Mathematics in independent component analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos-Verl.
2003
|
| Schriftenreihe: | Nichtlineare und stochastische Physik
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 179 S. graph. Darst. |
| ISBN: | 3832501274 |
Internformat
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| 100 | 1 | |a Theis, Fabian J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics in independent component analysis |c vorgelegt von Fabian J. Theis |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2003 | |
| 300 | |a XVI, 179 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Nichtlineare und stochastische Physik |v 9 | |
| 502 | |a Zugl.: Regensburg, Univ., Diss., 2002 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
PREFACE
V
CONTENTS
XIII
I
BASIC
PRINCIPLES
1
1
BASICS
3
1.1
NOTATION
.
3
1.2
MATRIX
EQUIVALENCE
.
3
1.2.1
MEASURES
OF
EQUIVALENCE
.
4
1.3
PROBABILITY
THEORY
.
5
1.3.1
RANDOM
FUNCTIONS
.
5
1.3.2
OPERATIONS
ON
RANDOM
VECTORS
.
9
1.3.3
COVARIANCE
.
11
1.3.4
EXAMPLES
OF
PROBABILITY
DISTRIBUTIONS
.
11
1.3.5
KURTOSIS
.
13
1.3.6
SAMPLING
.
14
1.4
INFORMATION
THEORY
.
15
1.5
APPROXIMATION
OF
PROBABILITY
DENSITIES
.
17
2
INDEPENDENT
COMPONENT
ANALYSIS
AND
BLIND
SOURCE
SEPA
RATION
21
2.1
INTRODUCTION
.
21
2.2
PRINCIPAL
COMPONENT
ANALYSIS
.
22
2.3
INDEPENDENT
COMPONENT
ANALYSIS
.
23
2.3.1
INTRODUCTION
.
23
2.3.2
CONTRAST
.
23
2.3.3
DEFINITION
OF
ICA
.
24
2.4
BLIND
SOURCE
SEPARATION
.
27
2.4.1
INTRODUCTION
.
27
2.4.2
DEFINITION
OF
BSS
.
27
2.4.3
LINEAR
BSS
.
28
2.4.4
NONLINEAR
BSS
.
29
2.5
UNIQUENESS
RESULTS
.
30
2.5.1
UNIQUENESS
OF
STANDARD
LINEAR
ICA
.
30
2.5.2
UNIQUENESS
OF
POSTNONLINEAR
ICA
.
32
2.5.3
NON-UNIQUENESS
OF
NONLINEAR
ICA
.
33
2.6
BLIND
MIXING
MODEL
RECOVERY
AND
BLIND
SOURCE
RECOVERY
.
.
33
2.6.1
LINEAR
BMMR
.
34
2.6.2
LINEAR
BSR
.
34
II
LINEAR
ICA
37
3
SYMMETRIC
LINEAR
ICA
39
3.1
GEOMETRIC
ICA
.
39
3.1.1
THE
GEOICA
ALGORITHM
.
40
3.1.2
EXAMPLE
.
45
3.1.3
GEOMETRIC
CONSIDERATIONS
.
46
3.1.4
FORMAL
MODEL
OF
THE
GEOMETRIC
ALGORITHM
.
49
3.1.5
LIMIT
POINTS
OF
THE
GEOMETRIC
ALGORITHM
.
50
3.1.6
UPDATE
RULES
WITHOUT
SIGN
FUNCTIONS
.
55
3.2
FASTGEO:
A
HISTOGRAM-BASED
ALGORITHM
.
55
3.2.1
ACCURACY
.
58
3.2.2
EXAMPLES
.
61
3.3
GEOMETRIC
ICA
IN
HIGHER
DIMENSIONS
.
65
3.3.1
MIXING
DIMENSION
REDUCTION
.
66
3.3.2
EXPERIMENTAL
RESULTS
.
69
3.4
CONCLUSIONS
.
72
4
OVERCOMPLETE
LINEAR
ICA
75
4.1
TWO-STEP
APPROACH
TO
THE
SEPARATION
.
76
4.2
GEOMETRIC
BMMR
.
76
4.2.1
THE
OVERCOMPLETE
GEOICA
ALGORITHM
.
77
4.2.2
UNIQUENESS
OF
GEOMETRIC
BMMR
.
79
4.2.3
THE
NEURAL
GEOMETRIC
BMMR
ALGORITHM
.
82
4.2.4
FORMAL
MODEL
OF
THE
GEOMETRIC
BMMR
ALGORITHM
.
83
4.2.5
LIMIT
POINTS
OF
THE
GEOMETRIC
BMMR
ALGORITHM
.
85
4.3
OVERCOMPLETE
FASTGEO
.
88
4.4
BLIND
SOURCE
RECOVERY
.
90
4.4.1
MAXIMUM
LIKELIHOOD
REGULARIZATION
.
91
4.4.2
SHORTEST-PATH
ALGORITHM
.
92
4.5
EXPERIMENTAL
RESULTS
.
94
4.5.1
NEURAL
ALGORITHM
.
94
4.5.2
OVERCOMPLETE
FASTGEO
.
