Date of Award

Spring 5-9-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Applied Mathematics

First Advisor

Stephen Becker

Second Advisor

Jem Corcoran

Third Advisor

Manuel Lladser

Fourth Advisor

David Bortz

Fifth Advisor

Farhad Pourkamali Anaraki

Abstract

This thesis consists of three distinct projects. The first is a study of microbial aggregate fragmentation, in which we develop a dynamical model of aggregate deformation and breakage and use it to obtain a post-fragmentation density function. The second and third projects deal with dimensionality reduction in machine learning problems. In the second project, we derive a one-pass sparsified Gaussian mixture model to perform clustering analysis on high-dimensional streaming data. The model estimates parameters in dense space while storing and performing computations in a compressed space. In the final project, we build an expert system classifier with a Bayesian network for use on high-volume streaming data. Our approach is specialized to reduce the number of observations while obtaining sufficient labeled training data in a regime of extreme class-imbalance and expensive oracle queries.

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