Independent component analysis based on marginal density estimation using weighted Parzen windows

This work proposes a novel algorithm for independent component analysis (ICA) based on marginal density estimation. The proposed ICA algorithm aims to search for an effective demixing matrix as well as weighted Parzen window (WPW) representations for marginal densities of independent components so as to express a factorial joint density for high dimensional observations. Following the linear mixture assumption, independent component analysis is mathematically translated to minimizing the Kullback–Leibler (KL) divergence of independent components. By using Potts encoding, we express the KL divergence in an approximating form, which is shown to be tractable with respect to the WPW parameters as well as the demixing matrix and can be minimized by two interactive dynamic modules derived by the annealed expectation-maximization method and the natural gradient descent method, respectively. By numerical simulations, we test the proposed ICA algorithm with observations separately sampled from linear mixtures of independent sources and real world signals, including fetal electrocardiograms, mixed facial images and event-related potentials, extensively showing its accuracy and reliability for independent component analysis in comparison with some other popular ICA algorithms.