97
4.6
CONCLUSIONS
.
99
III
NONLINEAR
ICA
105
5
NONLINEAR
ANALYSIS
MODELS
107
5.1
NEURAL
NETWORKS
.
108
5.1.1
INTRODUCTION
.
108
5.1.2
LAYERED
NEURAL
NETWORKS
.
110
5.1.3
NEURAL
NETWORK
ANALYSIS
MODEL
.
110
5.2
POSTNONLINEAR
ICA
.
112
XIV
5.3
OTHER
MIXING
MODELS
.
112
6
COMPARISON
OF
MAXIMUM
ENTROPY
AND
MINIMAL
MUTUAL
IN
FORMATION
113
6.1
INTRODUCTION
.
114
6.2
MAIN
THEOREM
.
114
6.3
CONCLUSIONS
.
122
7
PATTERN
REPULSION
125
7.1
INTRODUCTION
.
125
7.2
MODEL
.
125
7.3
PATTERN
REPULSION
.
126
7.3.1
THE
PARTICLE
REPULSION
ANALOGUE
.
126
7.3.2
CONDITIONS
ON
PATTERN
DENSITY
DISTRIBUTIONS
.
126
7.3.3
ESTIMATION
OF
THE
TOTAL
PATTERN
ENERGY
.
127
7.3.4
THE
DENSITY
UNIFORMIZATION
METHOD
.
127
7.3.5
MARQUES-ALMEIDA
THEOREM
.
129
7.3.6
GRADIENT
OF
THE
TOTAL
PATTERN
ENERGY
FUNCTION
.
130
7.4
EXPERIMENTAL
RESULTS
.
131
7.5
CONCLUSIONS
.
134
8
NONLINEAR
GEOMETRIC
ICA
135
8.1
ALGORITHM
.
135
8.1.1
RING
STEP
.
136
8.1.2
RECOVERY
STEP
.
137
8.2
EXPERIMENTAL
RESULTS
.
141
8.3
CONCLUSION
.
145
9
SUMMARY
AND
CONCLUSIONS
149
A
THE
SKITOVITCH-DARMOIS
THEOREM
155
A.L
THE
THEOREM
.
155
A.2
CRAMER
'
S
THEOREM
.
156
A.3
ENTIRE
FUNCTIONS
.
156
A.4
CHARACTERISTIC
FUNCTIONS
.
157
A.
5
RIDGE
FUNCTIONS
.
161
A.6
PROOF
OF
THE
SKITOVITCH-DARMOIS
THEOREM
IN
THE
RATIONAL
CASE
164
BIBLIOGRAPHY
167
NOMENCLATURE
174
INDEX
176
XV |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV016550395 |
| illustrated | Illustrated |
| indexdate | 2024-08-23T00:21:07Z |
| institution | BVB |
| isbn | 3832501274 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010225096 |
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| physical | XVI, 179 S. graph. Darst. |
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| publisher | Logos-Verl. |
| record_format | marc |
| series | Nichtlineare und stochastische Physik |
| series2 | Nichtlineare und stochastische Physik |
| spelling | Theis, Fabian J. Verfasser aut Mathematics in independent component analysis vorgelegt von Fabian J. Theis Berlin Logos-Verl. 2003 XVI, 179 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nichtlineare und stochastische Physik 9 Zugl.: Regensburg, Univ., Diss., 2002 Signalquelle (DE-588)4181273-6 gnd rswk-swf Faktorenanalyse (DE-588)4016338-6 gnd rswk-swf Signaltrennung (DE-588)4181278-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Signalquelle (DE-588)4181273-6 s Signaltrennung (DE-588)4181278-5 s Faktorenanalyse (DE-588)4016338-6 s Algorithmus (DE-588)4001183-5 s DE-604 Nichtlineare und stochastische Physik 9 (DE-604)BV021858997 9 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010225096&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Theis, Fabian J. Mathematics in independent component analysis Nichtlineare und stochastische Physik Signalquelle (DE-588)4181273-6 gnd Faktorenanalyse (DE-588)4016338-6 gnd Signaltrennung (DE-588)4181278-5 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4181273-6 (DE-588)4016338-6 (DE-588)4181278-5 (DE-588)4001183-5 (DE-588)4113937-9 |
| title | Mathematics in independent component analysis |
| title_auth | Mathematics in independent component analysis |
| title_exact_search | Mathematics in independent component analysis |
| title_full | Mathematics in independent component analysis vorgelegt von Fabian J. Theis |
| title_fullStr | Mathematics in independent component analysis vorgelegt von Fabian J. Theis |
| title_full_unstemmed | Mathematics in independent component analysis vorgelegt von Fabian J. Theis |
| title_short | Mathematics in independent component analysis |
| title_sort | mathematics in independent component analysis |
| topic | Signalquelle (DE-588)4181273-6 gnd Faktorenanalyse (DE-588)4016338-6 gnd Signaltrennung (DE-588)4181278-5 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Signalquelle Faktorenanalyse Signaltrennung Algorithmus Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010225096&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021858997 |
| work_keys_str_mv | AT theisfabianj mathematicsinindependentcomponentanalysis |