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Constrained monotone EM algorithms for finite mixture of multivariate Gaussians. (English) Zbl 1445.62116

Summary: The likelihood function for normal multivariate mixtures may present both local spurious maxima and also singularities and the latter may cause the failure of the optimization algorithms. Theoretical results assure that imposing some constraints on the eigenvalues of the covariance matrices of the multivariate normal components leads to a constrained parameter space with no singularities and at least a smaller number of local maxima of the likelihood function. Conditions assuring that an EM algorithm implementing such constraints maintains the monotonicity property of the usual EM algorithm are provided. Different approaches are presented and their performances are evaluated and compared using numerical experiments.

MSC:

62H12 Estimation in multivariate analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62-08 Computational methods for problems pertaining to statistics
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