition algorithms, and simplify the determination of the optimal number of clusters in the data set. The algorithms implement maximum likelihood mixture decomposition of multivariate t-distributions, a robust parametric extension of gaussian mixture decomposition. We achieve improved convergence capability relative to the expectation–maximization (EM) approach by deriving deterministic annealing EM (DAEM) algorithms for this mixture model and turning them into agglomerative algorithms (going through a monotonically decreasing number of components), an approach we term deterministic agglomeration EM (DAGEM). Two versions are derived, based on two variants of DAEM for mixture models. Simulation studies demonstrate the algorithms’ performance for mixtures with isotropic and non-isotropic covariances in two and 10 dimensions with known or unknown levels of outlier contamination.