A Critical Comparison of ICA Algorithms

Abstract

Independent component analysis (ICA), is a statistical method for transforming a multi-dimensional random vector into components that are statistically as independent from each other as possible. Recently, in a paper by H. Attias [1], a model called independent factor analysis trained by an Expectation Maximisation (EM) algorithm has been proposed which seems to supersede all earlier work, since it can cope with arbitrary source distributions and non-square mixing matrices. In this thesis we will first explain what ICA is, what are the different ways to solve the ICA problem and present some algorithms with a special highlight on IFA. Then we will propose some methods to reduce the dimensionality and to estimate the noise using PCA and Factor Analysis (FA) tools. Finally we will compare FastICA [13] and IFA, present a method to solve the ICA problem in the case of many sensors and significant noise, then apply this method on a concrete problem: MEG analysis.