Independent Component Analysis: Blind Source Separation

Abstract

Independent Component Analysis (ICA) is a technique used since middle 80s, and due to all its applications, it has been a common research topic. Simplifying the concept, with the ICA technique we can separate multivariate additive signals. Despite that there are other methods to do so, ICA can do it without knowing nothing (or barely nothing) of the signals and context. Along this thesis the basic algorithm for Independent Component Analysis will be explained. It is called FastICA and was invented by Aapo Hyvärinen as a simply and versatile algorithm with a scheme of fixed-point iterations. This means an algorithm that search the convergence of a vector with iterations, similar to the Newton’s method. This technique is not that simple though, the mathematic and theoretical background is quite complex. But in order to understand how the algorithm works, all of the concepts will be explained step by step.