## Independent Component AnalysisA comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative. |

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### Contents

1 | |

13 | |

BASIC INDEPENDENT COMPONENT ANALYSIS | 145 |

EXTENSIONS AND RELATED METHODS | 291 |

APPLICATIONS OF ICA | 389 |

449 | |

476 | |

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### Common terms and phrases

algorithm applied approach approximation assumed autocorrelation basis vectors blind deconvolution blind source separation CDMA Chapter coefﬁcients computed considered constant constraint convergence convolutive mixtures correlation corresponding cost function covariance matrix criterion cumulants data vector decorrelation deﬁned deﬁnition denote density function derived diagonal differential entropy difﬁcult dimension discussed eigenvalues eigenvectors elements entropy equation example FastICA FastICA algorithm ﬁlter ﬁnd ﬁnding ﬁrst ﬁxed ﬁxed-point gaussian distribution given gives gradient algorithm higher-order ICA estimation ICA methods independent component analysis iteration kurtosis learning rule least-squares mapping maximization mean-square error minimization mixing matrix mutual information natural gradient negentropy noise nonlinear nonlinear ICA observed obtained on-line optimization orthogonal parameters principal components principle prior probability density properties random variables random vector sample scalar Section separating matrix shows signal processing source signals sparse coding statistically independent subspace sufﬁcient supergaussian symmetric theorem transformation uncorrelated unit variance zero mean

### Popular passages

Page 472 - R. Hari, and E. Oja. Independent component analysis for identification of artifacts in Magnetoencephalographic recordings.

Page 458 - A family of fixed-point algorithms for independent component analysis. In Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP '97), pages 3917-3920, Munich, Germany, 1997. 193. A. Hyvarinen. One-unit contrast functions for independent component analysis: A statistical analysis.

Page 458 - A. Hyvarinen. New approximations of differential entropy for independent component analysis and projection pursuit.

Page 451 - In Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP '98), pages 3613-3616, Seattle, Washington, 1998.

Page 470 - EP Simoncelli and EH Adelson, "Noise removal via Bayesian wavelet coring," in Proc 3rd IEEE Int'l Conf on Image Proc, I, pp.

Page 470 - EP Simoncelli and O. Schwartz. Modeling surround suppression in VI neurons with a statistically-derived normalization model.

Page 454 - DL Donoho, IM Johnstone, G. Kerkyacharian, and D. Picard. Wavelet shrinkage: Asymptopia?