Non-parametric approach to ICA using kernel density estimation

Independent Component Analysis (ICA) has found a wide range of applications in signal processing and multimedia, ranging from speech cleaning to face recognition. This paper presents a non-parametric approach to the ICA problem that is robust towards outlier effects. The algorithm, for the first time in the field of ICA, adopts an intuitive and direct approach, focusing on the very definition of independence itself; i.e. the joint probability density function (pdf) of independent sources is factorial over the marginal distributions. This is contrary to traditional Independent Component Analysis (ICA) algorithms, which achieve the objective by attempting to fulfill necessary conditions (but not sufficient) for independence. For example, the Jade algorithm attempts to approximate independence by minimizing higher order statistics. In the proposed algorithm, kernel density estimation is employed to provide a good approximation of the distributions that are required to be estimated. This estimation technique is inherently robust towards outlier effects. The application of kernel density estimation also enables the algorithm to be free from the assumptions of source distributions. Experimental results show that the algorithm is able to perform separation of sources in the presence of outliers, whereas existing algorithms like Jade and Infomax break down under such conditions. The results have also shown that the proposed non-parametric approach is generally source distribution independent. In addition, it is able to separate non-gaussian zero-kurtotic signals unlike the traditional ICA algorithms like Jade and Infomax.