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

• Published in: Neural networks Vol. 21; no. 7; pp. 914 - 924
• Main Authors: Wu, Jiann-Ming, Chen, Meng-Hong, Lin, Zheng-Han
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.09.2008; Elsevier Science
• Subjects: Algorithms; Applied sciences; Biological and medical sciences; Blind source separation; Coding, codes; Computer Simulation; Computerized, statistical medical data processing and models in biomedicine; Density estimation; Detection, estimation, filtering, equalization, prediction; Electrocardiography - methods; Electroencephalography - methods; Entropy; Evoked Potentials - physiology; Exact sciences and technology; Humans; Independent factor analysis; Information, signal and communications theory; Kullback–Leibler divergence; Mean field annealing; Medical management aid. Diagnosis aid; Medical sciences; Miscellaneous; Nonlinear Dynamics; Potts encoding; Principal Component Analysis; Signal and communications theory; Signal processing; Signal Processing, Computer-Assisted; Signal, noise; Statistics, Nonparametric; Telecommunications and information theory; Weighted Parzen window; Density estimation; Kullback–Leibler divergence; Mean field annealing; Potts encoding; Blind source separation; Entropy; Weighted Parzen window; Independent factor analysis; Signal mixing; Divergence; Density measurement; Signal estimation; Kullback-Leibler divergence; Gradient descent; Accuracy; Multidimensional analysis; Coding; Facies; Electrocardiography; Work; Gradient method; Annealing; Independent component analysis; Interactive system; Descent method; Observation; Signal processing; Numerical simulation; Reliability; EM algorithm; Event evoked potential
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2008.01.005

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.