Self-organizing maps

Springer, 2001 - Computers - 501 pages

The Self-Organizing Map (SOM), with its variants, is the most popular artificial neural network algorithm in the unsupervised learning category. 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. A new area is organization of very large document collections. The SOM is also one of the most realistic models of the biological brain functions.This new edition includes a survey of over 2000 contemporary studies to cover the newest results; the 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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This is a wonderfully written, and excellent book. It assumes only minimal background knowledge but imparts a great deal of insight. I love the way that the author describes this area and the connections with deep and beautiful mathematics. Read full review

A very nice 'handbook' of sorts for users of SOMs.

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- doucette@spatial.maine.edu - Amazon.com -

The material is presented clearly and comprehensively from the unique perspective of the SOM originator himself. The inclusion of exhaustive references is particularly useful for the prospective ... Read full review

Self Organizing Maps_动态符号

Editorial Review - baidu.com

Self-organizing maps (soms) are a data visualization technique invented by Professor Teuvo Kohonen which reduce the dimensions of data through the use of ... Read full review

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Selected pages

1 Mathematical Preliminaries	1

11 Mathematical Concepts and Notations 111 Vector Space Concepts	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 121 Measures of Similarity and Distance in Vector Spaces	17

122 Measures of Similarity and Distance Between Symbol Strings	21

56 Dynamical Elements Added to the SOM	204

571 Initialization of the SOM for Strings	205

573 TieBreak Rules	206

58 Operator Maps	207

59 EvolutionaryLearning SOM 591 EvolutionaryLearning Filters	211

592 SelfOrganization According to a Fitness Function	212

510 Supervised SOM	215

511 The AdaptiveSubspace SOM ASSOM 5111 The Problem of Invariant Features	216

123 Averages Over Nonvectorial Variables	28

13 Statistical Pattern Analysis 131 Basic Probabilistic Concepts	29

132 Projection Methods	34

133 Supervised Classification	39

134 Unsupervised Classification	44

14 The Subspace Methods of Classification 141 The Basic Subspace Method	46

142 Adaptation of a Model Subspace to Input Subspace	49

143 The Learning Subspace Method LSM	53

15 Vector Quantization 151 Definitions	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

167 Practical Experiments	69

21 Models Paradigms and Methods	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

28 When Do We Have to Use Neural Computing?	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

2131 Hebbs Law	91

2132 The RiccatiType Learning Law	92

Vpx 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 341 Ordering of Reference Vectors in the Input Space	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 3121 Earlier Studies	152

3122 Numerical Check of Point Densities in a Finite OneDimensional SOM	153

313 Practical Advice for the Construction of Good Maps	159

3141 Attribute Maps with Full Data Matrix	161

315 Using Gray Levels to Indicate Clusters in the SOM	165

3161 Local Principal Components	166

3162 Contribution of a Variable to Cluster Structures	169

317 Speedup of SOM Computation 3171 Shortcut Winner Search	170

3172 Increasing the Number of Units in the SOM	172

3173 Smoothing	175

3174 Combination of Smoothing Lattice Growing and SOM Algorithm	176

41 Conditions for Abstract Feature Maps in the Brain	177

42 Two Different Lateral Control Mechanisms	178

421 The WTA Function Based on Lateral Activity Control	179

422 Lateral Control of Plasticity	184

44 System Models of SOM and Their Simulations	185

46 Similarities Between the Brain Maps and Simulated Feature Maps	188

463 Overlapping Maps	189

51 Overview of Ideas to Modify the Basic 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

5112 Relation Between Invariant Features and Linear Subspaces	218

5113 The ASSOM Algorithm	222

5114 Derivation of the ASSOM Algorithm by Stochastic Approximation	226

5115 ASSOM Experiments	228

512 FeedbackControlled AdaptiveSubspace SOM FASSOM	242

61 Optimal Decision	245

64 The BatchLVQl	251

69 General Considerations	254

610 The HypermapType LVQ	256

611 The LVQSOM	261

7 Applications	263

71 Preprocessing of Optic Patterns	264

711 Blurring	265

713 Spectral Analysis	266

715 Recapitulation of Features of Optic Patterns	267

72 Acoustic Preprocessing	268

731 Selection of Input Variables and Their Scaling	269

732 Analysis of Large Systems	270

75 Transcription of Continuous Speech	274

76 Texture Analysis	280

77 Contextual Maps	281

771 Artifically Generated Clauses	283

772 Natural Text	285

781 Statistical Models of Documents	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 791 Simultaneous Learning of Input and Output Parameters	299

