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Analysis of the maximal posterior partition in the Dirichlet Process Gaussian Mixture Model. (arXiv:1606.03275v2 [math.ST] UPDATED)
来源于:arXiv
Mixture models are a natural choice in many applications, but it can be
difficult to place an apriori upper bound on the number of components. To
circumvent this, investigators are turning increasingly to Dirichlet process
mixture models (DPMMs) and, more generally, Pitman-Yor mixtures. These models
are well suited to Bayesian density estimation. An interesting question is
whether they can be turned to the problem of {\em classification} or {\em
clustering}, which involves allocating observations to clusters. This is
becoming increasingly widely used among investigators. This article considers
the MAP (maximal posterior partition) clustering for the Gauss-Gauss DPM (where
the cluster means have Gaussian distribution and, for each cluster, the
observations within the cluster have Gaussian distribution; the number and
sizes of the clusters generated according to a Chinese Restaurant Process). It
is proved that the convex hulls of the clusters created by the MAP are pairwise
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