Independent Component Analysis: A Tutorial Introduction

Abstract

Independent component analysis (ICA) is becoming an increasingly important tool for analyzing large data sets. In essence, ICA separates an observed set of signal mixtures into a set of statistically independent component signals, or source signals. In so doing, this powerful method can extract relatively small amount of useful information typically found in large data sets. The applications for ICA range from speech processing, brain imaging, and electrical brain signals to telecommunications and stock predictions. In Independent Component Analysis, Jim Stone presents essentials of ICA and related techniques (projection pursuit and complexity pursuit) in a tutorial style, using intuitive examples described in simple geometric terms. The treatment fills need for a basic primer on ICA that can be used by readers of varying levels of mathematical sophistication, including engineers, cognitive scientists, and neuroscientists who need to know essentials of this evolving method. An overview establishes strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on key observations that different physical processes generate outputs that are statistically independent of each other. The book then describes what Stone calls the mathematical nuts and bolts of how ICA works. Presenting only essential mathematical proofs, Stone guides reader through an exploration of fundamental characteristics of ICA. Topics covered include geometry of mixing and unmixing; methods for blind source separation; and applications of ICA, including voice mixtures, EEG, fMRI, and fetal heart monitoring. The appendixes provide a vector matrix tutorial, plus basic demonstration computer code that allows reader to see how each mathematical method described in text translates into working Matlab computer code.