792 Another Simple RobotArm Control	303

710 Telecommunications 7101 Adaptive Detector for Quantized Signals	304

7102 Channel Equalization in the Adaptive QAM	305

7103 ErrorTolerant Transmission of Images by a Pair of SOMs	306

7111 Symmetric Autoassociative Mapping	308

7112 Asymmetric Heteroassociative Mapping	309

81 Necessary Requirements	311

82 Desirable Auxiliary Features	313

831 SOM_PAK	315

832 SOM Toolbox	317

834 Viscovery SOMine	318

841 File Formats	319

842 Description of the Programs in SOMLPAK	322

843 A Typical Training Sequence	326

85 NeuralNetworks Software with the SOM Option	327

91 An Analog Classifier Circuit	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

97 The TInMANN Chip	342

98 NBISOM_25 Chip	344

101 Books and Review Articles	347

102 Early Works on Competitive Learning	348

103 Status of the Mathematical Analyses 1031 ZeroOrder Topology Classical VQ Results	349

1033 Alternative Architectures	350

1034 Functional Variants	351

1035 Theory of the Basic SOM	352

105 Diverse Applications of SOM 1051 Machine Vision and Image Analysis	358

1053 Speech Analysis and Recognition	360

1054 Acoustic and Musical Studies	361

1057 Industrial and Other RealWorld Measurements	362

1058 Process Control	363

10511 Physics	364

10513 Biomedical Applications Without Image Processing	365

10515 Data Processing and Analysis	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

Other editions - View all

Self-organizing maps‎

Teuvo Kohonen
No preview available - 1997

Self-organizing maps‎

Teuvo Kohonen
No preview available - 1995

Common terms and phrases

accuracy adaptive algorithm analysis applications approximation array Artificial Neural Networks ASSOM assumed asymptotic basic basis vectors brain cells classification clustering codebook vectors components computing convergence corresponding cortex defined denoted density function described dimensionality discussed in Sect distance distribution dot product dynamic elements equation Euclidean feature filters initial input data input samples input vector labels lattice learning learning-rate factor Levenshtein distance linear linear subspace map units mathematical matrix memory method model vectors neighborhood function neighboring neuron nodes nonlinear operation optimal orthogonal output parameters pattern recognition phoneme point density principal curves probability density function problem projection quantization error random reference vectors relating respectively scalar Self-Organizing Map sequence signal space similar speech recognition statistical step stochastic strings subset subspace supervised learning symbol synaptic tion topology transformation two-dimensional values variables vector quantization visual Voronoi tessellation wavelets whereby winner words zero

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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

Places mentioned in this book Maps KML

Piscataway, NJ - Page 409
1993 IEEE Workshop on Neural Networks }or Signal Processing (IEEE Service Center, Piscataway, NJ 1993) [3.49] B. ...
more pages: 423 439 442 453

Los Alamitos, CA - Page 468
Press, Los Alamitos, CA 1991) M. Bodruzzaman. S. Zein-Sabatto. O. Omitowoju. M. Malkani: In Proc. WCNN'95. World Congress on Neural Networks. (INNS. ...

Hillsdale, NJ - Page 419
1993 Connectiomst Models Summer School (Lawrence Erlbaum, Hillsdale, NJ 1994) [10.77] J. Sirosh, R. Miikkulainen: In Proc. ICNN'93 Int. ...

New York, NY - Page 404
Hartigan: Clustering Algorithms (Wiley, New York, NY 1975) [1 .54] H. Spath: Cluster Analysis Algorithms for Data Reduction and Classification of ...
more pages: 403 414 415

Bellingham, WA - Page 474
Bellingham, WA 1993) AB Baruah, LE Atlas. ADC Holden: In Proc. IJCNN'91, Int. Joint Conf, on Neural Networks (IEEE Service Center. ...
more pages: 417

Espoo - Page 409
Kohonen: Report A33 (Helsinki University of Technology, Laboratory of Computer and Information Science, Espoo 1996) [3.40] JS Rodrigues, ...

Fukushima - Page 389

Helsinki - Page 408
Torkkola: Technical Report A30 (Helsinki University of Technology, Laboratory of Computer and Information Science, Helsinki 1996) [3.28] H. ...

Chicago - Page 73

College Park, MD - Page 403

About the author (2001)

Kohonen from the Academy of Science

Bibliographic information

Title	Self-organizing maps Volume 30 of Springer series in information sciences Physics and astronomy online library
Author	Teuvo Kohonen
Edition	3, illustrated
Publisher	Springer, 2001
ISBN	3540679219, 9783540679219
Length	501 pages
Subjects	Computers / Artificial Intelligence Computers / Neural Networks Neural networks (Computer science) Neural networks Computer science Science / Life Sciences / Biophysics Self-organizing maps Self-organizing systems Technology & Engineering / Electrical