Keywords

Low Rank Regularization, Discriminant Analysis, OASIS, ADNI

Abstract

Discriminant analysis techniques, while extensively studied for traditional datasets, have rarely been adapted to address the complexities of high-dimensional tensor data. Recent advances in tensor decomposition, as reviewed by Burch et al. (2025), highlight methods such as CP, Tucker, HOSVD, and t-SVD, which offer robust frameworks for handling multi-dimensional biomedical data, including neuroimaging. In this paper, we propose a novel approach that integrates low-rank regularization techniques with tensor structures to tackle high-dimensional matrix and tensor data. Building on the Multi-Projection Optimal Scoring Discriminant Analysis (ROSDA) method by Huang & Zhang (2020), which employs multi-directional projection pursuit for robust classification, our method leverages Tucker decomposition to enforce low-rank constraints, enhancing scalability and interpretability. We validate the proposed techniques using real neuroimaging datasets from Alzheimer’s patients, sourced from the Open Access Series of Imaging Studies (OASIS) and the Alzheimer’s Disease Neuroimaging Initiative (ADNI), demonstrating their efficacy in capturing latent patterns in high-dimensional biomedical data.

Completion Date

2025

Semester

Spring

Committee Chair

Huang, Hsin-Hsiung

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Statistics and Data Science

Identifier

DP0029323

Document Type

Dissertation/Thesis

Campus Location

Orlando (Main) Campus

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