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Gamma Hidden Markov Model as a Probabilistic Nonnegative Matrix Factorization
KTH, School of Electrical Engineering (EES), Communication Theory.
KTH, School of Electrical Engineering (EES), Communication Theory.
KTH, School of Electrical Engineering (EES), Communication Theory.
2013 (English)In: 2013 Proceedings of the 21st European Signal Processing Conference (EUSIPCO), European Signal Processing Conference , 2013, 6811626- p.Conference paper (Refereed)
Abstract [en]

Among different Nonnegative Matrix Factorization (NMF) approaches, probabilistic NMFs are particularly valuable when dealing with stochastic signals, like speech. In the current literature, little attention has been paid to develop NMF methods that take advantage of the temporal dependencies of data. In this paper, we develop a hidden Markov model (HMM) with a gamma distribution as output density function. Then, we reformulate the gamma HMM as a probabilistic NMF. This shows the analogy of the proposed HMM and NMF, and will lead to a new probabilistic NMF approach in which the temporal dependencies are also captured inherently by the model. Furthermore, we propose an expectation maximization (EM) algorithm to estimate all the model parameters. Compared to the available probabilistic NMFs that model data with Poisson, multinomial, or exponential distributions, the proposed NMF is more suitable to be used with continuous-valued data. Our experiments using speech signals shows that the proposed approach leads to a better compromise between sparsity, goodness of fit, and temporal modeling compared to state-of-the-art.

Place, publisher, year, edition, pages
European Signal Processing Conference , 2013. 6811626- p.
Keyword [en]
Hidden Markov Model (HMM), Nonnegative Matrix Factorization (NMF), Expectation Maximization (EM) algorithm
National Category
Engineering and Technology Electrical Engineering, Electronic Engineering, Information Engineering
URN: urn:nbn:se:kth:diva-124355ISI: 000341754500239ScopusID: 2-s2.0-84901293275ISBN: 978-099286260-2OAI: diva2:634174
2013 21st European Signal Processing Conference, EUSIPCO 2013; Marrakech; Morocco; 9 September 2013 through 13 September 2013

QC 20130703

Available from: 2013-06-28 Created: 2013-06-28 Last updated: 2014-10-20Bibliographically approved

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