Parallel Implementations of Parsimonious Gaussian Mixture Models and Extensions

Abstract

Cluster analysis is the process of finding underlying group structures in a set of data. Model-based clustering has an array of swiftly growing literature surrounding this topic; however, a Gaussian mixture model has always been a prevalent model in model-based clustering literature. More specially, when dealing with high-dimensional data, the parsimonious Gaussian mixture model has shown great computational efficiency because the number of covariance parameters is linear with the number of variables for each model in the family. Parsimonious Gaussian mixture models generalize the mixture of factor analyzers model. For each group, the number of factors q has traditionally been held constant. An extension to the parsimonious Gaussian mixture model family is developed allowing q to be a vector of equal length to the number of components. Although the parsimonious Gaussian mixture model family has shown great computational potential, this new extension takes away from the aforementioned feat with rapidly growing parameter combinations to fit. Parallel computational techniques are explored throughout this thesis to improve computational runtime and allow the rapidly growing number of parameter combinations to be fit in a realistic time frame, especially in the case of high-dimensional data. The techniques are applied to real data to assess performance and computational efficiency.