Keywords

Quantum Computing, Least Squares Support Vector Data Description, Kernel Methods, One-Class Classification, Harrow-Hassidim Lloyd Algorithm

Abstract

Kernel-based one-class classification (OCC) methods leverage kernel functions and are widely used for anomaly detection due to their ability to map data into high-dimensional feature spaces. One such model is Least Squares Support Vector Data Description (LS-SVDD), which aims to construct a minimum volume hypersphere that encompasses the target class observations. A pivotal component in the construction of the hypersphere is the choice of kernel. In this study, the Radial Basis Function (RBF) kernel is compared to a quantum kernel constructed through quantum feature maps. The two kernel methods are compared across four distributional shift scenarios—mean shift, rotating covariance, correlation drift, and Gaussian mixture—at three dimensionalities through simulations. Additionally, the two kernel methods are also evaluated using real-world data through an illustrative example. Furthermore, the Harrow-Hassidim-Lloyd (HHL) quantum algorithm was examined as a potential speedup for solving linear systems of equations within the LS-SVDD framework in quantum space.

Completion Date

2026

Semester

Spring

Committee Chair

Maboudou, Edgard

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Statistics & Data Science

Document Type

Dissertation/Thesis

Identifier

DP0053272

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