Independent component analysis
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2001
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| Schriftenreihe: | Adaptive and learning systems for signal processing, communications, and control
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| 100 | 1 | |a Hyvärinen, Aapo |e Verfasser |0 (DE-588)1055801146 |4 aut | |
| 245 | 1 | 0 | |a Independent component analysis |c Aapo Hyvärinen ; Juha Karhunen ; Erkki Oja |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 2001 | |
| 300 | |a XXI, 481 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Adaptive and learning systems for signal processing, communications, and control | |
| 650 | 4 | |a Analyse en composantes principales | |
| 650 | 7 | |a Analyse en composantes principales |2 ram | |
| 650 | 4 | |a Analyse multivariée | |
| 650 | 7 | |a Analyse multivariée |2 ram | |
| 650 | 7 | |a analyse composante indépendante |2 inriac | |
| 650 | 7 | |a corrélation |2 inriac | |
| 650 | 7 | |a déconvolution |2 inriac | |
| 650 | 7 | |a maximum vraisemblance |2 inriac | |
| 650 | 7 | |a modèle non gaussien |2 inriac | |
| 650 | 7 | |a tenseur |2 inriac | |
| 650 | 7 | |a théorie estimation |2 inriac | |
| 650 | 0 | 7 | |a Komponentenanalyse |0 (DE-588)4133251-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Signalverarbeitung |0 (DE-588)4054947-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Oja, Erkki |e Verfasser |4 aut | |
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Datensatz im Suchindex
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| DE-BY-UBR_media_number | TEMP11720673 |
| _version_ | 1822685372782477312 |
| adam_text | Contents
Preface
xvii
1
Introduction
1
1.1
Linear
representation of
multivariate data
1
1.1.1
The general statistical setting
1
1.1.2
Dimension reduction methods
2
1.1.3
Independence as a guiding principle
3
1.2
Blind source separation
3
1.2.1
Observing mixtures of unknown signals
4
1.2.2
Source separation based on independence
5
1.3
Independent component analysis
6
1.3.1
Definition
6
1.3.2
Applications
7
1.3.3
How to find the independent components
7
1.4
History of
ICA
11
Vi
CONTENTS
Part I MATHEMATICAL PRELIMINARIES
2
Random Vectors and Independence
15
2.1
Probability distributions and densities
15
2.1.1
Distribution of a random variable
15
2.1.2
Distribution of a random vector
17
2.1.3
Joint and marginal distributions
18
2.2
Expectations and moments
19
2.2.1
Definition and general properties
19
2.2.2
Mean vector and correlation matrix
20
2.2.3
Covariances and joint moments
22
2.2.4
Estimation of expectations
24
2.3
Uncorrelatedness and independence
24
2.3.1
Uncorrelatedness and whiteness
24
2.3.2
Statistical independence
27
2.4
Conditional densities and
Bayes
rule
28
2.5
The multivariate
gaussian
density
31
2.5.1
Properties of the
gaussian
density
32
2.5.2
Central limit theorem
34
2.6
Density of a transformation
35
2.7
Higher-order statistics
36
2.7.1
Kurtosis and classification of densities
37
2.7.2
Cumulants,
moments, and their properties
40
2.8
Stochastic processes
* 43
2.8.1
Introduction and definition
43
2.8.2
Stationarity, mean, and autocorrelation
45
2.8.3
Wide-sense stationary processes
46
2.8.4
Time averages and ergodicity
48
2.8.5
Power spectrum
49
2.8.6
Stochastic signal models
50
2.9
Concluding remarks and references
51
Problems
52
3
Gradients and Optimization Methods
57
3.1
Vector and matrix gradients
57
3.1.1
Vector gradient
57
3.1.2
Matrix gradient
59
3.1.3
Examples of gradients
59
CONTENTS
VU
3.1.4 Taylor
series
expansions
62
3.2
Learning rules for unconstrained optimization
63
3.2.1
Gradient descent
63
3.2.2
Second-order learning
65
3.2.3
The natural gradient and relative gradient
67
3.2.4
Stochastic gradient descent
68
3.2.5
Convergence of stochastic on-line algorithms
