Author ORCID Identifier
0000-0002-0724-699X
Defense Date
2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematical Sciences
First Advisor
Dr. Anh T. Bui
Second Advisor
Dr. Chenlu Ke
Third Advisor
Dr. Yanjun Qian
Fourth Advisor
Dr. Mohammad Shadab Siddiqui
Abstract
High-dimensional data analysis presents diverse challenges, including the curse of dimensionality, the complexities of working with datasets that combine large feature spaces with limited sample sizes, and difficulties in identifying meaningful relationships among variables. As datasets grow in size and complexity across different fields, it is increasingly important to develop practical approaches for extracting essential information from such data. Dimension reduction methods address these challenges by alleviating the effects of high dimensionality, enhancing the ability to reveal hidden patterns, and uncovering latent structures within the data to support further analysis. Some methods reduce dimensionality while preserving all relevant information, offering insights into the structure of high-dimensional data. Others aim to identify latent factors that explain variability within the data, providing a deeper understanding of complex trends.
One primary contribution is the development of a local support vector machine-based dimension reduction framework. This methodology handles continuous and binary responses, as well as linear and nonlinear reduction, in a unified framework. By utilizing localization, the method relaxes stringent probabilistic assumptions required by global methods. Numerical experiments and real-world data applications demonstrate its efficacy in preserving relevant information while effectively reducing dimensionality.
The research further addresses the challenge of identifying unknown part-to-part variation sources in custom manufacturing processes. By developing a variation model estimated via a conditional autoencoder, the study enables the discovery of unanticipated variation patterns even with limited sample sizes from different designs. This approach successfully reveals critical interactions between latent variation sources and manufacturing parameters, providing a practical tool for variation reduction in low-volume production.
Additionally, the dissertation explores the application of generative artificial intelligence in healthcare by defining clinical trajectories. High-dimensional weight records of liver transplantation patients are transformed into interpretable latent factors to capture essential temporal patterns. This approach not only highlights the hidden structure within clinical data but also provides a basis for investigating potential contributors to post-surgery weight outcomes. Collectively, these projects provide innovative frameworks for extracting essential information from complex datasets to solve real-world problems.
Rights
© The Author, Linxi Li
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
5-5-2026