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

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

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]**

Spectrogram of demixed
**rhythmic source **signal by BGS-NMF

**harmonic source** signal by BGS-NMF

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

Spectrogram of demixed
**rhythmic source **signal by BGS-NMF

**harmonic source**
signal by BGS-NMF

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

Spectrogram of demixed
**rhythmic source **signal by BGS-NMF

**harmonic source** signal by BGS-NMF

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

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

Spectrogram of demixed
**harmonic source** signal by BGS-NMF