* 71
3.3
Learning rules for constrained optimization
73
3.3.1
The
Lagrange
method
73
3.3.2
Projection methods
73
3.4
Concluding remarks and references
75
Problems
75
4
Estimation Theory
77
4.1
Basic concepts
78
4.2
Properties of estimators
80
4.3
Method of moments
84
4.4
Least-squares estimation
86
4.4.1
Linear least-squares method
86
4.4.2
Nonlinear and generalized least squares
* 88
4.5
Maximum likelihood method
90
4.6
Bayesian estimation
* 94
4.6.1
Minimum mean-square error estimator
94
4.6.2
Wiener filtering
96
4.6.3
Maximum a posteriori (MAP) estimator
97
4.7
Concluding remarks and references
99
Problems
101
5
Information Theory
105
5.1
Entropy
105
5.1.1
Definition of entropy
105
5.1.2
Entropy and coding length
107
5.1.3
Differential entropy
108
5.1.4
Entropy of a transformation
109
5.2
Mutual information
110
5.2.1
Definition using entropy
110
5.2.2
Definition using Kullback-Leibler divergence
110
viii CONTENTS
5.3
Maximum
entropy 111
5.3.1
Maximum entropy distributions 111
5.3.2
Maximality property of
gaussian
distribution
112
5.4
Negentropy
112
5.5
Approximation of entropy by
cumulants
113
5.5.1
Polynomial density expansions
113
5.5.2
Using expansions for entropy approximation
114
5.6
Approximation of entropy by nonpolynomial functions
115
5.6.1
Approximating the maximum entropy
116
5.6.2
Choosing the nonpolynomial functions
117
5.6.3
Simple special cases
118
5.6.4
Illustration
119
5.7
Concluding remarks and references
120
Problems
121
Appendix proofs
122
Principal Component Analysis and Whitening
125
6.1
Principal components
125
6.1.1
PC A by variance maximization
127
6.1.2
PCA by
minimum MSE
compression
128
6.1.3
Choosing the number of principal components
129
6.1.4
Closed-form computation of PCA
131
6.2
PCA by on-line learning
132
6.2.1
The stochastic gradient ascent algorithm
133
6.2.2
The subspace learning algorithm
134
6.2.3
The PAST algorithm
* 135
6.2.4
PCA and back-propagation learning
* 136
6.2.5
Extensions of PCA to nonquadratic criteria
* 137
6.3
Factor analysis
138
6.4
Whitening
140
6.5
Orthogonalization
141
6.6
Concluding remarks and references
143
Problems
144
CONTENTS
¡X
Part II BASIC INDEPENDENT COMPONENT ANALYSIS
7
What is Independent Component Analysis?
147
7.1
Motivation
147
7.2
Definition of independent component analysis
151
7.2.1
ICA as
estimation of a generative model
151
7.2.2
Restrictions in
ICA
152
7.2.3
Ambiguities of
ICA
154
7.2.4
Centering the variables
154
7.3
Illustration of
ICA
155
7.4
ICA
is stronger that whitening
158
7.4.1
Uncorrelatedness and whitening
158
7.4.2
Whitening is only half
ICA
160
7.5
Why
gaussian
variables are forbidden
161
7.6
Concluding remarks and references
163
Problems
164
8
ICA
by Maximization of Nongaussianity
165
8.1
Nongaussian is independent
166
8.2
Measuring nongaussianity by kurtosis
171
8.2.1
Extrema
give independent components
171
8.2.2
Gradient algorithm using kurtosis
175
8.2.3
A fast fixed-point algorithm using kurtosis
178
8.2.4
Examples
179
8.3
Measuring nongaussianity by negentropy
182
8.3.1
Critique of kurtosis
182
8.3.2
Negentropy as nongaussianity measure
182
8.3.3
Approximating negentropy
183
8.3.4
Gradient algorithm using negentropy
185
8.3.5
A fast fixed-point algorithm using negentropy
188
8.4
Estimating several independent components
192
8.4.1
Constraint of uncorrelatedness
192
8.4.2
Deflationary orthogonalization
194
8.4.3
Symmetric orthogonalization
194
8.5
ICA
and projection pursuit
197
8.5.1
Searching for interesting directions
197
8.5.2
Nongaussian is interesting
197
8.6
Concluding remarks and references
198
X
CONTENTS
Problems 199
Appendix
proofs
201
9
ICA
by Maximum Likelihood Estimation
203
9.1
The likelihood of the
ICA
model
203
9.1.1
Deriving the likelihood
203
9.1.2
Estimation of the densities
204
9.2
