Bayesian variable selection in clustering via dirichlet process mixture models

Abstract

The increased collection of high-dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures. In this disserta- tion, I propose a model-based method that addresses the two problems simultane- ously. I use Dirichlet process mixture models to define the cluster structure and to introduce in the model a latent binary vector to identify discriminating variables. I update the variable selection index using a Metropolis algorithm and obtain inference on the cluster structure via a split-merge Markov chain Monte Carlo technique. I evaluate the method on simulated data and illustrate an application with a DNA microarray study. I also show that the methodology can be adapted to the problem of clustering functional high-dimensional data. There I employ wavelet thresholding methods in order to reduce the dimension of the data and to remove noise from the observed curves. I then apply variable selection and sample clustering methods in the wavelet domain. Thus my methodology is wavelet-based and aims at clustering the curves while identifying wavelet coefficients describing discriminating local features. I exemplify the method on high-dimensional and high-frequency tidal volume traces measured under an induced panic attack model in normal humans.