Title :
Gamma hidden Markov model as a probabilistic Nonnegative Matrix Factorization
Author :
Mohammadiha, Nasser ; Bastiaan Kleijn, W. ; Leijon, Arne
Author_Institution :
Dept. of Electr. Eng., KTH R. Inst. of Technol., Stockholm, Sweden
Abstract :
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.
Keywords :
expectation-maximisation algorithm; gamma distribution; hidden Markov models; matrix decomposition; speech processing; Poisson distributions; continuous-valued data; expectation maximization algorithm; exponential distributions; gamma HMM; gamma distribution; gamma hidden Markov model; multinomial distributions; output density function; probabilistic NMFs; probabilistic nonnegative matrix factorization; speech signals; stochastic signals; Density functional theory; Hidden Markov models; Markov processes; Probabilistic logic; Sparse matrices; Speech; Vectors; Expectation Maximization (EM) algorithm; Hidden Markov Model (HMM); Nonnegative Matrix Factorization (NMF);
Conference_Titel :
Signal Processing Conference (EUSIPCO), 2013 Proceedings of the 21st European
Conference_Location :
Marrakech