Algorithms for maximum likelihood estimation
207
9.2.1
Gradient algorithms
207
9.2.2
A fast fixed-point algorithm
209
9.3
The infomax principle
211
9.4
Examples
213
9.5
Concluding remarks and references
214
Problems
218
Appendix proofs
219
10
ICA
by Minimization of Mutual Information
221
10.1
Defining
ICA
by mutual information
221
10.1.1
Information-theoretic concepts
221
10.1.2
Mutual information as measure of dependence
222
10.2
Mutual information and nongaussianity
223
10.3
Mutual information and likelihood
224
10.4
Algorithms for minimization of mutual information
224
10.5
Examples
225
10.6
Concluding remarks and references
225
Problems
227
11
ICA
by
Tensorial
Methods
229
11.1
Definition of
cumulant
tensor
229
11.2
Tensor eigenvalues give independent components
230
11.3
Tensor decomposition by a power method
232
11.4
Joint approximate diagonalization of eigenmatrices
234
11.5
Weighted correlation matrix approach
235
11.5.1
The
E
OBI algorithm
235
11.5.2
From
FOBI
to JADE
235
11.6
Concluding remarks and references
236
Problems
237
CONTENTS
XI
12
ICA
by
Nonlinear Decorrelation and Nonlinear PCA 239
12.1
Nonlinear correlations and independence
240
12.2
The
Hérault-Jutten
algorithm
242
12.3
The Cichocki-Unbehauen algorithm
243
12.4
The estimating functions approach
* 245
12.5
Equivariant adaptive separation via independence
247
12.6
Nonlinear principal components
249
12.7
The nonlinear PCA criterion and
ICA
251
12.8
Learning rules for the nonlinear PCA criterion
254
12.8.1
The nonlinear subspace rule
254
12.8.2
Convergence of the nonlinear subspace rule
* 255
12.8.3
Nonlinear recursive least-squares rule
258
12.9
Concluding remarks and references
261
Problems
262
13
Practical Considerations
263
13.1
Preprocessing by time filtering
263
13.1.1
Why time filtering is possible
264
13.1.2
Low-pass filtering
265
13.1.3
High-pass filtering and innovations
265
13.1.4
Optimal filtering
266
13.2
Preprocessing by PCA
267
13.2.1
Making the mixing matrix square
267
13.2.2
Reducing noise and preventing overlearning
268
13.3
How many components should be estimated?
269
13.4
Choice of algorithm
271
13.5
Concluding remarks and references
272
Problems
272
14
Overview and Comparison of Basic
ICA
Methods
273
14.1
Objective functions vs. algorithms
273
14.2
Connections between
ICA
estimation principles
274
14.2.1
Similarities between estimation principles
274
14.2.2
Differences between estimation principles
275
14.3
Statistically optimal nonlinearities
276
14.3.1
Comparison of asymptotic variance
* 276
14.3.2
Comparison of robustness
* 277
14.3.3
Practical choice of nonlinearity
279
Xli CONTENTS
14.4
Experimental
comparison of
ICA
algorithms
280
14.4.1
Experimental set-up and algorithms
281
14.4.2
Results for simulated data
282
14.4.3
Comparisons with real-world data
286
14.5
References
287
14.6
Summary of basic
ICA
287
Appendix Proofs
289
Part III EXTENSIONS AND RELATED METHODS
15
Noisy
ICA
293
15.1
Definition
293
15.2
Sensor noise vs. source noise
294
15.3
Few noise sources
295
15.4
Estimation of the mixing matrix
295
15.4.1
Bias removal techniques
296
15.4.2
Higher-order
cumulant
methods
298
15.4.3
Maximum likelihood methods
299
15.5
Estimation of the noise-free independent components
299
15.5.1
Maximum a posteriori estimation
299
15.5.2
Special case of shrinkage estimation
300
15.6
Denoising by sparse code shrinkage
303
15.7
Concluding remarks
304
16
ICA
with Overcomplete Bases
305
16.1
Estimation of the independent components
306
16.1.1
Maximum likelihood estimation
306
16.1.2
The case of supergaussian components
307
16.2
Estimation of the mixing matrix
307
16.2.1
Maximizing joint likelihood
307
16.2.2
Maximizing likelihood approximations
308
16.2.3
Approximate estimation by quasiorthogonality
309
16.2.4
Other approaches
311
16.3
