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A state-space approach to dynamic nonnegative matrix factorization
University of Oldenburg, Germany.
University of Illinois .
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
University of Oldenburg, Germany.
2015 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 4, 949-959 p.Article in journal (Refereed) Published
Abstract [en]

Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade. A significant amount of attention has been given to develop NMF algorithms that are suitable to model time series with strong temporal dependencies. In this paper, we propose a novel state-space approach to perform dynamic NMF (D-NMF). In the proposed probabilistic framework, the NMF coefficients act as the state variables and their dynamics are modeled using a multi-lag nonnegative vector autoregressive (N-VAR) model within the process equation. We use expectation maximization and propose a maximum-likelihood estimation framework to estimate the basis matrix and the N-VAR model parameters. Interestingly, the N-VAR model parameters are obtained by simply applying NMF. Moreover, we derive a maximum a posteriori estimate of the state variables (i.e., the NMF coefficients) that is based on a prediction step and an update step, similarly to the Kalman filter. We illustrate the benefits of the proposed approach using different numerical simulations where D-NMF significantly outperforms its static counterpart. Experimental results for three different applications show that the proposed approach outperforms two state-of-the-art NMF approaches that exploit temporal dependencies, namely a nonnegative hidden Markov model and a frame stacking approach, while it requires less memory and computational power.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2015. Vol. 63, no 4, 949-959 p.
Keyword [en]
Constrained Kalman filtering, nonnegative dynamical system (NDS), nonnegative matrix factorization (NMF), prediction, probabilistic latent component analysis (PLCA)
National Category
Signal Processing
URN: urn:nbn:se:kth:diva-157745DOI: 10.1109/TSP.2014.2385655ISI: 000348457800011ScopusID: 2-s2.0-84921749170OAI: diva2:771534

QC 20141219

Available from: 2014-12-14 Created: 2014-12-14 Last updated: 2015-03-03Bibliographically approved

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