Electronic Theses and Dissertations Archive

Date

2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Committee Chair

Bentuo Zheng

Committee Member

Ching-Chi Yang

Committee Member

Irena Lasiecka

Committee Member

Lih-Yuan Deng

Committee Member

Majid Noroozi

Abstract

The standard Radial Basis Function (RBF) kernel assigns equal importance to all features, which may be suboptimal when features differ in their ability to separate classes. To address this limitation, this dissertation introduces the Self-Weighted INput-Guided (SWING) kernel, a feature-weighted RBF kernel with a rigorous theoretical foundation. Under Gaussian assumptions with shared class-conditional covariance, explicit expressions for the expected kernel-target alignment of both the standard RBF kernel and the SWING kernel are derived. Verifiable conditions are established under which the SWING kernel achieves higher expected alignment than the standard RBF kernel, and the existence of an optimal weight vector is proven. To implement the proposed framework, the SWING algorithm is developed to select feature weights via alignment maximization. Extensive simulation studies under both independent and dependent feature settings demonstrate that the SWING kernel consistently outperforms the standard RBF kernel, yielding statistically significant improvements in classification accuracy ranging from 0.5% to 5%. This work provides both theoretical guarantees and a practical optimization procedure for feature-weighted kernel learning, with applications in educational assessment, learning analytics, and other binary classification problems involving features with unequal discriminative power.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to ProQuest/Clarivate.

Notes

Open Access

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