Keywords

Discriminant Analysis, Tucker Decomposition, Low-Rank Regularization

Abstract

Robust discriminant analysis with optimal scoring has been shown effective for classifying high-dimensional matrix data, particularly in the context of two-dimensional images. The proposed method presents an extension of the Multi-Projection Optimal Scoring Discriminant Analysis framework introduced by Huang \& Zhang (2020), incorporating low-rank Tucker decomposition and regularization techniques to address higher-dimensional cases. The enhanced method is designed to effectively handle tensor-structured data, which is prevalent in imaging applications. The model creates a sparse discriminant projection tensor B that captures class-specific features, such as ball-like patterns in image data and indicators of Alzheimer’s disease in Magnetic Resonance Imaging (MRI) scans. A robust loss function is employed to mitigate the impact of noise and improve convergence stability within the model. Experimental results using synthetic image datasets of ball images with noisy backgrounds and OASIS neuroimaging data demonstrate significantly improved performance in high-dimensional settings, which is supported by numerical evaluations and diagnostic visualizations.

Completion Date

2025

Semester

Fall

Committee Chair

Hsin-Hsiung Huang

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Statistics

Format

PDF

Identifier

DP0029822

Document Type

Thesis

Campus Location

Orlando (Main) Campus

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