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Hyvarinen A. — Independent Component Analysis
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Название: Independent Component AnalysisАвтор: Hyvarinen A. Аннотация: Hyvarinen and fellow researchers Juhu Karhunen and Erkki Oja (all Helsinki U. of Technology) introduce independent component analysis as a statistical and computational technique for revealing hidden factors that underlie sets of random variables, measurements, or signals. Readers are intended to be from such disciplines as statistics, signal processing, neural networks, information theory, and engineering, and to have a grounding in college calculus, matrix algebra, probability theory, and statistics. Exercise problems and computer assignments facilitate the book's use in a graduate course.
Язык: Рубрика: Математика /Вероятность /Статистика и приложения /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2001Количество страниц: 505Добавлена в каталог: 04.06.2005Операции: Положить на полку |
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Maximum likelihood, in CDMA 424. See also Likelihood Mean function 45 Mean vector 21 Mean-square error 81 94 Mean-square error, minimization for PCA 128 MEG 407 Minimization of function 57 Minimum description length 131 Minimum-phase filter 370 Minor components 135 Mixture of gaussians 322 329 ML See Maximum likelihood MMSE estimator 424 MMSE-ICA detector 434 437—438 Model order choosing 131 271 Modified GTM method 323 Moment generating function 41 Moment method 84 Moments 20 37 41—42 Moments, central 22 Moments, nonpolynomial 207 Momentum term 426 Moving average (MA) process 51 Multilayer perceptron 136 328 Multipath propagation 420 Multiple access communications 417 Multiple access interference (MAI) 421 Multiuser detection 421 Mutual information 221—222 319 Mutual information, and Kullback — Leibler divergence 110 Mutual information, and likelihood 224 Mutual information, and nongaussianity 223 Mutual information, approximation of 223—224 Mutual information, definition 110 Mutual information, minimization of 221 Near-far problem 421 424 Negentropy 222 Negentropy, approximation 113 115 183 Negentropy, approximation, by cumulants 113 Negentropy, approximation, by nonpolynomial functions 115 Negentropy, as measure of nongaussianity 182 Negentropy, as nongaussianity measure 182 Negentropy, definition 112 Negentropy, optimality 277 Neural networks 36 Neurons 408 Newton's method 66 Noise 446 Noise, as independent components 295 Noise, in the ICA model 293 Noise, reduction by low-pass filtering 265 Noise, reduction by nonlinear filtering 300 Noise, reduction by PCA 268 Noise, reduction by shrinkage 300 Noise, reduction by shrinkage, application on images 398 Noise, sensor vs. source 294 Noisy ICA, application, image processing 398 Noisy ICA, application, telecommunications 423 Noisy ICA, estimation of ICs 299 Noisy ICA, estimation of ICs, by MAR 299 Noisy ICA, estimation of ICs, by maximum likelihood 299 Noisy ICA, estimation of ICs, by shrinkage 300 Noisy ICA, estimation of mixing matrix 295 Noisy ICA, estimation of mixing matrix, bias removal techniques 296 Noisy ICA, estimation of mixing matrix, by cumulant methods 298 Noisy ICA, estimation of mixing matrix, by FastICA 298 Noisy ICA, estimation of mixing matrix, by maximum likelihood 299 Nongaussianity 165 Nongaussianity, and projection pursuit 197 Nongaussianity, is interesting 197 Nongaussianity, measured by kurtosis 171 182 Nongaussianity, measured by negentropy 182 Nongaussianity, optimal measure is negentropy 277 Nonlinear BSS 315 Nonlinear BSS, definition 316 Nonlinear ICA 315 Nonlinear ICA, definition 316 Nonlinear ICA, existence and uniqueness 317 Nonlinear ICA, post-nonlinear mixtures 319 Nonlinear ICA, using ensemble learning 328 Nonlinear ICA, using modified GTM method 323 Nonlinear ICA, using self-organizing map (SOM) 320 Nonlinear mixing model 315 Nonlinearity in algorithm, choice of 276 280 Nonstationarity, and tracking 72 133 135 178 Nonstationarity, definition 46 Nonstationarity, measuring by autocorrelations 347 