Bayesian non-negative matrix factorization with adaptive sparsity and smoothness prior

0500888 - ÚTIA 2020 RIV US eng J - Journal Article
Tichý, Ondřej - Bódiová, Lenka - Šmídl, Václav
Bayesian non-negative matrix factorization with adaptive sparsity and smoothness prior.
IEEE Signal Processing Letters. Roč. 26, č. 3 (2019), s. 510-514. ISSN 1070-9908. E-ISSN 1558-2361
R&D Projects: GA ČR GA18-07247S
Institutional support: RVO:67985556
Keywords : Non-negative matrix factorization * Covariance matrix model * Blind source separation * Variational Bayes method * Dynamic renal scintigraphy
OECD category: Automation and control systems
Impact factor: 3.105, year: 2019
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2019/AS/tichy-0500888.pdf https://ieeexplore.ieee.org/document/8633424

Non-negative matrix factorization (NMF) is generally an ill-posed problem which requires further regularization. Regularization of NMF using the assumption of sparsity is common as well as regularization using smoothness. In many applications it is natural to assume that both of these assumptions hold together. To avoid ad hoc combination of these assumptions using weighting coefficient, we formulate the problem using a probabilistic model and estimate it in a Bayesian way. Specifically, we use the fact that the assumptions of sparsity and smoothness are different forms of prior covariance matrix modeling. We use a generalized model that includes both sparsity and smoothness as special cases and estimate all its parameters using the variational Bayes method. The resulting matrix factorization algorithm is compared with state-of-the-art algorithms on large clinical dataset of 196 image sequences from dynamic renal scintigraphy. The proposed algorithm outperforms other algorithms in statistical evaluation.
Permanent Link: http://hdl.handle.net/11104/0293325