Independent Component Analysis: A Tutorial Introduction (Bradford Books)

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. A tutorial-style introduction to a class of methods for extracting independent signals from a mixture of signals originating from different physical sources; includes MatLab computer code examples. 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.

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.

Contents......Page 8 Preface......Page 12 Acknowledgments......Page 14 Abbreviations......Page 16 Mathematical Symbols......Page 18 I INDEPENDENT COMPONENT ANALYSIS AND BLIND SOURCE SEPARATION......Page 20 1 Overview of Independent Component Analysis......Page 24 2 Strategies for Blind Source Separation......Page 32 II THE GEOMETRY OF MIXTURES......Page 38 3 Mixing and Unmixing......Page 40 4 Unmixing Using the Inner Product......Page 50 5 Independence and Probability Density Functions......Page 70 III METHODS FOR BLIND SOURCE SEPARATION......Page 88 6 Projection Pursuit......Page 90 7 Independent Component Analysis......Page 98 8 Complexity Pursuit......Page 130 9 Gradient Ascent......Page 138 10 Principal Component Analysis and Factor Analysis......Page 148 IVAPPLICATIONS......Page 156 11 Applications of ICA......Page 158 VAPPENDICES......Page 168 A A Vector Matrix Tutorial......Page 170 B Projection Pursuit Gradient Ascent......Page 176 C Projection Pursuit: Stepwise Separation of Sources......Page 182 D ICA Gradient Ascent......Page 184 E Complexity Pursuit Gradient Ascent......Page 192 F Principal Component Analysis for Preprocessing Data......Page 198 G Independent Component Analysis Resources......Page 202 H Recommended Reading......Page 204 References......Page 206 Index......Page 210 It is often said that we suffer from "information overload," whereas we actually suffer from "data overload."