Automatic relevance determination in nonnegative matrix factorization with the β-divergence
This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the β-divergence. The β-divergence is a family of cost functions that includes the squared euclidean distance, Kullback-Leibler (KL) and Itakura-Saito (IS) divergences as special cases. Le...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 35(2013), 7 vom: 15. Juli, Seite 1592-605 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
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2013
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the β-divergence. The β-divergence is a family of cost functions that includes the squared euclidean distance, Kullback-Leibler (KL) and Itakura-Saito (IS) divergences as special cases. Learning the model order is important as it is necessary to strike the right balance between data fidelity and overfitting. We propose a Bayesian model based on automatic relevance determination (ARD) in which the columns of the dictionary matrix and the rows of the activation matrix are tied together through a common scale parameter in their prior. A family of majorization-minimization (MM) algorithms is proposed for maximum a posteriori (MAP) estimation. A subset of scale parameters is driven to a small lower bound in the course of inference, with the effect of pruning the corresponding spurious components. We demonstrate the efficacy and robustness of our algorithms by performing extensive experiments on synthetic data, the swimmer dataset, a music decomposition example, and a stock price prediction task |
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| Beschreibung: | Date Completed 30.12.2013 Date Revised 11.03.2022 published: Print Citation Status MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2012.240 |