Complex-valued neural networks with multi-valued neurons:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2011
|
| Series: | Studies in computational intelligence
353 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 262 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783642203527 3642203523 |
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| 100 | 1 | |a Aizenberg, Igor |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Complex-valued neural networks with multi-valued neurons |c Igor Aizenberg |
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| 300 | |a XV, 262 S. |b Ill., graph. Darst. |c 24 cm | ||
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Record in the Search Index
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|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 WHY WE NEED COMPLEX-VALUED NEURAL NETWORKS? 1
1.1 NEURONS AND NEURAL NETWORKS: BASIC FOUNDATIONS AND HISTORICAL VIEW 1
1.1.1 WHAT IS A NEURAL NETWORK? 1
1.1.2 THE NEURON 3
1.1.3 LINEAR SEPARABILITY AND NON-LINEAR SEPARABILITY: XOR PROBLEM 6
1.2 LEARNING: BASIC FUNDAMENTALS 8
1.2.1 HEBBIAN LEARNING 8
1.2.2 PERCEPTRON AND ERROR-CORRECTION LEARNING 11
1.2.3 LEARNING ALGORITHM 16
1.2.4 EXAMPLES OF APPLICATION OF THE LEARNING ALGORITHM BASED ON THE
ERROR-CORRECTION RULE 18
1.2.5 LIMITATION OF THE PERCEPTRON. MINSKY'S AND PAPERT'S WORK 21 1.3
NEURAL NETWORKS: POPULAR TOPOLOGIES 22
1.3.1 XOR PROBLEM: SOLUTION USING A FEEDFORWARD NEURAL NETWORK 22
1.3.2 POPULAR REAL-VALUED ACTIVATION FUNCTIONS 24
1.3.3 MULTILAYER FEEDFORWARD NEURAL NETWORK (MLF) AND ITS
BACKPROPAGATION LEARNING 26
1.3.4 HOPFIELD NEURAL NETWORK 35
1.3.5 CELLULAR NEURAL NETWORK 37
1.4 INTRODUCTION TO COMPLEX-VALUED NEURONS AND NEURAL NETWORKS 38 1.4.1
WHY WE NEED THEM? 38
1.4.2 HIGHER FUNCTIONALITY 40
1.4.3 IMPORTANCE OF PHASE AND ITS PROPER TREATMENT 42
1.4.4 COMPLEX-VALUED NEURAL NETWORKS: BRIEF HISTORICAL OBSERVATION AND
STATE OF THE ART 48
1.5 CONCLUDING REMARKS TO CHAPTER 1 52
2 THE MULTI-VALUED NEURON 55
2. 1 MULTIPLE-VALUED THRESHOLD LOGIC OVER THE FIELD OF COMPLEX NUMBERS
55
2.1.1 MULTIPLE-VALUED LOGIC OVER THE FIELD OF COMPLEX NUMBERS 56 2.1.2
MULTIPLE-VALUED THRESHOLD FUNCTIONS OVER THE FIELD OF COMPLEX NUMBERS 58
2.2 MULTI-VALUED NEURON (MVN) 65
2.2.1 DISCRETE MVN 65
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010478745
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
2.2.2 CONTINUOUS MVN 67
2.3 EDGED SEPARATION OF N-DIMENSIONAL SPACE 71
2.3.1 IMPORTANT BACKGROUND 71
2.3.2 SEPARATION OF AN N-DIMENSIONAL SPACE 74
2.3.3 K-EDGE 82
2.3.4 PROPERTIES OF THE K-EDGE 84
2.3.5 EDGED SEPARATION AND MVN: SUMMARY 90
2.4 MVN AND A BIOLOGICAL NEURON 92
2.5 CONCLUDING REMARKS TO CHAPTER 2 94
3 MVN LEARNING 95
3.1 MVN LEARNING ALGORITHM 95
3.1.1 MECHANISM OF MVN LEARNING 96
3.1.2 LEARNING STRATEGY 100
3.2 MVN LEARNING RULE BASED ON THE CLOSENESS TO THE DESIRED OUTPUT IN
