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Adaptive Prototype-Based Classification via Graph Theoretic and Topological Methods


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dc.contributor.advisorCeyhan, Elvan
dc.contributor.authorEckert, Jordan
dc.date.accessioned2025-07-31T18:47:10Z
dc.date.available2025-07-31T18:47:10Z
dc.date.issued2025-07-31
dc.identifier.urihttps://etd.auburn.edu/handle/10415/9925
dc.description.abstractIn 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.rightsEMBARGO_GLOBALen_US
dc.subjectMathematics and Statisticsen_US
dc.titleAdaptive Prototype-Based Classification via Graph Theoretic and Topological Methodsen_US
dc.typePhD Dissertationen_US
dc.embargo.lengthMONTHS_WITHHELD:12en_US
dc.embargo.statusEMBARGOEDen_US
dc.embargo.enddate2026-07-31en_US
dc.contributor.committeeBillor, Nedret
dc.contributor.committeeSchenck, Hal
dc.contributor.committeeZheng, Jingyi
dc.creator.orcid0000-0003-0873-5952en_US

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