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9783540679219

Self-Organizing Maps

by ; ;
  • ISBN13:

    9783540679219

  • ISBN10:

    3540679219

  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2000-11-01
  • Publisher: Springer Verlag
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Supplemental Materials

What is included with this book?

Summary

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.

Table of Contents

Mathematical Preliminaries
1(71)
Mathematical Concepts and Notations
2(15)
Vector Space Concepts
2(6)
Matrix Notations
8(3)
Eigenvectors and Eigenvalues of Matrices
11(2)
Further Properties of Matrices
13(2)
On Matrix Differential Calculus
15(2)
Distance Measures for Patterns
17(12)
Measures of Similarity and Distance in Vector Spaces
17(4)
Measures of Similarity and Distance Between Symbol Strings
21(7)
Averages Over Nonvectorial Variables
28(1)
Statistical Pattern Analysis
29(17)
Basic Probabilistic Concepts
29(5)
Projection Methods
34(5)
Supervised Classification
39(5)
Unsupervised Classification
44(2)
The Subspace Methods of Classification
46(13)
The Basic Subspace Method
46(3)
Adaptation of a Model Subspace to Input Subspace
49(4)
The Learning Subspace Method (LSM)
53(6)
Vector Quantization
59(5)
Definitions
59(1)
Derivation of the VQ Algorithm
60(2)
Point Density in VQ
62(2)
Dynamically Expanding Context
64(7)
Setting Up the Problem
65(1)
Automatic Determination of Context-Independent Productions
66(1)
Conflict Bit
67(1)
Construction of Memory for the Context-Dependent Productions
68(1)
The Algorithm for the Correction of New Strings
68(1)
Estimation Procedure for Unsucessful Searches
69(1)
Practical Experiments
69(2)
Neural Modeling
71(34)
Models, Paradigms, and Methods
71(1)
A History of Some Main Ideas in Neural Modeling
72(3)
Issues on Artificial Intelligence
75(1)
On the Complexity of Biological Nervous Systems
76(2)
What the Brain Circuits Are Not
78(1)
Relation Between Biological and Artificial Neural Networks
79(2)
What Functions of the Brain Are Usually Modeled?
81(1)
When Do We Have to Use Neural Computing?
81(1)
Transformation, Relaxation, and Decoder
82(3)
Categories of ANNs
85(2)
A Simple Nonlinear Dynamic Model of the Neuron
87(2)
Three Phases of Development of Neural Models
89(2)
Learning Laws
91(5)
Hebb's Law
91(1)
The Riccati-Type Learning Law
92(3)
The PCA-Type Learning Law
95(1)
Some Really Hard Problems
96(3)
Brain Maps
99(6)
The Basic SOM
105(72)
A Qualitative Introduction to the SOM
106(3)
The Original Incremental SOM Algorithm
109(6)
The ``Dot-Product SOM''
115(1)
Other Preliminary Demonstrations of Topology-Preserving Mappings
116(11)
Ordering of Reference Vectors in the Input Space
116(4)
Demonstrations of Ordering of Responses in the Output Space
120(7)
Basic Mathematical Approaches to Self-Organization
127(11)
One-Dimensional Case
128(4)
Constructive Proof of Ordering of Another One-Dimensional SOM
132(6)
The Batch Map
138(4)
Initialization of the SOM Algorithms
142(1)
On the ``Optimal'' Learning-Rate Factor
143(2)
Effect of the Form of the Neighborhood Function
145(1)
Does the SOM Algorithm Ensue from a Distortion Measure?
146(2)
An Attempt to Optimize the SOM
148(4)
Point Density of the Model Vectors
152(7)
Earlier Studies
152(1)
Numerical Check of Point Densities in a Finite One-Dimensional SOM
153(6)
Practical Advice for the Construction of Good Maps
159(2)
Examples of Data Analyses Implemented by the SOM
161(4)
Attribute Maps with Full Data Matrix
161(4)
Case Example of Attribute Maps Based on Incomplete Data Matrices (Missing Data): ``Poverty Map''
165(1)
Using Gray Levels to Indicate Clusters in the SOM
165(1)
Interpretation of the SOM Mapping
166(4)
``Local Principal Components''
166(3)
Contribution of a Variable to Cluster Structures
169(1)
Speedup of SOM Computation
170(7)
Shortent Winner Search
170(2)
Increasing the Number of Units in the SOM
172(3)
Smoothing
175(1)
Combination of Smoothing. Lattice Growing. and SOM Algorithm
176(1)
Physiological Interpretation of SOM
177(14)
Conditions for Abstract Feature Maps in the Brain
177(1)
Two Different Lateral Control Mechanisms
178(7)
The WTA Function. Based on Lateral Activity Control
179(5)
Lateral Control of Plasticity
184(1)
Learning Equation
185(1)
System Models of SOM and Their Simulations
185(3)
Recapitulation of the Features of the Physiological SOM Model
188(1)
Similarities Between the Brain Maps and Simulated Feature Maps
188(3)
Magnification
189(1)
Imperfect Maps