TERMS OF ANGULAR DISTANCE 102
3.2.1 BASIC FUNDAMENTALS 102
3.2.2 CONVERGENCE THEOREM 107
3.3 MVN ERROR-CORRECTION LEARNING RULE 112
3.3.1 BASIC FUNDAMENTALS 112
3.3.2 CONVERGENCE THEOREM 116
3.3.3 EXAMPLE OF ERROR-CORRECTION LEARNING 122
3.4 HEBBIAN LEARNING AND MVN 125
3.5 CONCLUDING REMARKS TO CHAPTER 3 '. 131
4 MULTILAYER FEEDFORWARD NEURAL NETWORK BASED ON MULTI-VALUED NEURONS
(MLMVN) 133
4.1 INTRODUCTION TO DERIVATIVE-FREE BACKPROPAGATION LEARNING 133 4.2
MVN-BASED MULTILAYER NEURAL NETWORK AND ERROR BACKPROPAGATION. 138
4.2.1 SIMPLE MLMVN: A SINGLE HIDDEN LAYEAR AND A SINGLE OUTPUT NEURON
138
4.2.2 MLMVN AND BACKPROPAGATION LEARNING: THE GENERAL CASE 143
4.3 MLMVN LEARNING ALGORITHM AND THE CONVERGENCE THEOREM 152 4.3.1 BASIC
FUNDAMENTALS 152
4.3.2 MLMVN LEARNING ALGORITHM 155
4.3.3 CONVERGENCE THEOREM 157
4.3.4 IMPORTANT ADVANTAGES OF THE MLMVN LEARNING ALGORITHM 163 4.4
EXAMPLES OF MLMVN APPLICATIONS 164
4.4.1 SIMPLE EXAMPLE: 3-CLASS CLASSIFICATION PROBLEM 164 4.4.2
MACKEY-GLASS TIME SERIES PREDICTION 168
4.5 CONCLUDING REMARKS TO CHAPTER4 171
5 MULTI-VALUED NEURON WITH A PERIODIC ACTIVATION FUNCTION. 173 5.1
UNIVERSAL BINARY NEURON (UBN): TWO-VALUED MVN WITH A PERIODIC ACTIVATION
FUNCTION 173
IMAGE 3
CONTENTS XV
5.1.1 A PERIODIC ACTIVATION FUNCTION FOR K=2 173
5.1.2 IMPLEMENTATION OF THE PARITY N FUNCTION USING A SINGLE NEURON 176
5.1.3 PROJECTION OF A TWO-VALUED NON-LINEARLY SEPARABLE FUNCTION INTO AN
M-VALUED THRESHOLD FUNCTION 177 5.1.4 UBN LEARNING 181
5.2 K-VALUED MVN WITH A PERIODIC ACTIVATION FUNCTION 183
5.2.1 SOME IMPORTANT FUNDAMENTALS 183
5.2.2 PERIODIC ACTIVATION FUNCTION FOR DISCRETE MVN 184 5.2.3 LEARNING
ALGORITHM FOR MVN-P 187
5.3 SIMULATION RESULTS FOR K-VALUED MVN WITH A PERIODIC ACTIVATION
FUNCTION 192
5.3.1 IRIS 192
5.3.2 TWO SPIRALS 195
5.3.3 BREAST CANCER WISCONSIN (DIAGNOSTIC) 196
5.3.4 SONAR 197
5.3.5 PARITY N PROBLEM 197
5.3.6 MOD K ADDITION OF NK-VALUED VARIABLES 198
5.4 CONCLUDING REMARKS TO CHAPTER 5 206
6 APPLICATIONS OF MVN AND MLMVN 207
6.1 IDENTIFICATION OF BLUR AND ITS PARAMETERS USING MLMVN 207 6.1.1
IMPORTANCE OF BLUR AND ITS PARAMETERS IDENTIFICATION 208 6.1.2
SPECIFICATION OF THE PSF RECOGNITION PROBLEM 210
6.1.3 CHOICE OF THE FEATURES 211
6.1.4 OUTPUT DEFINITION: "WINNER TAKES IT ALL RULE" FOR MLMVN 214
6.1.5 SIMULATION RESULTS 217
6.2 FINANCIAL TIME SERIES PREDICTION USING MLMVN 220
6.2.1 MATHEMATICAL MODEL 220
6.2.2 IMPLEMENTATION AND SIMULATION RESULTS 223
6.3 MVN-BASED ASSOCIATIVE MEMORIES 226
6.3.1 A CNN-MVN-BASED ASSOCIATIVE MEMORY 227
6.3.2 A HOPFIELD MVN-BASED ASSOCIATIVE MEMORY 231 6.3.3 MVN-BASED
ASSOCIATIVE MEMORY WITH RANDOM CONNECTIONS 236
6.3.4 AN MVN-BASED ASSOCIATIVE MEMORY WITH ROTATION INVARIANT
ASSOCIATION 240
6.4 SOME OTHER APPLICATIONS OF MVN-BASED NEURAL NETWORKS AND CONCLUDING
REMARKS TO CHAPTER 6 245
CONCLUDING REMARKS. .
.249
REFERENCES. . . .
. 253
INDEX
.261 |
| any_adam_object | 1 |
