Blind source separation for groundwater pressure analysis based on nonnegative matrix factorization

2014 ◽  
Vol 50 (9) ◽  
pp. 7332-7347 ◽  
Author(s):  
Boian S. Alexandrov ◽  
Velimir V. Vesselinov
Keyword(s):  
Blind Source Separation ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Source Separation ◽  
Nonnegative Matrix ◽  
Pressure Analysis

scholarly journals Pattern Expression Nonnegative Matrix Factorization: Algorithm and Applications to Blind Source Separation

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Junying Zhang ◽  
Le Wei ◽  
Xuerong Feng ◽  
Zhen Ma ◽  
Yue Wang
Keyword(s):  
Blind Source Separation ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Learning Algorithm ◽  
Source Separation ◽  
Nonnegative Matrix ◽  
Heterogeneity Correction ◽  
Two Parameters ◽  
Common Situation ◽  
Basis Vectors

Independent component analysis (ICA) is a widely applicable and effective approach in blind source separation (BSS), with limitations that sources are statistically independent. However, more common situation is blind source separation for nonnegative linear model (NNLM) where the observations are nonnegative linear combinations of nonnegative sources, and the sources may be statistically dependent. We propose a pattern expression nonnegative matrix factorization (PE-NMF) approach from the view point of using basis vectors most effectively to express patterns. Two regularization or penalty terms are introduced to be added to the original loss function of a standard nonnegative matrix factorization (NMF) for effective expression of patterns with basis vectors in the PE-NMF. Learning algorithm is presented, and the convergence of the algorithm is proved theoretically. Three illustrative examples on blind source separation including heterogeneity correction for gene microarray data indicate that the sources can be successfully recovered with the proposed PE-NMF when the two parameters can be suitably chosen from prior knowledge of the problem.

scholarly journals Underdetermined Blind Source Separation Combining Tensor Decomposition and Nonnegative Matrix Factorization

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 521 ◽  
Author(s):  
Yuan Xie ◽  
Kan Xie ◽  
Junjie Yang ◽  
Shengli Xie
Keyword(s):  
Blind Source Separation ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Source Separation ◽  
Nonnegative Matrix ◽  
Tensor Decomposition ◽  
Model Parameters ◽  
Separation Performance ◽  
Underdetermined Blind Source Separation ◽  
Source Signals

Underdetermined blind source separation (UBSS) is a hot topic in signal processing, which aims at recovering the source signals from a number of observed mixtures without knowing the mixing system. Recently, expectation-maximization algorithm shows a great potential in the UBSS. However, the final separation results depend strongly on the parameter initialization, leading to poor separation performance. In this paper, we propose an effective algorithm that combines tensor decomposition and nonnegative matrix factorization (NMF). In the proposed algorithm, we first employ tensor decomposition to estimate the mixing matrix, and NMF source model is used to estimate the source spectrogram factors. Then a series of iterations are derived to update the model parameters. At the same time, the spatial images of source signals are estimated with Wiener filters constructed from the learned parameters. Therefore, time-domain sources can be obtained through inverse short-time Fourier transform. Finally, plenty of experimental results demonstrate the effectiveness and advantages of our proposed algorithm over the compared algorithms.

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