A non-parametric approach for independent component analysis using kernel density estimation

Learning using independent component analysis (ICA) has found a wide range of applications in the area of computer vision and pattern analysis, ranging from face recognition to speech separation. 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. In the proposed algorithm, kernel density estimation is employed to approximate the underlying distributions. There are two major advantages of our algorithm. First, existing algorithms focus on learning the independent components 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, which are not robust to outliers. Comparatively, our technique is inherently robust towards outlier effects. Second, since the learning employs kernel density estimation, it is naturally free from the assumptions of source distributions (unlike the Infomax algorithm). 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.