Self-Organizing Maps

Front Cover
Springer, 2001 - Computers - 501 pages
5 Reviews
The Self-Organizing Map (SOM), with its variants, is the most popular artificial neural network algorithm in the unsupervised learning category. About 4000 research articles on it have appeared in the open literature, and many industrial projects use the SOM as a tool for solving hard real-world problems. Many fields of science have adopted the SOM as a standard analytical tool: in statistics, signal processing, control theory, financial analyses, experimental physics, chemistry and medicine. The SOM solves difficult high-dimensional and nonlinear problems such as feature extraction and classification of images and acoustic patterns, adaptive control of robots, and equalization, demodulation, and error-tolerant transmission of signals in telecommunications. A new area is organization of very large document collections. Last but not least, it may be mentioned that the SOM is one of the most realistic models of the biological brain function. This new edition includes a survey of over 2000 contemporary studies to cover the newest results; case examples were provided with detailed formulae, illustrations, and tables; a new chapter on Software Tools for SOM was written, other chapters were extended or reorganized.
  

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Contents

1 Mathematical Preliminaries
1
11 Mathematical Concepts and Notations
2
112 Matrix Notations
8
113 Eigenvectors and Eigenvalues of Matrices
11
114 Further Properties of Matrices
13
115 On Matrix Differential Calculus
15
12 Distance Measures for Patterns
17
122 Measures of Similarity and Distance Between Symbol Strings
21
572 The Batch Map for Strings
206
The SOM of Phonemic Transcriptions
207
59 EvolutionaryLearning SOM
211
592 SelfOrganization According to a Fitness Function
212
510 Supervised SOM
215
511 The AdaptiveSubspace SOM ASSOM
216
5112 Relation Between Invariant Features and Linear Subspaces
218
5113 The ASSOM Algorithm
222

123 Averages Over Nonvectorial Variables
28
13 Statistical Pattern Analysis
29
132 Projection Methods
34
133 Supervised Classification
39
134 Unsupervised Classification
44
14 The Subspace Methods of Classification
46
142 Adaptation of a Model Subspace to Input Subspace
49
143 The Learning Subspace Method LSM
53
15 Vector Quantization
59
152 Derivation of the VQ Algorithm
60
153 Point Density in VQ
62
16 Dynamically Expanding Context
64
161 Setting Up the Problem
65
162 Automatic Determination of ContextIndependent Productions
66
163 Conflict Bit
67
164 Construction of Memory for the ContextDependent Productions
68
166 Estimation Procedure for Unsuccessful Searches
69
2 Neural Modeling
71
22 A History of Some Main Ideas in Neural Modeling
72
23 Issues on Artificial Intelligence
75
24 On the Complexity of Biological Nervous Systems
76
25 What the Brain Circuits Are Not
78
26 Relation Between Biological and Artificial Neural Networks
79
27 What Functions of the Brain Are Usually Modeled?
81
29 Transformation Relaxation and Decoder
82
210 Categories of ANNs
85
211 A Simple Nonlinear Dynamic Model of the Neuron
87
212 Three Phases of Development of Neural Models
89
213 Learning Laws
91
2132 The RiccatiType Learning Law
92
2133 The PCAType Learning Law
95
214 Some Really Hard Problems
96
215 Brain Maps
99
3 The Basic SOM
105
31 A Qualitative Introduction to the SOM
106
32 The Original Incremental SOM Algorithm
109
33 The DotProduct SOM
115
34 Other Preliminary Demonstrations of TopologyPreserving Mappings
116
342 Demonstrations of Ordering of Responses in the Output Space
120
35 Basic Mathematical Approaches to SelfOrganization
127
351 OneDimensional Case
128
352 Constructive Proof of Ordering of Another OneDimensional SOM
132
36 The Batch Map
138
37 Initialization of the SOM Algorithms
142
38 On the Optimal LearningRate Factor
143
39 Effect of the Form of the Neighborhood Function
145
310 Does the SOM Algorithm Ensue from a Distortion Measure?
146
311 An Attempt to Optimize the SOM
148
312 Point Density of the Model Vectors
152
3122 Numerical Check of Point Densities in a Finite OneDimensional SOM
153
313 Practical Advice for the Construction of Good Maps
159
314 Examples of Data Analyses Implemented by the SOM
161
Poverty Map
165
316 Interpretation of the SOM Mapping
166
3162 Contribution of a Variable to Cluster Structures
169
317 Speedup of SOM Computation
170
3172 Increasing the Number of Units in the SOM
172
3173 Smoothing
175
3174 Combination of Smoothing Lattice Growing and SOM Algorithm
176
4 Physiological Interpretation of SOM
177
42 Two Different Lateral Control Mechanisms
178
421 The WTA Function Based on Lateral Activity Control
179
422 Lateral Control of Plasticity
184
43 Learning Equation
185
45 Recapitulation of the Features of the Physiological SOM Model
188
461 Magnification
189
5 Variants of SOM
191
52 Adaptive Tensorial Weights
194
53 TreeStructured SOM in Searching
197
54 Different Definitions of the Neighborhood
198
55 Neighborhoods in the Signal Space
200
56 Dynamical Elements Added to the SOM
204
57 The SOM for Symbol Strings
205
5114 Derivation of the ASSOM Algorithm by Stochastic Approximation
226
5115 ASSOM Experiments
228
512 FeedbackControlled AdaptiveSubspace SOM FASSOM
242
6 Learning Vector Quantization
245
62 The LVQ1
246
63 The OptimizedLearningRate LVQ1 OLVQ1
250
64 The BatchLVQ1
251
65 The BatchLVQ1 for Symbol Strings
252
67 The LVQ3
253
68 Differences Between LVQ1 LVQ2 and LVQ3
254
610 The HypermapType LVQ
256
611 The LVQSOM
261
7 Applications
263
71 Preprocessing of Optic Patterns
264
711 Blurring
265
712 Expansion in Terms of Global Features
266
714 Expansion in Terms of Local Features Wavelets
267
72 Acoustic Preprocessing
268
73 Process and Machine Monitoring
269
732 Analysis of Large Systems
270
74 Diagnosis of Speech Voicing
274
76 Texture Analysis
280
77 Contextual Maps
281
771 Artifically Generated Clauses
283
772 Natural Text
285
78 Organization of Large Document Files
286
782 Construction of Very Large WEBSOM Maps by the Projection Method
292
783 The WEBSOM of All Electronic Patent Abstracts
296
79 RobotArm Control
299
792 Another Simple RobotArm Control
303
710 Telecommunications
304
7102 Channel Equalization in the Adaptive QAM
305
7103 ErrorTolerant Transmission of Images by a Pair of SOMs
306
711 The SOM as an Estimator
308
7112 Asymmetric Heteroassociative Mapping
309
8 Software Tools for SOM
311
82 Desirable Auxiliary Features
313
83 SOM Program Packages
315
832 SOM Toolbox
317
833 Nenet Neural Networks Tool
318
84 Examples of the Use of SOIV_PAK
319
842 Description of the Programs in SOM_PAK
322
843 A Typical Training Sequence
326
85 NeuralNetworks Software with the SOM Option
327
9 Hardware for SOM
329
92 Fast Digital Classifier Circuits
332
93 SIMD Implementation of SOM
337
94 Transputer Implementation of SOM
339
95 SystolicArray Implementation of SOM
341
96 The COKOS Chip
342
98 NBISOM_25 Chip
344
10 An Overview of SOM Literature
347
102 Early Works on Competitive Learning
348
103 Status of the Mathematical Analyses
349
1032 Alternative Topological Mappings
350
1034 Functional Variants
351
1035 Theory of the Basic SOM
352
104 The Learning Vector Quantization
358
1052 Optical Character and Script Reading
360
1054 Acoustic and Musical Studies
361
1055 Signal Processing and Radar Measurements
362
1058 Process Control
363
1059 Robotics
364
10512 Chemistry
365
10514 Neurophysiological Research
366
10516 Linguistic and AI Problems
367
10517 Mathematical and Other Theoretical Problems
368
106 Applications of LVQ
369
107 Survey of SOM and LVQ Implementations
370
11 Glossary of Neural Terms
373
References
403
Index
487
Copyright

