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
STARS Citation
Hurtado, Michael, "Sparse Low-rank Tensor Logistic Regression with Applications in Neuroimaging" (2025). Graduate Thesis and Dissertation post-2024. 155.
https://stars.library.ucf.edu/etd2024/155