Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman–Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some tasks, this assumption is undesirable. For exam...

Estimation of the number components (or order) a finite mixture model is long standing and challenging problem in statistics. We propose Group-Sort-Fuse (GSF) procedure—a new penalized likelihood approach for simultaneous estimation order mixing measure multidimensional models. Unlike methods which fit compare mixtures with varying orders using criteria involving complexity, our directly penali...

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent...

Mixture Model Averaging for Clustering Yuhong Wei University of Guelph, 2012 Advisor: Dr. Paul D. McNicholas Model-based clustering is based on a finite mixture of distributions, where each mixture component corresponds to a different group, cluster, subpopulation, or part thereof. Gaussian mixture distributions are most often used. Criteria commonly used in choosing the number of components in...

Consider the task of summarizing the data in Figure 1. A common technique for performing this task is to use a statistical model known as a mixture model. Relative to many other models for estimating densities, mixture models have a number of advantages. First, mixture models can summarize data that contain multiple modes. In this sense, they are more powerful than distributions from the expone...