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References from web pages

Self-Organizing Maps
Self-organizing maps (soms) are a data visualization technique invented by Professor Teuvo Kohonen which reduce the dimensions of data through the use of ...
davis.wpi.edu/ ~matt/ courses/ soms/

Kohonen Neural Network Package
This code is being released in connection with: An introduction to Artificial Intelligence: Janet Finlay and Alan Dix, UCL Press, 1996. ...
www.hiraeth.com/ books/ ai96/ kohonen.html

Self-organizing map - Wikipedia, the free encyclopedia
A self-organizing map (SOM) is a type of artificial neural network that is trained using unsupervised learning to produce a low-dimensional (typically two ...
en.wikipedia.org/ wiki/ Self-organizing_map

Self-Organizing Maps
Self-Organizing Maps. “Kohonen Nets”. Feature Maps. (a form of competitive learning) ... Self-Organizing Maps (soms). •. Similar to LVQ clustering ...
www.cs.vu.nl/ ~elena/ slides03/ som.pdf

Case Study: Visualizing Customer Segmentations Produced by Self ...
Self-Organizing Maps. Springer, 1995. KOHONEN, T., HYNNINEN, J., KANGAS, J., LAAK-. SONEN, J. SOMPAK: The Self-Organizing Map Pro-. gram Package, ...
doi.ieeecomputersociety.org/ 10.1109/ VISUAL.1997.663922

Neural Networks : Advances in Self-Organizing Maps - Published by ...
Every two years, the “Workshop on Self-Organizing Maps” (WSOM) covers the new developments in the field. The WSOM series of conferences was initiated in ...
linkinghub.elsevier.com/ retrieve/ pii/ S0893608006000888

Self-organizing maps of massive document collections - Neural ...
It is possible to construct an indefinite number of Self-organizing Maps, ..... classification with self-organizing maps: Some lessons learned. ...
ieeexplore.ieee.org/ iel5/ 6927/ 18622/ 00857865.pdf?arnumber=857865

Advanced visualization of self-organizing maps with vector fields
Self-Organizing Maps have been applied in various industrial applications and have proven to be a valuable data mining tool. In order to fully benefit from ...
portal.acm.org/ citation.cfm?id=1167870.1167891& coll=GUIDE& dl=& CFID=15151515& CFTOKEN=6184618

Winner-Relaxing Self-Organizing Maps -- Claussen 17 (5): 996 ...
A new family of self-organizing maps, the winner-relaxing Kohonen algorithm, is introduced as a generalization of a variant given by Kohonen in 1991. ...
neco.mitpress.org/ cgi/ content/ full/ 17/ 5/ 996

Mnemonic soms: Recognizable Shapes for Self-Organizing Maps 1 ...
paper, a variant of self-organizing maps following standard SOM training ... We therefore propose using standard self-organizing maps where nodes are ...
www.ifs.tuwien.ac.at/ ~mayer/ publications/ pdf/ may_wsom05.pdf

About the author (2001)

Kohonen from the Academy of Science