An Epanechnikov Kernel Based Method for Source Separation in Post-Nonlinear Mixtures

In the context of the nonlinear Blind Source Separation problem, Post-Nonlinear mixtures can be separated via Mutual Information minimization. In this case, methods based on score functions can be used and the recovered sources distributions can be estimated by kernel methods. Usually a Gaussian kernel function is used. However, other kernel functions with interesting properties can be used, such as the Epanechnikov kernel. Based on this, we apply the Epanechnikov kernel to estimate the pdf and the relative gradient, in order to recover the sources. Also, we compare a classic Gaussian kernel with the Epanechnikov kernel, showing that the latter performs better than the former.