Probabilistic sparse non-negative matrix factorization

Jesper Løve Hinrich, Morten Mørup

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


In this paper, we propose a probabilistic sparse non-negative matrix factorization model that extends a recently proposed variational Bayesian non-negative matrix factorization model to explicitly account for sparsity. We assess the influence of imposing sparsity within a probabilistic framework on either the loading matrix, score matrix, or both and further contrast the influence of imposing an exponential or truncated normal distribution as prior. The probabilistic methods are compared to conventional maximum likelihood based NMF and sparse NMF on three image datasets; (1) A (synthetic) swimmer dataset, (2) The CBCL face dataset, and (3) The MNIST handwritten digits dataset. We find that the probabilistic sparse NMF is able to automatically learn the level of sparsity and find that the existing probabilistic NMF as well as the proposed probabilistic sparse NMF prunes inactive components and thereby automatically learns a suitable number of components. We further find that accounting for sparsity can provide more part based representations but for the probabilistic modeling the choice of priors and how sparsity is imposed can have a strong influence on the extracted representations.
Original languageEnglish
Title of host publicationLatent Variable Analysis and Signal Separation : 14th International Conference, LVA/ICA 2018, Guildford, UK, July 2–5, 2018, Proceedings
EditorsYannick Deville , Sharon Gannot , Russell Mason , Mark D. Plumbley , Dominic Ward
Number of pages11
Publication date2018
ISBN (Print)978-3-319-93763-2
ISBN (Electronic)978-3-319-93764-9
Publication statusPublished - 2018
Event14th International Conference on Latent Variable Analysis and Signal Separation - University of Surrey, Guildford, United Kingdom
Duration: 2 Jul 20185 Jul 2018
Conference number: 14


Conference14th International Conference on Latent Variable Analysis and Signal Separation
LocationUniversity of Surrey
CountryUnited Kingdom
SeriesLecture Notes in Computer Science


  • Bayesian modeling
  • Non-negative matrix factorization
  • Sparse non-negative matrix factorization
  • Sparsity

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