Graduation Semester and Year

Fall 2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dr. Ren-Cang Li

Second Advisor

Dr. Li Wang

Third Advisor

Dr. Keaton Hamm

Fourth Advisor

Dr. Shan Sun-Mitchell

Abstract

As the digital world continues to grow in the age of big data, there beckons a need for efficient and robust methods for data exploration. Under the umbrella of machine learning, feature selection positions itself as a fruitful approach that uncovers buried truths and illuminates important features of data, all while minimizing long-term storage requirements. In this work, we introduce a set of novel single-view and multi-view supervised feature selection models which are embedded with orthogonality constraints to maintain data's structural integrity while confining the optimal solution's search space.

Taking advantage of the underlying framework of these types of models, researchers have recently reformulated them as eigenvector and eigenvalue problems. Tapping into the extensively researched realm of numerical linear algebra, we solve these models with highly efficient and theoretically driven spectral theory based methods, and perform numerical experiments to compare our models with state-of-the-art feature selection techniques.

Keywords

orthogonal, feature selection, data science, self consistent field iteration, eigenvalue, eigenvector, machine learning, dimensionality reduction

Disciplines

Data Science | Numerical Analysis and Computation | Numerical Analysis and Scientific Computing | Other Mathematics

License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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Available for download on Friday, October 30, 2026

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