2023/09/24 by Duc‐Toan Nguyen, Nguyen, Duc Toan, Eric C. Chi +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Computation (stat.CO) #FOS: Computer and information sciences #Face and Expression Recognition #Gene expression and cancer classification #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2309.13733
openalex publication_date 2023/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF for the identifiable recovery of rank-deficient matrices in the presence of noise. The performance of their formulation, however, requires the selection of a tuning parameter whose optimal value depends on the unknown noise level. In this work, we propose an alternative formulation of minimum-volume NMF inspired by the square-root lasso and its tuning-free properties. Our formulation also requires the selection of a tuning parameter, but its optimal value does not depend on the noise level. To fit our NMF model, we propose a majorization-minimization (MM) algorithm that comes with global convergence guarantees. We show empirically that the optimal choice of our tuning parameter is insensitive to the noise level in the data.