Independent Component Analysis: An Introduction

Independent Component Analysis (ICA) can be described in several ways, one of which is as a technique that seeks to find a set directions (components) underlying multivariate data that are most independent of one another. While there are several ICA models and many ICA methods, in this report we focus on the most basic model and one of the most popular and simple algorithms; the One-Unit FastICA algorithm. ICA is based on several very interesting results in probability, statistics, information theory, and non-linear optimization theory. Most of the introductory publications on this topic leave these results unattended. The aim of this report is to fill this gap. Throughout this report each of these results, including its proof, is introduced in accordance with the ICA subproblem it attempts solve or underlying principle it attempts to explain.