Kohonen Self-Organizing Maps

1995
ISBN: 978-3-642-97610-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 30, 362 Seiten, eBook

Reihe: Springer Series in Information Sciences

The book we have at hand is the fourth monograph I wrote for Springer Verlag. The previous one named "Self-Organization and Associative Mem ory" (Springer Series in Information Sciences, Volume 8) came out in 1984. Since then the self-organizing neural-network algorithms called SOM and LVQ have become very popular, as can be seen from the many works re viewed in Chap. 9. The new results obtained in the past ten years or so have warranted a new monograph. Over these years I have also answered lots of questions; they have influenced the contents of the present book. I hope it would be of some interest and help to the readers if I now first very briefly describe the various phases that led to my present SOM research, and the reasons underlying each new step. I became interested in neural networks around 1960, but could not in terrupt my graduate studies in physics. After I was appointed Professor of Electronics in 1965, it still took some years to organize teaching at the uni versity. In 1968 - 69 I was on leave at the University of Washington, and D. Gabor had just published his convolution-correlation model of autoasso ciative memory. I noticed immediately that there was something not quite right about it: the capacity was very poor and the inherent noise and crosstalk were intolerable. In 1970 I therefore sugge~ted the auto associative correlation matrix memory model, at the same time as J.A. Anderson and K. Nakano.

Zielgruppe

Research

Autoren/Hrsg.

Kohonen, Teuvo

Inhaltsverzeichnis

1. Mathematical Preliminaries.- 1.1 Mathematical Concepts and Notations.- 1.2 Distance Measures for Patterns.- 1.3 Statistical Pattern Recognition.- 1.4 The Robbins-Monro Stochastic pproximation.- 1.5 The Subspace Methods of Classification.- 1.6 Dynamically Expanding Context.- 2. Justification of Neural Modeling.- 2.1 Models, Paradigms, and Methods.- 2.2 On the Complexity of Biological Nervous Systems.- 2.3 Relation Between Biological and Artificial Neural Networks.- 2.4 What Functions of the Brain Are Usually Modeled?.- 2.5 When Do We Have to Use Neural Computing?.- 2.6 Transformation, Relaxation, and Decoder.- 2.7 Categories of ANNs.- 2.8 Competitive-Learning Networks.- 2.9 Three Phases of Development of Neural Models.- 2.10 A Simple Nonlinear Dynamic Model of the Neuron.- 2.11 Learning Laws.- 2.12 Brain Maps.- 3. The Basic SOM.- 3.1 The SOM Algorithm in the Euclidean Space.- 3.2 The “Dot-Product SOM”.- 3.3 Preliminary Demonstrations of Topology-Preserving Mappings.- 3.4 Basic Mathematical Approaches to Self-Organization.- 3.5 Initialization of the SOM Algorithms.- 3.6 On the “Optimal” Learning-Rate Factor.- 3.7 Effect of the Form of the Neighborhood Function.- 3.8 Magnification Factor.- 3.9 Practical Advice for the Construction of Good Maps.- 3.10 Examples of Data Analyses Implemented by the SOM.- 3.11 Using Gray Levels to Indicate Clusters in the SOM.- 3.12 Derivation of the SOM Algorithm in the General Metric.- 3.13 What Kind of SOM Actually Ensues from the Distortion Measure?.- 3.14 Batch Computation of the SOM (“Batch Map”).- 4. Physiological Interpretation of SOM.- 4.1 Two Different Lateral Control Mechanisms.- 4.2 Learning Equation.- 4.3 System Models of SOM and Their Simulations.- 4.4 Recapitulation of the Features of the Physiological SOM Model.-5. Variants of SOM.- 5.1 Overview of Ideas to Modify the Basic SOM.- 5.2 Adaptive Tensorial Weights.- 5.3 Tree-Structured SOM in Searching.- 5.4 Different Definitions of the Neighborhood.- 5.5 Neighborhoods in the Signal Space.- 5.6 Dynamical Elements Added to the SOM.- 5.7 Operator Maps.- 5.8 Supervised SOM.- 5.9 Adaptive-Subspace SOM (ASSOM) for the Implementation of Wavelets and Gabor Filters.- 5.10 Feedback-Controlled Adaptive-Subspace SOM (FASSOM) ….- 6. Learning Vector Quantization.- 6.1 Optimal Decision.- 6.2 The LVQ1.- 6.3 The Optimized-Learning-Rate LVQ1 (OLVQ1).- 6.4 The LVQ2 (LVQ2.1).- 6.5 The LVQ3.- 6.6 Differences Between LVQ1, LVQ2 and LVQ3.- 6.7 General Considerations.- 6.8 The Hypermap-Type LVQ.- 6.9 The “LVQ-SOM”.- 7. Applications.- 7.1 Preprocessing.- 7.2 Process and Machine State Monitoring.- 7.3 Diagnosis of Speech Voicing.- 7.4 Transcription of Continuous Speech.- 7.5 Texture Analysis.- 7.6 Contextual Maps.- 7.7 Robot-Arm Control I.- 7.8 Robot-Arm Control II.- 8. Hardware for SOM.- 8.1 An Analog Classifier Circuit.- 8.2 A Fast Digital Classifier Circuit.- 8.3 SIMD Implementation of SOM.- 8.4 Transputer Implementation of SOM.- 8.5 Systolic-Array Implementation of SOM.- 8.6 The COKOS Chip.- 8.7 The TInMANN Chip.- 9. An Overview of SOM Literature.- 9.1 General.- 9.2 Early Works on Competitive Learning.- 9.3 Status of the Mathematical Analyses.- 9.4 Survey of General Aspects of the SOM.- 9.5 Modifications and Analyses of LVQ.- 9.6 Survey of Diverse Applications of SOM.- 9.7 Applications of LVQ.- 9.8 Survey of SOM and LVQ Implementations.- 10. Glossary of “Neural” Terms.- References.