Concluding remarks
313
CONTENTS xiii
17 Nonlinear
ICA
315
17.1
Nonlinear
ICA
and BSS
315
17.1.1
The nonlinear
ICA
and BSS problems
315
17.1.2
Existence and uniqueness of nonlinear
ICA
317
17.2
Separation of post-nonlinear mixtures
319
17.3
Nonlinear BSS using self-organizing maps
320
17.4
A generative topographic mapping approach
* 322
17.4.1
Background
322
17.4.2
The modified GTM method
323
17.4.3
An experiment
326
17.5
An ensemble learning approach to nonlinear BSS
328
17.5.1
Ensemble learning
328
17.5.2
Model structure
329
17.5.3
Computing Kullbach-Leibler cost function
* 330
17.5.4
Learning procedure
* 332
17.5.5
Experimental results
333
17.6
Other approaches
337
17.7
Concluding remarks
339
18
Methods using Time Structure
341
18.1
Separation by autocovariances
342
18.1.1
An alternative to nongaussianity
342
18.1.2
Using one time lag
343
18.1.3
Extension to several time lags
344
18.2
Separation by nonstationarity of variances
346
18.2.1
Using local autocorrelations
347
18.2.2
Using cross-cumulants
349
18.3
Separation principles unified
351
18.3.1
Comparison of separation principles
351
18.3.2
Kolmogorojf complexity as unifying framework
352
18.4
Concluding remarks
354
Xiv CONTENTS
19 Convolutive
Mixtures and
Blind Deconvolution 355
19.1 Blind deconvolution 356
19.1.1 Problem
definition
356
19.1.2 Bus
s
gang methods
357
19.1.3 Cumulant-based
methods
358
19.1.4 Blind deconvolution
using
linear
ICA
360
19.2 Blind
separation of
convolutive
mixtures
361
19.2.1 The convolutive BSS
problem
361
19.2.2
Reformulation as ordinary
ICA
363
19.2.3
Natural gradient methods
364
19.2.4
Fourier transform methods
365
19.2.5
Spatiotemporal
decorrelation methods
367
19.2.6
Other methods for convolutive mixtures
367
19.3
Concluding remarks
368
Appendix Discrete-time filters and the z-transform
369
20
Other Extensions
371
20.1
Priors on the mixing matrix
371
20.1.1
Motivation for prior information
371
20.1.2
Classic priors
372
20.1.3
Sparse priors
374
20.1.4
Spatiotemporal ICA
377
20.2
Relaxing the independence assumption
378
20.2.1
Multidimensional ICA
379
20.2.2
Independent subspace analysis
380
20.2.3
Topographic ICA
382
20.3
Complex-valued data
383
20.3.1
Basic concepts of complex random variables
383
20.3.2
Indeterminacy of the independent components
384
20.3.3
Choice of the nongaussianity measure
385
20.3.4
Consistency of estimator
386
20.3.5
Fixed-point algorithm
386
20.3.6
Relation to independent subspaces
387
20.4
Concluding remarks
387
CONTENTS
XV
Part IV
APPLICATIONS
OF ICA
21
Feature Extraction by
ICA
391
21.1
Linear representations
392
21.1.1
Definition
392
21.1.2 Gabor
analysis
392
21.1.3
Wavelets
394
21.2
ICA
and Sparse Coding
396
21.3
Estimating
ICA
bases from images
398
21.4
Image denoising by sparse code shrinkage
398
21.4.1
Component statistics
399
21.4.2
Remarks on windowing
400
21.4.3
Denoising results
401
21.5
Independent subspaces and topographic
ICA
401
21.6
Neurophysiological connections
403
21.7
Concluding remarks
405
22
Brait
ι
Imaging Applications
407
22.1
Electro- and magnetoencephalography
407
22.1.1
Classes of brain imaging techniques
407
22.1.2
Measuring electric activity in the brain
408
22.1.3
Validity of the basic
ICA
model
409
22.2
Artifact identification from
EEG
and MEG
410
22.3
Analysis of evoked magnetic fields
411
22.4
ICA
applied on other measurement techniques
413
22.5
Concluding remarks
414
23
Telecommunications
417
23.1
Multiuser detection and CDMA communications
417
23.2
CDMA signal model and
ICA
422
23.3
Estimating fading channels
424
23.3.1
Minimization of complexity
424
23.3.2
Channel estimation
*
426
23.3.3
Comparisons and discussion
428
23.4
Blind separation of convolved CDMA mixtures
*
430
23.4.1
Feedback architecture
430
23.4.2 Semiblind
separation method
431
23.4.3
Simulations and discussion
