Bayesian Group Sparse Learning for Nonnegative Matrix Factorization

Jen-Tzung Chien and Hsin-Lung Hsieh

 

ABSTRACT

Nonnegative matrix factorization (NMF) is developed for parts-based representation of nonnegative data with the sparseness constraint. The degree of sparseness plays an important role for model regularization. This paper presents the Bayesian group sparse learning for NMF and applies it for single-channel source separation. This method establishes the common bases and individual bases to characterize the shared information and residual noise in observed signals, respectively. Laplacian scale mixture distribution is introduced for sparse coding with a sparseness control parameter. A Markov chain Monte Carlo procedure is presented to infer two groups of parameters and their hyperparameters through sampling according to conditional posterior distributions. Experiments on separating audio signals into rhythmic source signals and harmonic source signals show that the proposed method outperforms baseline NMF and Bayesian NMF in terms of signal-to-noise ratio.

Audio Source Signals: (1) bass + piano & mixture matrix = [1.2667 -1.9136]

bass1               piano2 

  


Mixture waveform

 
 

Spectrogram of demixed rhythmic source signal by BGS-NMF

 

Spectrogram of demixed harmonic source signal by BGS-NMF

 

 

Audio Source Signals: (2) drum + guitar & mixture matrix = [1.1667 -1.9136]

drum3               guitar3

  

 

Mixture waveform

 

Spectrogram of demixed rhythmic source signal by BGS-NMF

 

Spectrogram of demixed harmonic source signal by BGS-NMF

 

 

Audio Source Signals: (3) drum + violin & mixture matrix = [-1.2667 1.6136]

drum4              violin1

  

 

Mixture waveform

  

Spectrogram of demixed rhythmic source signal by BGS-NMF

 

Spectrogram of demixed harmonic source signal by BGS-NMF

 

 

Audio Source Signals: (4) cymbal + organ & mixture matrix = [1.8667 1.1136]

cymbal1              organ1

  

Mixture waveform

 

 

Spectrogram of demixed rhythmic source signal by BGS-NMF

 

Spectrogram of demixed harmonic source signal by BGS-NMF

 

 

Audio Source Signals: (5) drum + saxophone & mixture matrix = [-1.1667 2.8136]

drum6             saxophone1

  

Mixture waveform

 

 

Spectrogram of demixed rhythmic source signal by BGS-NMF

 

Spectrogram of demixed harmonic source signal by BGS-NMF

  

 

Audio Source Signals: (6) cymbal + singing & mixture matrix = [1.9617 1.1510]

 

cymbal2            singing1

 

 

Mixture waveform 

 

 
Spectrogram of demixed rhythmic source signal by BGS-NMF

Spectrogram of demixed harmonic source signal by BGS-NMF