189(1)
Overlapping Maps
189(2)
Variants of SOM
191(54)
Overview of Ideas to Modify the Basic SOM
191(1)
Adaptive Tensorial Weights
191(6)
Tree-Structured SOM in Searching
197(1)
Different Definitions of the Neighborhood
198(2)
Neighborhoods in the Signal Space
200(1)
Dynamical Elements Added to the SOM
201(4)
The SOM for Symbol Strings
205(2)
Initialization of the SOM for Strings
205(1)
The Batch Map for Strings
206(1)
Tie-Break Rules
206(1)
A Simple Example: The SOM of Phonemic Transcriptions
207(1)
Operator Maps
207(4)
Evolutionary-Learning SOM
211(4)
Evolutionary-Learning Filters
211(1)
Self-Organization According to a Fitness Function
212(3)
Supervised SOM
215(1)
The Adaptive-Subspace SOM (ASSOM)
216(26)
The Problem of Invariant Features
216(2)
Relation Between Invariant Features and Linear Subspaces
218(4)
The ASSOM Algorithm
222(4)
Derivation of the ASSOM Algorithm by Stochastic Approximation
226(2)
ASSOM Experiments
228(14)
Feedback-Controlled Adaptive-Subspace SOM (FASSOM)
242(3)
Learning Vector Quantization
245(18)
Optimal Decision
245(1)
The LVQ1
246(4)
The Optimized-Learning-Rate LVQ1 (OLVQ1)
250(1)
The Batch-LVQ1
251(1)
The Batch-LVQ1 for Symbol Strings
252(1)
The LVQ2 (LVQ2.1)
252(1)
The LVQ3
253(1)
Differences Between LVQ1. LVQ2 and LVQ3
254(1)
General Considerations
254(2)
The Hypermap-Type LVQ
256(5)
The ``LVQ-SOM''
261(2)
Applications
263(48)
Preprocessing of Optic Patterns
264(4)
Blurring
265(1)
Expansion in Terms of Global Features
266(1)
Spectral Analysis
266(1)
Expansion in Terms of Local Features (Wavelets)
267(1)
Recapitulation of Features of Optic Patterns
267(1)
Acoustic Preprocessing
268(1)
Process and Machine Monitoring
269(2)
Selection of Input Variables and Their Scaling
269(1)
Analysis of Large Systems
270(1)
Diagnosis of Speech Voicing
271(1)
Transcription of Continuous Speech
271(9)
Texture Analysis
280(1)
Contextual Maps
281(5)
Artifically Generated Clauses
283(2)
Natural Text
285(1)
Organization of Large Document Files
286(13)
Statistical Models of Documents
286(6)
Construction of Very Large WEBSOM Maps by the Projection Method
292(4)
The WEBSOM of All Electronic Patent Abstracts
296(3)
Robot-Arm Control
299(5)
Simultaneous Learning of Input and Output Parameters
299(4)
Another Simple Robot-Arm Control
303(1)
Telecommunications
304(4)
Adaptive Detector for Quantized Signals
304(1)
Channel Equalization in the Adaptive QAM
305(1)
Error-Tolerant Transmission of Images by a Pair of SOMs
306(2)
The SOM as an Estimator
308(3)
Symmetric (Autoassociative) Mapping
308(1)
Asymmetric (Heteroassociative) Mapping
309(2)
Software Tools for SOM
311(18)
Necessary Requirements
311(2)
Desirable Auxiliary Features
313(2)
SOM Program Packages
315(4)
SOM PAK
315(2)
SOM Toolbox
317(1)
Nenet (Neural Networks Tool)
318(1)
Viscovery SOMine
318(1)
Examples of the Use of SOM PAK
319(8)
File Formats
319(3)
Description of the Programs in SOM PAK
322(4)
A Typical Training Sequence
326(1)
Neural-Networks Software with the SOM Option
327(2)
Hardware for SOM
329(18)
An Analog Classifier Circuit
329(3)
Fast Digital Classifier Circuits
332(5)
SIMD Implementation of SOM
337(2)
Transputer Implementation of SOM
339(2)
Systolic-Array Implementation of SOM
341(1)
The COKOS Chip
342(1)
The TlnMANN Chip
342(2)
NBISOM 25 Chip
344(3)
An Overview of SOM Literature
347(26)
Books and Review Articles
347(1)
Early Works on Competitive Learning
348(1)
Status of the Mathematical Analyses
349(9)
Zero-Order Topology (Classical VQ) Results
349(1)
Alternative Topological Mappings
350(1)
Alternative Architectures
350(1)
Functional Variants
351(1)
Theory of the Basic SOM
352(6)
The Learning Vector Quantization
358(1)
Diverse Applications of SOM
358(11)
Machine Vision and Image Analysis
358(2)
Optical Character and Script Reading
360(1)
Speech Analysis and Recognition
360(1)
Acoustic and Musical Studies
361(1)
Signal Processing and Radar Measurements
362(1)
Telecommunications
362(1)
Industrial and Other Real-World Measurements
362(1)
Process Control
363(1)
Robotics
364(1)
Electronic-Circuit Design
364(1)
Physics
364(1)
Chemistry
365(1)
Biomedical Applications Without Image Processing
365(1)
Neurophysiological Research
366(1)
Data Processing and Analysis
366(1)
Linguistic and AI Problems
367(1)
Mathematical and Other Theoretical Problems
368(1)
Applications of LVQ
369(1)
Survey of SOM and LVQ Implementations
370(3)
Glossary of ``Neural'' Terms
373(30)
References 403(84)
Index 487

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