Data-Driven Algorithms for Generalized Low-Rank Matrix Recovery

Author

• Chandra S. Kundu, University of Central FloridaFollow

ORCID

0000-0001-8967-0593

Keywords

Euclidean distance geometry; robust matrix completion; deep unfolding; hyperspectral imaging; ultrasound imaging;

Abstract

Generalized low-rank matrix recovery is a fundamental statistical tool that provides a unifying framework for important data science problems such as Euclidean distance geometry, robust principal component analysis, and matrix completion. It arises in applications such as sensor localization, molecular conformation, ultrasound imaging, video processing, and hyperspectral imaging. In these applications, data are often incomplete, corrupted by outliers, and governed by inherent geometrical patterns such as triangle inequalities due to hardware limitations, cost constraints, and physical phenomena. A central challenge is designing scalable, theoretically grounded methods that can effectively impute missing entries, provide robust outlier tolerance, exploit structural and geometric properties, and leverage data-driven adaptation. This dissertation develops theoretical and algorithmic frameworks for generalized low-rank recovery across these settings. First, we study Euclidean distance geometry in an anchor-target model, where the goal is to estimate point configurations from partially observed and corrupted distance measurements. We develop SREDG, a provable method that combines Nyström reconstruction with robust PCA to recover point configurations from limited anchor information in the presence of outliers. The approach is further advanced through RoDEoDB, which employs a non-orthogonal dual-basis formulation that operates directly on Gram matrix blocks to relax challenging constraints, thereby improving robustness and recoverability. Both methods consistently demonstrate accurate recovery in sensor localization and molecular conformation tasks. Next, for robust matrix completion that simultaneously handles randomly missing entries and outliers, we propose LRMC, a learnable framework with low computational complexity and guaranteed linear convergence. Its performance can be improved through data-driven training with deep unfolding. We also develop WMCSGD, which efficiently incorporates prior subspace information through a weighted formulation. A machine learning strategy is used to predict near-optimal weights, significantly improving recovery performance in scenarios with shared prior information. Both methods achieve superior performance compared with state-of-the-art methods on various real-world datasets.

Completion Date

2026

Semester

Spring

Committee Chair

Cai, HanQin

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

School of Data, Mathematical, and Statistical Sciences

Format

PDF

Document Type

Dissertation

Identifier

DP0053285

Release Date

5-15-2027

STARS Citation

Kundu, Chandra S., "Data-Driven Algorithms for Generalized Low-Rank Matrix Recovery" (2026). Graduate Studies Theses and Dissertations 2026. 100.
https://stars.library.ucf.edu/gradstudies_etd_2026/100