Mathematics in Independent Component Analysis

70 Chapter 2. Neural Computation 16:1827-1850, 2004
A New Concept for Separability Problems in BSS 1841
4.2 Global Hessian Diagonalization Using Kernel-Based Density Approximation.
In practice, it is usually not possible to approximate the density
locally with sufficiently high accuracy, so a better approximation using
the typically global information of X has to be found. We suggest using
kernel-based density estimation to get an energy function with minima at
the BSS solutions together with a global Hessian diagonalization in the following.
The idea is to construct a measure for separatedness of the densities
(hence independence) based on theorem 1. A possible measure could be the
norm of the summed-up separators �
i