| author | Aizenberg, Igor |
| author_facet | Aizenberg, Igor |
| author_role | aut |
| author_sort | Aizenberg, Igor |
| author_variant | i a ia |
| building | Verbundindex |
| bvnumber | BV040105790 |
| classification_rvk | ST 301 |
| ctrlnum | (OCoLC)725000575 (DE-599)DNB1010478745 |
| dewey-full | 006.32 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.32 |
| dewey-search | 006.32 |
| dewey-sort | 16.32 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-21T00:30:52Z |
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| language | English |
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| physical | XV, 262 S. Ill., graph. Darst. 24 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Studies in computational intelligence |
| series2 | Studies in computational intelligence |
| spelling | Aizenberg, Igor Verfasser aut Complex-valued neural networks with multi-valued neurons Igor Aizenberg Berlin ; Heidelberg Springer 2011 XV, 262 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Studies in computational intelligence 353 Literaturangaben Komplexe Zahl (DE-588)4128698-4 gnd rswk-swf Neuronales Netz (DE-588)4226127-2 gnd rswk-swf Neuronales Netz (DE-588)4226127-2 s Komplexe Zahl (DE-588)4128698-4 s DE-604 Erscheint auch als Online-Ausgabe Complex-Valued Neural Networks with Multi-Valued Neurons Studies in computational intelligence 353 (DE-604)BV020822171 353 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3683333&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024962241&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aizenberg, Igor Complex-valued neural networks with multi-valued neurons Studies in computational intelligence Komplexe Zahl (DE-588)4128698-4 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| subject_GND | (DE-588)4128698-4 (DE-588)4226127-2 |
| title | Complex-valued neural networks with multi-valued neurons |
| title_auth | Complex-valued neural networks with multi-valued neurons |
| title_exact_search | Complex-valued neural networks with multi-valued neurons |
| title_full | Complex-valued neural networks with multi-valued neurons Igor Aizenberg |
| title_fullStr | Complex-valued neural networks with multi-valued neurons Igor Aizenberg |
| title_full_unstemmed | Complex-valued neural networks with multi-valued neurons Igor Aizenberg |
| title_short | Complex-valued neural networks with multi-valued neurons |
| title_sort | complex valued neural networks with multi valued neurons |
| topic | Komplexe Zahl (DE-588)4128698-4 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| topic_facet | Komplexe Zahl Neuronales Netz |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3683333&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024962241&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV020822171 |
| work_keys_str_mv | AT aizenbergigor complexvaluedneuralnetworkswithmultivaluedneurons |