22,008 research outputs found
Gaussian mixture gain priors for regularized nonnegative matrix factorization in single-channel source separation
We propose a new method to incorporate statistical priors on the solution of the nonnegative matrix factorization (NMF) for single-channel source separation (SCSS) applications. The Gaussian mixture model (GMM) is used as a log-normalized gain prior model for the NMF solution. The normalization makes the prior models energy independent. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vectors. In this work, the NMF decomposition weights are enforced to consider statistical prior information on the weight combination patterns that the trained basis vectors can jointly receive for each source in the observed mixed signal. The NMF solutions for the weights are encouraged to increase the loglikelihood with the trained gain prior GMMs while reducing the NMF reconstruction error at the same time
Hidden Markov models as priors for regularized nonnegative matrix factorization in single-channel source separation
We propose a new method to incorporate rich statistical priors, modeling temporal gain sequences in the solutions of nonnegative matrix factorization (NMF). The proposed method can be used for single-channel source separation (SCSS) applications. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vectors. In this work, the NMF decomposition weights are enforced to consider statistical and temporal prior information on the weight combination patterns that the trained basis vectors can jointly receive for each source in the observed mixed signal. The Hidden Markov Model (HMM) is used as a log-normalized gains (weights) prior model for the NMF solution. The normalization makes the prior models energy independent. HMM is used as a rich model that characterizes the statistics of sequential data. The NMF solutions for the weights are encouraged to increase the log-likelihood with the trained gain prior HMMs while reducing the NMF reconstruction error at the same time
Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets
Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence
(NMF-KL) is one of the most significant NMF problems and equivalent to
Probabilistic Latent Semantic Indexing (PLSI), which has been successfully
applied in many applications. For sparse count data, a Poisson distribution and
KL divergence provide sparse models and sparse representation, which describe
the random variation better than a normal distribution and Frobenius norm.
Specially, sparse models provide more concise understanding of the appearance
of attributes over latent components, while sparse representation provides
concise interpretability of the contribution of latent components over
instances. However, minimizing NMF with KL divergence is much more difficult
than minimizing NMF with Frobenius norm; and sparse models, sparse
representation and fast algorithms for large sparse datasets are still
challenges for NMF with KL divergence. In this paper, we propose a fast
parallel randomized coordinate descent algorithm having fast convergence for
large sparse datasets to archive sparse models and sparse representation. The
proposed algorithm's experimental results overperform the current studies' ones
in this problem
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