Convex Divergence ICA for Blind Source Separation

Jen-Tzung Chien and Hsin-Lung Hsieh

 

ABSTRACT

Independent component analysis (ICA) is vital for unsupervised learning and blind source separation (BSS). The ICA unsupervised learning procedure attempts to demix the observation vectors and identify the salient features or mixture sources. This work presents a novel contrast function for evaluating the dependence among sources. A convex divergence measure is developed by applying the convex functions to the Jensen’s inequality. Adjustable with a convexity parameter, this inequality-based divergence measure has a wide range of the steepest descents to reach its minimum value. A convex divergence ICA (C-ICA) is constructed and a nonparametric C-ICA algorithm is derived with different convexity parameters where the non-Gaussianity of source signals is characterized by the Parzen window-based distribution. Experimental results indicate that the specialized C-ICA significantly reduces the number of learning epochs during estimation of the demixing matrix. The convergence speed is improved by using the scaled natural gradient algorithm. Experiments on the BSS of instantaneous, noisy and convolutive mixtures of speech and music signals further demonstrate the superiority of the proposed C-ICA to JADE, Fast-ICA and the nonparametric ICA based on mutual information.

Source Signals                              Signal 1   Signal 2  Signal 3

Mixed Signals   (instantaneous mixture)             Signal 1   Signal 2  Signal 3

Demixed Signals (instantaneous mixture) (FastICA)   Signal 1   Signal 2   Signal 3

Demixed Signals (instantaneous mixture) (KL-ICA)    Signal 1   Signal 2   Signal 3

Demixed Signals (instantaneous mixture) (C-ICA)     Signal 1   Signal 2   Signal 3

Mixed Signals   (noisy mixture)                     Signal 1   Signal 2   Signal 3

Demixed Signals (noisy mixture) (FastICA)           Signal 1   Signal 2   Signal 3

Demixed Signals (noisy mixture) (KL-ICA)            Signal 1   Signal 2   Signal 3

Demixed Signals (noisy mixture) (C-CIA)             Signal 1   Signal 2   Signal 3

Mixed Signals   (convolutive mixture)               Signal 1             Signal 3 

Demixed Signals (convolutive mixture) (KL-ICA)      Signal 1             Signal 3

Demixed Signals (convolutive mixture) (C-ICA)       Signal 1             Signal 3

 

Downloads  

Download the readme.txt.

Download the codes of C-ICA: C-ICA.rar

This is a Matlab implementation of C-ICA.

The released C-ICA.rar contains

1. C_ICA.m: full source code of C-ICA algorithm.

2. Spheredata.m: source code of the function that performs the whitening process.