Convex Cauchy Schwarz Independent Component Analysis for Blind Source Separation

TL;DR

This paper introduces a novel convex Cauchy Schwarz divergence measure for ICA and BSS, enabling improved separation performance through convexity control and pairwise iterative schemes, validated on speech and music signals.

Contribution

It develops a new CCS divergence measure with adjustable convexity, and proposes two non parametric ICA algorithms using gradient descent and Jacobi methods for high-dimensional BSS.

Findings

Outperforms FastICA, RobustICA, and C ICA in various scenarios

Effective in separating noise-free and noisy speech and music signals

Demonstrates superior metric performance in comparative tests

Abstract

We present a new high performance Convex Cauchy Schwarz Divergence (CCS DIV) measure for Independent Component Analysis (ICA) and Blind Source Separation (BSS). The CCS DIV measure is developed by integrating convex functions into the Cauchy Schwarz inequality. By including a convexity quality parameter, the measure has a broad control range of its convexity curvature. With this measure, a new CCS ICA algorithm is structured and a non parametric form is developed incorporating the Parzen window based distribution. Furthermore, pairwise iterative schemes are employed to tackle the high dimensional problem in BSS. We present two schemes of pairwise non parametric ICA algorithms, one is based on gradient decent and the second on the Jacobi Iterative method. Several case study scenarios are carried out on noise free and noisy mixtures of speech and music signals. Finally, the superiority of the proposed CCS ICA algorithm is demonstrated in metric comparison performance with FastICA, RobustICA, convex ICA (C ICA), and other leading existing algorithms.