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Activity Number: 534
Type: Contributed
Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #316480
Title: Flexible Functional Clustering Using Dirichlet Processes
Author(s): Christoph Hellmayr* and Alan Gelfand
Companies: Duke University and Duke University
Keywords: Functional Data ; Clustering ; Bayesian Nonparametrics ; Dirichlet Process ; Gaussian Process
Abstract:

Clustering as a technique is regularly employed in a variety of contexts, most often in exploratory data analysis. Clustering using a statistical model can be achieved by employing Dirichlet process mixtures over the quantities to be clustered. In a Bayesian setting using conjugate priors a Gibbs sampler can be built that results in a very natural idea of "clustering" - a latent class structure is built into the sampler that assigns each observation to a realization of the Dirichlet process mixture at each iteration of the sampler. We consider clustering multivariate function data, i.e., model based clustering where each observation is a collection of surfaces. We model multivariate functional data by using an appropriate multivariate Gaussian process as a basis function for the Dirichlet process. This framework enables prediction of new observations and interpolation at unobserved points in the underlying input space. We explore the usefulness and problems that arise in this method through a number of simulation studies. We also use it on two real data sets, comparing it to other methods for multivariate functional clustering.


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