Constrained monotone EM algorithms for mixtures of multivariate t distributions
- 234 Downloads
Mixtures of multivariate t distributions provide a robust parametric extension to the fitting of data with respect to normal mixtures. In presence of some noise component, potential outliers or data with longer-than-normal tails, one way to broaden the model can be provided by considering t distributions. In this framework, the degrees of freedom can act as a robustness parameter, tuning the heaviness of the tails, and downweighting the effect of the outliers on the parameters estimation. The aim of this paper is to extend to mixtures of multivariate elliptical distributions some theoretical results about the likelihood maximization on constrained parameter spaces. Further, a constrained monotone algorithm implementing maximum likelihood mixture decomposition of multivariate t distributions is proposed, to achieve improved convergence capabilities and robustness. Monte Carlo numerical simulations and a real data study illustrate the better performance of the algorithm, comparing it to earlier proposals.
KeywordsFinite mixture models EM algorithm t Distribution Clustering
Unable to display preview. Download preview PDF.
- Biernacki, C.: (2004). An asymptotic upper bound of the likelihood to prevent Gaussian mixture from degenerating. Technical report, Université de Franche-Comté Google Scholar
- Greselin, F., Ingrassia, S.: A note on constrained EM algorithms for mixtures of elliptical distributions. In: Advances in Data Analysis, Data Handling and Business Intelligence, Proceedings of 32nd Annual Conference of German Classification Society, 53 (2008) Google Scholar