Kohonen Self-Organization and Associative Memory

2. Auflage 1988
ISBN: 978-3-662-00784-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 8, 312 Seiten, eBook

Reihe: Springer Series in Information Sciences

Two significant things have happened since the writing of the first edition in 1983. One of them is recent arousal of strong interest in general aspects of "neural computing", or "neural networks", as the previous neural models are nowadays called. The incentive, of course, has been to develop new com puters. Especially it may have been felt that the so-called fifth-generation computers, based on conventional logic programming, do not yet contain in formation processing principles of the same type as those encountered in the brain. All new ideas for the "neural computers" are, of course, welcome. On the other hand, it is not very easy to see what kind of restrictions there exist to their implementation. In order to approach this problem systematically, cer tain lines of thought, disciplines, and criteria should be followed. It is the pur pose of the added Chapter 9 to reflect upon such problems from a general point of view. Another important thing is a boom of new hardware technologies for dis tributed associative memories, especially high-density semiconductor circuits, and optical materials and components. The era is very close when the parallel processors can be made all-optical. Several working associative memory archi tectures, based solely on optical technologies, have been constructed in recent years. For this reason it was felt necessary to include a separate chapter (Chap. 10) which deals with the optical associative memories. Part of its con tents is taken over from the first edition.

Zielgruppe

Research

Autoren/Hrsg.

