Work

Penalizing Low-Rank Matrix Factorization: From theoretical connections to practical applications

Year: 2025

Type: article

Abstract: Low-rank (LR) factorization techniques aim to represent data in a low-dimensional space by identifying fundamental sources. Standard LR approaches often require additional constraints to account for real-world complexity, resulting in penalized low-rank matrix factorizations . These techniques incorporate penalties or regularization terms to improve robustness and adaptability to practical constraints, bridging theoretical research with real-world applications. This paper explores a nonnegative constrained low-rank decomposition technique, namely, Nonnegative Matrix Factorization (NMF), and its constrained variants as powerful tools for analyzing nonnegative data. We cover theoretical foundations and practical implementations, review algorithms for standard NMF, and address challenges in setting hyperparameters for penalized variants. We emphasize applications in omics data analysis with a model that incorporates biological constraints to extract meaningful insights, and highlight applications in environmental data analysis.

Source: Journal of Computational Mathematics and Data Science

DOI: 10.1016/j.jcmds.2025.100111

Authors: Nicoletta Del Buono, Flavia Esposito, Laura Selicato

Institutions: University of Bari Aldo Moro, Water Research Institute, National Research Council

Language: English

Topic: Face and Expression Recognition

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,070

Funder: Universita degli Studi di Bari Aldo Moro