Adaptive Prototype-Based Classification via Graph Theoretic and Topological Methods
Metadata Field | Value | Language |
---|---|---|
dc.contributor.advisor | Ceyhan, Elvan | |
dc.contributor.author | Eckert, Jordan | |
dc.date.accessioned | 2025-07-31T18:47:10Z | |
dc.date.available | 2025-07-31T18:47:10Z | |
dc.date.issued | 2025-07-31 | |
dc.identifier.uri | https://etd.auburn.edu/handle/10415/9925 | |
dc.description.abstract | In statistical learning, many modern methods represent data using graphs to capture structure and relationships. Among these, class cover catch digraphs (CCCDs) were origi- nally introduced to address the class cover problem (CCP) and have since been applied to classification and clustering tasks. This dissertation addresses two distinct, yet complemen- tary, challenges in statistical learning: (i) classification performance degradation under class imbalance and class overlap, and (ii) reducing data cardinality through a novel, principled prototype selection method. We propose modified CCCD variants that improve robustness and generalization in imbalanced and overlapped class settings while preserving the geomet- ric intuition of the original CCCD framework. These contributions enhance the practical utility of CCCD classifiers. In addition, we introduce a topological data analysis (TDA)- based framework for selecting representative subsets (prototypes) from large datasets. We show that this approach preserves classification performance while substantially reducing data size. Such methods are crucial in resource-constrained environments where memory and computation are limited. Together, these contributions advance both algorithmic and geometric aspects of prototype learning and offer practical tools for scalable, interpretable, and efficient classification. | en_US |
dc.rights | EMBARGO_GLOBAL | en_US |
dc.subject | Mathematics and Statistics | en_US |
dc.title | Adaptive Prototype-Based Classification via Graph Theoretic and Topological Methods | en_US |
dc.type | PhD Dissertation | en_US |
dc.embargo.length | MONTHS_WITHHELD:12 | en_US |
dc.embargo.status | EMBARGOED | en_US |
dc.embargo.enddate | 2026-07-31 | en_US |
dc.contributor.committee | Billor, Nedret | |
dc.contributor.committee | Schenck, Hal | |
dc.contributor.committee | Zheng, Jingyi | |
dc.creator.orcid | 0000-0003-0873-5952 | en_US |