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Hyvarinen A. — Independent Component Analysis
Hyvarinen A. — Independent Component Analysis



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Название: Independent Component Analysis

Автор: 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: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 505

Добавлена в каталог: 04.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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