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Independent Component Analysis(英文版).pdf

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    Independent Component Analysis
    Copyright
    Contents
    Preface
    Ch1 Introduction
    Part1 Mathematical Preliminaries
    Ch2 Random Vectors & Independence
    Ch3 Gradients & Optimization Methods
    Ch4 Estimation Theory
    Ch5 Information Theory
    Ch6 Principal Component Analysis & Whitening
    Part2 Basic Independent Component Analysis
    Ch7 What is Independent Component Analysis?
    Ch8 ICA by Maximization of Nongaussianity
    Ch9 ICA by Maximum Likelihood Estimation
    Ch10 ICA by Minimization of Mutual Information
    Ch11 ICA by Tensorial Methods
    Ch12 ICA by Nonlinear Decorrelation & Nonlinear PCA
    Ch13 Practical Considerations
    Ch14 Overview & Comparison of Basic ICA Methods
    Part3 Extensions & Related Methods
    Ch15 Noisy ICA
    Ch16 ICA with Overcomplete Bases
    Ch17 Nonlinear ICA
    Ch18 Methods using Time Structure
    Ch19 Convolutive Mixtures & Blind Deconvolution
    Ch20 Other Extensions
    Part4 Applications of ICA
    Ch21 Feature Extraction by ICA
    Ch22 Brain Imaging Applications
    Ch23 Telecommunications
    Ch24 Other Applications
    References
    Index
    Backcover
    Independent Component Analysis
    Independent Component Ana&sis Aapo Hyvtirinen Juha Karhunen Erkki Oja New York / Chichester / Weinheim A Wiley-Interscience Publication JOHN WILEY & SONS, INC. / Toronto / Brisbane / Singapore
    Designations used by companies to distinguish their products are often claimed as trademarks. In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or ALL CAPITAL LETTERS. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration. Copyright  2001 by John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought. ISBN 0-471-22131-7 This title is also available in print as ISBN 0-471-40540-X. For more information about Wiley products, visit our web site at www.Wiley.com.
    Contents Preface 1 Introduction 1.1 1.2 1.3 Independence as a guiding principle Linear representation of multivariate data 1.1.1 The general statistical setting 1.1.2 Dimension reduction methods 1.1.3 Blind source separation 1.2.1 Observing mixtures of unknown signals 1.2.2 Independent component analysis 1.3.1 Definition 1.3.2 Applications 1.3.3 How to find the independent components Source separation based on independence 1.4 History of ICA xvii 1 1 1 2 3 3 4 5 6 6 7 7 11 v
    vi CONTENTS Part I MATHEMATICAL PRELIMINARIES 2 Random Vectors and Independence 2.1 2.2 Probability distributions and densities 2.1.1 Distribution of a random variable 2.1.2 Distribution of a random vector 2.1.3 Joint and marginal distributions Expectations and moments 2.2.1 Definition and general properties 2.2.2 Mean vector and correlation matrix 2.2.3 Covariances and joint moments 2.2.4 Estimation of expectations 2.3 Uncorrelatedness and independence 2.3.1 Uncorrelatedness and whiteness 2.3.2 Statistical independence 2.4 Conditional densities and Bayes’ rule 2.5 The multivariate gaussian density 2.5.1 Properties of the gaussian density 2.5.2 Central limit theorem 2.6 Density of a transformation 2.7 Higher-order statistics 2.8 Introduction and definition Stationarity, mean, and autocorrelation 2.7.1 Kurtosis and classification of densities 2.7.2 Cumulants, moments, and their properties Stochastic processes * 2.8.1 2.8.2 2.8.3 Wide-sense stationary processes 2.8.4 2.8.5 Power spectrum 2.8.6 Time averages and ergodicity Stochastic signal models 2.9 Concluding remarks and references Problems 3 Gradients and Optimization Methods 3.1 Vector and matrix gradients 3.1.1 Vector gradient 3.1.2 Matrix gradient 3.1.3 Examples of gradients 15 15 15 17 18 19 19 20 22 24 24 24 27 28 31 32 34 35 36 37 40 43 43 45 46 48 49 50 51 52 57 57 57 59 59
    CONTENTS vii 3.2 3.3 Taylor series expansions Second-order learning The natural gradient and relative gradient Stochastic gradient descent 3.1.4 Learning rules for unconstrained optimization 3.2.1 Gradient descent 3.2.2 3.2.3 3.2.4 3.2.5 Convergence of stochastic on-line algorithms * Learning rules for constrained optimization 3.3.1 3.3.2 Projection methods The Lagrange method 3.4 Concluding remarks and references Problems 4 Estimation Theory Basic concepts Properties of estimators 4.1 4.2 4.3 Method of moments 4.4 Least-squares estimation 4.4.1 4.4.2 Nonlinear and generalized least squares * Linear least-squares method 4.5 Maximum likelihood method 4.6 Bayesian estimation * 4.6.1 Minimum mean-square error estimator 4.6.2 Wiener filtering 4.6.3 Maximum a posteriori (MAP) estimator 4.7 Concluding remarks and references Problems 5 Information Theory 5.1 Entropy 5.1.1 Definition of entropy 5.1.2 Entropy and coding length 5.1.3 Differential entropy 5.1.4 Entropy of a transformation 5.2 Mutual information 5.2.1 Definition using entropy 5.2.2 Definition using Kullback-Leibler divergence 62 63 63 65 67 68 71 73 73 73 75 75 77 78 80 84 86 86 88 90 94 94 96 97 99 101 105 105 105 107 108 109 110 110 110
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