Independent Component Analysis by Entropy Maximization with Kernels

TL;DR

This paper introduces ICA-EMK, an efficient ICA algorithm that maximizes entropy with kernels, accurately estimates source PDFs, and enables parallel processing, outperforming existing methods on simulated and real data.

Contribution

The paper presents a novel ICA algorithm based on entropy maximization with kernels, improving PDF estimation and computational efficiency through parallelization.

Findings

ICA-EMK outperforms competing ICA algorithms in experiments.

The method effectively estimates source PDFs with global and local functions.

Parallel implementation enhances computational efficiency.

Abstract

Independent component analysis (ICA) is the most popular method for blind source separation (BSS) with a diverse set of applications, such as biomedical signal processing, video and image analysis, and communications. Maximum likelihood (ML), an optimal theoretical framework for ICA, requires knowledge of the true underlying probability density function (PDF) of the latent sources, which, in many applications, is unknown. ICA algorithms cast in the ML framework often deviate from its theoretical optimality properties due to poor estimation of the source PDF. Therefore, accurate estimation of source PDFs is critical in order to avoid model mismatch and poor ICA performance. In this paper, we propose a new and efficient ICA algorithm based on entropy maximization with kernels, (ICA-EMK), which uses both global and local measuring functions as constraints to dynamically estimate the PDF of the sources with reasonable complexity. In addition, the new algorithm performs optimization with respect to each of the cost function gradient directions separately, enabling parallel implementations on multi-core computers. We demonstrate the superior performance of ICA-EMK over competing ICA algorithms using simulated as well as real-world data.