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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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Akaike's information criterion 131 Algorithm, AMUSE 343 Algorithm, Bell — Sejnowski 207 Algorithm, Cichocki — Unbehauen 244 Algorithm, EASI 247 Algorithm, eigenvalue decomposition of cumulant tensor 230 Algorithm, eigenvalue decomposition of weighted correlation 235 Algorithm, fixed-point (FastICA) for complex-valued data 386 Algorithm, fixed-point (FastICA) for maximum likelihood estimation 209 Algorithm, fixed-point (FastICA) for tensor decomposition 232 Algorithm, fixed-point (FastICA) using kurtosis 178 Algorithm, fixed-point (FastICA) using negentropy 188 Algorithm, FOBI 235 Algorithm, gradient for maximum likelihood estimation 207 Algorithm, gradient, using kurtosis 175 Algorithm, gradient, using negentropy 185 Algorithm, Herault — Jutten 242 Algorithm, JADE 234 Algorithm, natural gradient for maximum likelihood estimation 208 430 Algorithm, nonlinear RLS 259 Algorithm, SOBI 344 Algorithm, TDSEP 344 Algorithms, choice of 271 Algorithms, connections between 274 Algorithms, effect of noise 286 Algorithms, experimental comparison 280 Algorithms, performance index 281 Algorithms, vs. objective functions 273 AMUSE 343 Apex 135 Applications, audio separation 446 Applications, brain imaging 407 Applications, brain modeling 403 Applications, communications 358 417 Applications, econometric 441 Applications, financial 441 Applications, image denoising 398 Applications, image feature extraction 311 391 Applications, industrial process monitoring 335 Applications, miscellaneous 448 Applications, vision research 403 Applications, visualization 197 ARMA process 51 Artifacts in EEG and MEG 410 Asymptotic variance 276 Autoassociative learning 136 249 Autocorrelations 45 47 Autocorrelations, as an alternative to nongaussianity 342 Autocorrelations, ICA estimation using 342 Autocorrelations, in telecommunications 424 Autoregressive (AR) process 50 445 Back-propagation learning 136 Basis vectors, and factor rotation 268 Basis vectors, Gabor 394 Basis vectors, ICA 398 Basis vectors, in overcomplete ICA 305 Basis vectors, of independent subspace 380 Basis vectors, of PC A subspace 128 Basis vectors, relation to filters in ICA 396 Basis vectors, wavelet 396 Batch learning 69 Bayes' rule 31 Bias 80 Blind deconvolution 355—356 Blind deconvolution, Bussgang methods 357 Blind deconvolution, CMA algorithm 358 Blind deconvolution, cumulant-based methods 358 Blind deconvolution, Godard algorithm 357 Blind deconvolution, multichannel 355 361 Blind deconvolution, Shalvi — Weinstein algorithm 359 Blind deconvolution, using linear ICA 360 Blind equalization See blind deconvolution Blind source separation 147 Brain imaging 407 Bussgang criterion 253 CDMA (Code Division Multiple Access) 417 CDMA signal model 422 Centering 154 Central limit theorem 34 166 Central moment 37 84 Characteristic function 41 Chip sequence 418 Cichocki — Unbehauen algorithm 244 Cocktail-party problem 147 361 446 Code length and entropy 107 Code length and Kolmogoroff complexity 352 Code length and mutual information 110 Complex-valued data 383 Complexity minimization 353 424 Compression by PC A 126 Compression Conjugate gradients 67 Consistency 80 Consistency of ICA methods 187 205 Convergence of on-line algorithms 71 Convergence, speed 65 Convolution 369 Convolutive mixtures 355 361 Convolutive mixtures, application in CDMA 430 Convolutive mixtures, Bussgang type methods 367 Convolutive mixtures, Fourier transform methods 365 Convolutive mixtures, natural gradient methods 364 Convolutive mixtures, using autocovariances 367 Convolutive mixtures, using higher-order statistics 367 Convolutive mixtures, using spatiotemporal decorrelation 367 Correlation 21 Correlation matrix 21—22 26 48 Correlation, and independence 240 Correlation, nonlinear 240 Covariance 22 Covariance matrix 22 Covariance matrix of estimation error 82 95 Cramer — Rao lower bound 82 92 Cross-correlation function 46 Cross-correlation matrix 22 Cross-covariance function 46 Cross-covariance matrix 23 Cross-cumulants 42 Cumulant generating function 41 Cumulant tensor 229 Cumulants 41—42 Cumulative distribution function 15 17 27 36 Cumulative distribution function, joint 19 Curve fitting 87 Cyclostationarity 368 Decorrelation 132 140 Decorrelation, nonlinear 239—240 244 Denoising of images 398 density See probability density Density expansions, Edgeworth 113 Density expansions, Gram — Charlier 113 Density expansions, polynomial 113 Discrete-valued components 261 299 311 distribution See probability density EASI algorithm 247 Edgeworth expansion 113 EEG 407 Electrocardiography 413 Electroencephalography 407 EM algorithm 93 Ensemble