Nonstationarity, measuring by cross-cumulants 349 Nonstationarity, separation by 346 Oja's rule 133 On-line learning 69 Optical imaging 413 Optimization methods 57 Optimization methods, constrained 73 Optimization methods, unconstrained 63 Order statistics 226 Orthogonalization 141 Orthogonalization, Gram — Schmidt 141 Orthogonalization, symmetric 142 Overcomplete bases, and image feature extraction 311 Overcomplete bases, estimation of ICs 306 Overcomplete bases, estimation of ICs, by maximum likelihood 306 Overcomplete bases, estimation of mixing matrix 307 Overcomplete bases, estimation of mixing matrix, by FastICA 309 Overcomplete bases, estimation of mixing matrix, by maximum likelihood 307 Overlearning 268 Overlearning and PCA 269 Overlearning and priors on mixing 371 Parameter vector 78 PAST 136 Performance index 81 PET 407 Positive semidefinite 21 Post-nonlinear mixtures 316 Posterior 94 Power method, higher-order 232 Power spectrum 49 Prediction of time series 443 Preprocessing 263 Preprocessing, by PCA 267 Preprocessing, centering 154 Preprocessing, filtering 264 Preprocessing, whitening 158 Principal component analysis 125 332 Principal component analysis, and complexity 425 Principal component analysis, and ICA 139 249 251 Principal component analysis, and whitening 140 Principal component analysis, by on-line learning 132 Principal component analysis, closed-form computation 132 Principal component analysis, nonlinear 249 Principal component analysis, number of components 129 Principal component analysis, with nonquadratic criteria 137 Principal curves 249 Prior 94 Prior, conjugate 375 Prior, for mixing matrix 371 Prior, Jeffreys' 373 Prior, quadratic 373 Prior, sparse 374 Prior, sparse, for mixing matrix 375 probability density 16 Probability density, a posteriori 94 Probability density, a priori 94 Probability density, conditional 28 Probability density, double exponential 39 171 Probability density, gaussian 16 42 Probability density, generalized gaussian 40 Probability density, joint 19 22 27 30 45 Probability density, Laplacian 39 171 Probability density, marginal 19 27 29 33 Probability density, multivariate 17 Probability density, of a transformation 35 Probability density, posterior 31 328 Probability density, prior 31 Probability density, uniform 36 39 171 Projection matrix 427 Projection method 73 Projection pursuit 197 286 Pseudoinverse 87 Quasiorthogonality 310 Quasiorthogonality, in FastICA 310 RAKE detector 424 434 437—438 RAKE-ICA detector 434 438 Random variable 15 Random vector 17 Recursive least-squares, for nonlinear PCA 259 Recursive least-squares, for PCA 135 Robustness 83 182 277 Sample mean 24 Sample moment 84 Self-organizing map (SOM) 320 Semiblind methods 387 424 432 Semiparametric 204 skewness 38 Smoothing 445 SOBI 344 Sparse code shrinkage 303 398 Sparse coding 396 Sparsity, measurement of 374 Spatiotemporal ICA 377 Spatiotemporal statistics 362 Sphered random vector 140 Spreading code 418 Stability See consistency Stationarity Stochastic approximation 71 Stochastic gradient ascent (SGA) 133 Stochastic processes 43 Subgaussian 38 Subspace MMSE detector 434 436 438 Subspace, learning algorithm for PCA 134 Subspace, noise 131 Subspace, nonlinear learning rule 254 Subspace, signal 131 Subspaces, independent 380 Subspaces, invariant-feature 380 Superefficiency 261 Supergaussian 39 Taylor series 62 TDSEP 344 Tensor methods for ICA 229 Time averages 48 Time structure 43 Time structure, ICA estimation using 341 Toeplitz matrix 48 Tracking in a nonstationary environment 72 Transfer function 370 Unbiasedness 80 Uncorrelatedness 24 27 33 Uncorrelatedness, constraint of 192 Uniform density 36 39 Uniform density, rotated 250 Variance 22 Variance, maximization 127 Vector, gradient of function 57 Vector, valued function 58 Visual cortex 403 Wavelets 394 Wavelets and ICA 398 Wavelets as preprocessing 267 White noise 50 Whiteness 25 Whitening 140 Whitening as preprocessing in ICA 158 Whitening by PCA expansion 140 Wiener filtering 96 Wiener filtering, nonlinear 300 z-transform 369
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