Independent Component Analysis: A Tutorial Introduction

Overview

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 the 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...

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Overview

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 the 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 the 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 the 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 the essentials of this evolving method.An overview establishes the strategy implicit in ICA in terms of its essentially physical underpinnings and describes how ICA is based on the 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 the reader through an exploration of the fundamental characteristics of ICA.Topics covered include the 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 the reader to see how each mathematical method described in the text translates into working Matlab computer code.

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What People Are Saying

From the Publisher
"Independent component analysis is a recent and powerful addition to the methods that scientists and engineers have available to explore large data sets in high-dimensional spaces. This book is a clearly written introduction to the foundations of ICA and the practical issues that arise in applying it to a wide range of problems." Terrence J. Sejnowski, Howard Hughes Medical Institute,Salk Institute for Biological Studies, and University of California, San Diego
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Product Details

  • ISBN-13: 9780262693158
  • Publisher: MIT Press
  • Publication date: 9/1/2004
  • Series: Bradford Books Series
  • Pages: 200
  • Product dimensions: 7.00 (w) x 9.00 (h) x 0.50 (d)

Meet the Author

James V. Stone is a Reader in the Psychology Department of the University of Sheffield. He is coauthor (with John P. Frisby) of the widely used text Seeing: The Computational Approach to Biological Vision (second edition, MIT Press, 2010), and author of IndependentComponent Analysis: A Tutorial Introduction (MIT Press, 2004).

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Table of Contents

I Independent component analysis and blind source separation 1
1 Overview of independent component analysis 5
2 Strategies for blind source separation 13
II The geometry of mixtures 19
3 Mixing and unmixing 21
4 Unmixing using the inner product 31
5 Independence and probability density functions 51
III Methods for blind source separation 69
6 Projection pursuit 71
7 Independent component analysis 79
8 Complexity pursuit 111
9 Gradient ascent 119
10 Principal component analysis and factor analysis 129
IV Applications 137
11 Applications of ICA 139
V Appendices 149
A A vector matrix tutorial 151
B Projection pursuit gradient ascent 157
C Projection pursuit : stepwise separation of sources 163
D ICA gradient ascent 165
E Complexity pursuit gradient ascent 173
F Principal component analysis for preprocessing data 179
G Independent component analysis resources 183
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