learning 328 entropy 222 Entropy, approximation 113 115 Entropy, approximation by cumulants 113 Entropy, approximation by nonpolynomial functions 115 Entropy, definition 105 Entropy, differential 108 Entropy, maximality of gaussian distribution 112 Entropy, maximum 111 Entropy, of transformation 109 Equivariance 248 Ergodicity 49 Error criterion 81 Estimate 78 Estimating function 245 Estimation 77 Estimation, adaptive 79 Estimation, asymptotically unbiased 80 Estimation, batch 79 Estimation, Bayesian 79 94 Estimation, consistent 80 Estimation, efficient 82 Estimation, error 80 Estimation, linear minimum MSE error 95 Estimation, maximum a posteriori (MAP) 97 Estimation, maximum likelihood 90 Estimation, minimum mean-square error 94 428 433 Estimation, moment 84 Estimation, of expectation 24 Estimation, off-line 79 Estimation, on-line 79 Estimation, recursive 79 Estimation, robust 83 Estimation, unbiased 80 Estimator See estimation (for general entry); Algorithm (for ICA entry) Evoked fields 411 Expectation 19 Expectation, conditional 31 Expectation, properties 20 Expectation-maximization (EM) algorithm 322 Factor analysis 138 Factor analysis, and ICA 139 268 Factor analysis, nonlinear 332 Factor analysis, nonlinear independent 332 Factor analysis, principal 138 Factor rotation 139—140 268 FastICA, for complex-valued data 437 FastICA, for maximum likelihood estimation 209 FastICA, for tensor decomposition 232 FastICA, using kurtosis 178 FastICA, using negentropy 188 Feature extraction by ICA 150 398 Feature extraction by independent subspace analysis 401 Feature extraction by topographic ICA 401 Feature extraction using overcomplete bases 311 Feedback architecture 431 Filtering, high-pass 265 Filtering, linear 96 Filtering, low-pass 265 Filtering, optimal 266 Filtering, taking innovation processes 266 Filtering, Wiener 96 Financial time series 441 FIR filter 369 Fisher information matrix 83 Fixed-point algorithm see FastICA FMRI 407 413 FOBI 235 Fourier transform 370 Fourth-order blind identification 235 Gabor analysis 392 Gabor analysis and ICA 398 Gauss — Newton method 67 Gaussian density 16 Gaussian density, forbidden in ICA 161 Gaussian density, multivariate 31 Gaussian density, properties 32 Generalized Hebbian algorithm (GHA) 134 Generative topographic mapping (GTM) 322 Gradient 57 Gradient descent, deterministic 63 Gradient descent, stochastic 68 Gradient, natural 67 208 244 247 Gradient, of function 57 Gradient, relative 67 247 Gram — Charlier expansion 113 Gram — Schmidt orthogonalization 141 Herault — Jutten algorithm 242 Hessian matrix 58 Higher-order statistics 36 ICA, ambiguities in 154 ICA, ambiguities in, complex-valued case 384 ICA, and factor rotation 140 268 ICA, and feature extraction 398 ICA, applications on images 401 ICA, definition 151 ICA, identifiability 152 154 ICA, identifiability, complex-valued case 384 ICA, multidimensional 379 ICA, noisy 293 ICA, overview of estimation principles 287 ICA, restrictions in 152 ICA, spatiotemporal 377 ICA, topographic 382 ICA, with complex-valued data 383 435 ICA, with convolutive mixtures 355 361 430 ICA, with overcomplete bases 305—306 ICA, with subspaces 380 IIR filter 369 Independence 27 30 33 Independent component analysis See ICA Independent subspace analysis 380 Independent subspace analysis, and complex-valued data 387 Independent subspace analysis, applications on images 401 Infomax 211 430 Innovation process 266 Intersymbol interference (ISI) 420 Jacobian matrix 58 JADE 234 Jeffreys' prior 373 Joint approximate diagonalization 234 Karhunen — Loeve transform 143 Kolmogoroff complexity 351 424—425 Kullback — Leibler divergence 110 kurtosis 38 Kurtosis, as nongaussianity measure 171 Kurtosis, nonrobustness 182 184 Kurtosis, relation with nonlinear PCA 252 Lagrange method 73 Laplacian density 39 171 Learning, algorithms 63 Learning, batch 69 Learning, on-line 69 Learning, rate 63 Least mean-square error 249 Least-squares method 86 Least-squares method, generalized 88 Least-squares method, linear 86 Least-squares method, nonlinear 89 93 Least-squares method, normal equations 87 Likelihood 90. See also Maximum likelihood Likelihood and mutual information 224 Likelihood and nonlinear PCA 253 Likelihood and posterior density 97 Likelihood of ICA model 203 Loss function 81 Magnetic resonance imaging 407 413 Magnetoencephalography 407 Magnetoneurography 413 MAP See Maximum a posteriori Marquardt — Levenberg algorithm 67 Matched filter 424 432 Matrix, determinant 61 Matrix, gradient of function 59 Matrix, Jacobian 36 Matrix, trace 62 Maximization of function 57 Maximum a posteriori 97 299 303 306 326 Maximum entropy 111 Maximum likelihood 90 203 322 Maximum likelihood, consistency of 205
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