432
xvi CONTENTS
23.5
Improving multiuser detection using complex
ICA
* 434
23.5.1
Data model
435
23.5.2
ICA
based receivers
436
23.5.3
Simulation results
438
23.6
Concluding remarks and references
439
24
Other Applications
441
24.1
Financial applications
441
24.1.1
Finding hidden factors in financial data
441
24.1.2
Time series prediction by
ICA
443
24.2
Audio separation
446
24.3
Further applications
448
References
449
Index
476
|
| any_adam_object | 1 |
| author | Hyvärinen, Aapo Karhunen, Juha Oja, Erkki |
| author_GND | (DE-588)1055801146 (DE-588)101121119X |
| author_facet | Hyvärinen, Aapo Karhunen, Juha Oja, Erkki |
| author_role | aut aut aut |
| author_sort | Hyvärinen, Aapo |
| author_variant | a h ah j k jk e o eo |
| building | Verbundindex |
| bvnumber | BV013819390 |
| callnumber-first | Q - Science |
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| callnumber-search | QA278 |
| callnumber-sort | QA 3278 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 234 SK 830 ST 300 |
| classification_tum | DAT 780f DAT 717f |
| ctrlnum | (OCoLC)248365948 (DE-599)BVBBV013819390 |
| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre | 1\p (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013819390 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:38:26Z |
| institution | BVB |
| isbn | 047140540X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009450085 |
| oclc_num | 248365948 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-29T DE-91 DE-BY-TUM DE-M347 DE-384 DE-739 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-29T DE-91 DE-BY-TUM DE-M347 DE-384 DE-739 DE-83 DE-11 DE-188 |
| physical | XXI, 481 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley |
| record_format | marc |
| series2 | Adaptive and learning systems for signal processing, communications, and control |
| spellingShingle | Hyvärinen, Aapo Karhunen, Juha Oja, Erkki Independent component analysis Analyse en composantes principales Analyse en composantes principales ram Analyse multivariée Analyse multivariée ram analyse composante indépendante inriac corrélation inriac déconvolution inriac maximum vraisemblance inriac modèle non gaussien inriac tenseur inriac théorie estimation inriac Komponentenanalyse (DE-588)4133251-9 gnd Signalverarbeitung (DE-588)4054947-1 gnd |
| subject_GND | (DE-588)4133251-9 (DE-588)4054947-1 (DE-588)4113937-9 |
| title | Independent component analysis |
| title_auth | Independent component analysis |
| title_exact_search | Independent component analysis |
| title_full | Independent component analysis Aapo Hyvärinen ; Juha Karhunen ; Erkki Oja |
| title_fullStr | Independent component analysis Aapo Hyvärinen ; Juha Karhunen ; Erkki Oja |
| title_full_unstemmed | Independent component analysis Aapo Hyvärinen ; Juha Karhunen ; Erkki Oja |
| title_short | Independent component analysis |
| title_sort | independent component analysis |
| topic | Analyse en composantes principales Analyse en composantes principales ram Analyse multivariée Analyse multivariée ram analyse composante indépendante inriac corrélation inriac déconvolution inriac maximum vraisemblance inriac modèle non gaussien inriac tenseur inriac théorie estimation inriac Komponentenanalyse (DE-588)4133251-9 gnd Signalverarbeitung (DE-588)4054947-1 gnd |
| topic_facet | Analyse en composantes principales Analyse multivariée analyse composante indépendante corrélation déconvolution maximum vraisemblance modèle non gaussien tenseur théorie estimation Komponentenanalyse Signalverarbeitung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009450085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hyvarinenaapo independentcomponentanalysis AT karhunenjuha independentcomponentanalysis AT ojaerkki independentcomponentanalysis |