Date of Award
Doctor of Philosophy (PhD)
Farhad Pourkamali Anaraki
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.
Kightley, Eric P., "Stokes, Gauss, and Bayes walk into a bar..." (2019). Applied Mathematics Graduate Theses & Dissertations. 144.