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. |
Contents
Introduction | 1 |
Random Vectors and Independence | 15 |
Gradients and Optimization Methods | 57 |
4 | 75 |
4 | 85 |
6 | 91 |
7 | 99 |
Information Theory | 105 |
Practical Considerations | 263 |
Overview and Comparison of Basic ICA Methods | 273 |
Noisy ICA | 293 |
ICA with Overcomplete Bases | 305 |
Nonlinear ICA | 315 |
Methods using Time Structure | 341 |
Convolutive Mixtures and Blind Deconvolution | 355 |
Other Extensions | 371 |
Principal Component Analysis and Whitening | 125 |
What is Independent Component Analysis? | 147 |
ICA by Maximization of Nongaussianity | 165 |
ICA by Maximum Likelihood Estimation | 203 |
ICA by Minimization of Mutual Information | 221 |
ICA by Tensorial Methods | 229 |
ICA by Nonlinear Decorrelation and Nonlinear PCA | 239 |
Other editions - View all
Common terms and phrases
applied approach approximation assumed basic ICA basis vectors blind deconvolution blind separation Blind Signal Separation 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 denote density function derived differential entropy discussed eigenvalues eigenvectors entropy equation example FastICA FastICA algorithm filter given gradient algorithm ICA estimation ICA methods ICA model IEEE Trans independent component analysis iteration kurtosis learning rule least-squares linear mapping maximization mean-square error minimization mixing matrix mutual information natural gradient negentropy Neural Networks noise nonlinear nonlinear ICA observed obtained on-line optimization orthogonal parameters principal component principle prior probability density problem Proc projection pursuit random variables random vector sample scalar Section separating matrix Signal Processing Signal Separation source signals sparse coding statistically independent subspace supergaussian theorem transformation uncorrelated zero mean