Kohonen, Teuvo

Inhaltsverzeichnis

1. Various Aspects of Memory.- 1.1 On the Purpose and Nature of Biological Memory.- 1.1.1 Some Fundamental Concepts.- 1.1.2 The Classical Laws of Association.- 1.1.3 On Different Levels of Modelling.- 1.2 Questions Concerning the Fundamental Mechanisms of Memory.- 1.2.1 Where Do the Signals Relating to Memory Act Upon?.- 1.2.2 What Kind of Encoding is Used for Neural Signals?.- 1.2.3 What are the Variable Memory Elements?.- 1.2.4 How are Neural Signals Addressed in Memory?.- 1.3 Elementary Operations Implemented by Associative Memory.- 1.3.1 Associative Recall.- 1.3.2 Production of Sequences from the Associative Memory.- 1.3.3 On the Meaning of Background and Context.- 1.4 More Abstract Aspects of Memory.- 1.4.1 The Problem of Infinite-State Memory.- 1.4.2 Invariant Representations.- 1.4.3 Symbolic Representations.- 1.4.4 Virtual Images.- 1.4.5 The Logic of Stored Knowledge.- 2. Pattern Mathematics.- 2.1 Mathematical Notations and Methods.- 2.1.1 Vector Space Concepts.- 2.1.2 Matrix Notations.- 2.1.3 Further Properties of Matrices.- 2.1.4 Matrix Equations.- 2.1.5 Projection Operators.- 2.1.6 On Matrix Differential Calculus.- 2.2 Distance Measures for Patterns.- 2.2.1 Measures of Similarity and Distance in Vector Spaces.- 2.2.2 Measures of Similarity and Distance Between Symbol Strings.- 2.2.3 More Accurate Distance Measures for Text.- 3. Classical Learning Systems.- 3.1 The Adaptive Linear Element (Adaline).- 3.1.1 Description of Adaptation by the Stochastic Approximation.- 3.2 The Perceptron.- 3.3 The Learning Matrix.- 3.4 Physical Realization of Adaptive Weights.- 3.4.1 Perceptron and Adaline.- 3.4.2 Classical Conditioning.- 3.4.3 Conjunction Learning Switches.- 3.4.4 Digital Representation of Adaptive Circuits.- 3.4.5 Biological Components.- 4. A New Approach to Adaptive Filters.- 4.1 Survey of Some Necessary Functions.- 4.2 On the “Transfer Function” of the Neuron.- 4.3 Models for Basic Adaptive Units.- 4.3.1 On the Linearization of the Basic Unit.- 4.3.2 Various Cases of Adaptation Laws.- 4.3.3 Two Limit Theorems.- 4.3.4 The Novelty Detector.- 4.4 Adaptive Feedback Networks.- 4.4.1 The Autocorrelation Matrix Memory.- 4.4.2 The Novelty Filter.- 5. Self-Organizing Feature Maps.- 5.1 On the Feature Maps of the Brain.- 5.2 Formation of Localized Responses by Lateral Feedback.- 5.3 Computational Simplification of the Process.- 5.3.1 Definition of the Topology-Preserving Mapping.- 5.3.2 A Simple Two-Dimensional Self-Organizing System.- 5.4 Demonstrations of Simple Topology-Preserving Mappings.- 5.4.1 Images of Various Distributions of Input Vectors.- 5.4.2 “The Magic TV”.- 5.4.3 Mapping by a Feeler Mechanism.- 5.5 Tonotopic Map.- 5.6 Formation of Hierarchical Representations.- 5.6.1 Taxonomy Example.- 5.6.2 Phoneme Map.- 5.7 Mathematical Treatment of Self-Organization.- 5.7.1 Ordering of Weights.- 5.7.2 Convergence Phase.- 5.8 Automatic Selection of Feature Dimensions.- 6. Optimal Associative Mappings.- 6.1 Transfer Function of an Associative Network.- 6.2 Autoassociative Recall as an Orthogonal Projection.- 6.2.1 Orthogonal Projections.- 6.2.2 Error-Correcting Properties of Projections.- 6.3 The Novelty Filter.- 6.3.1 Two Examples of Novelty Filter.- 6.3.2 Novelty Filter as an Autoassociative Memory.- 6.4 Autoassociative Encoding.- 6.4.1 An Example of Autoassociative Encoding.- 6.5 Optimal Associative Mappings.- 6.5.1 The Optimal Linear Associative Mapping.- 6.5.2 Optimal Nonlinear Associative Mappings.- 6.6 Relationship Between Associative Mapping, Linear Regression, and Linear Estimation.- 6.6.1 Relationship of the Associative Mapping to Linear Regression.- 6.6.2 Relationship of the Regression Solution to the Linear Estimator.- 6.7 Recursive Computation of the Optimal Associative Mapping..- 6.7.1 Linear Corrective Algorithms.- 6.7.2 Best Exact Solution (Gradient Projection).- 6.7.3 Best Approximate Solution (Regression).- 6.7.4 Recursive Solution in the General Case.- 6.8 Special Cases.- 6.8.1 The Correlation Matrix Memory.- 6.8.2 Relationship Between Conditional Averages and Optimal Estimator.- 7. Pattern Recognition.- 7.1 Discriminant Functions.- 7.2 Statistical Formulation of Pattern Classification.- 7.3 Comparison Methods.- 7.4 The Subspace Methods of Classification.- 7.4.1 The Basic Subspace Method.- 7.4.2 The Learning Subspace Method (LSM).- 7.5 Learning Vector Quantization.- 7.6 Feature Extraction.- 7.7 Clustering.- 7.7.1 Simple Clustering (Optimization Approach).- 7.7.2 Hierarchical Clustering (Taxonomy Approach).- 7.8 Structural Pattern Recognition Methods.- 8. More About Biological Memory.- 8.1 Physiological Foundations of Memory.- 8.1.1 On the Mechanisms of Memory in Biological Systems.- 8.1.2 Structural Features of Some Neural Networks.- 8.1.3 Functional Features of Neurons.- 8.1.4 Modelling of the Synaptic Plasticity.- 8.1.5 Can the Memory Capacity Ensue from Synaptic Changes?.- 8.2 The Unified Cortical Memory Model.- 8.2.1 The Laminar Network Organization.- 8.2.2 On the Roles of Interneurons.- 8.2.3 Representation of Knowledge Over Memory Fields.- 8.2.4 Self-Controlled Operation of Memory.- 8.3 Collateral Reading.- 8.3.1 Physiological Results Relevant to Modelling.- 8.3.2 Related Modelling.- 9. Notes on Neural Computing.- 9.1 First Theoretical Views of Neural Networks.- 9.2 Motives for the Neural Computing Research.- 9.3 What Could the Purpose of the Neural Networks be?.- 9.4 Definitions of Artificial “Neural Computing” and General Notes on Neural Modelling.- 9.5 Are the Biological Neural Functions Localized or Distributed?.- 9.6 Is Nonlinearity Essential to Neural Computing?.- 9.7 Characteristic Differences Between Neural and Digital Computers.- 9.7.1 The Degree of Parallelism of the Neural Networks is Still Higher than that of any “Massively Parallel” Digital Computer.- 9.7.2 Why the Neural Signals Cannot be Approximated by Boolean Variables.- 9.7.3 The Neural Circuits do not Implement Finite Automata.- 9.7.4 Undue Views of the Logic Equivalence of the Brain and Computers on a High Level.- 9.8 “Connectionist Models”.- 9.9 How can the Neural Computers be Programmed?.- 10. Optical Associative Memories.- 10.1 Nonholographic Methods.- 10.2 General Aspects of Holographic Memories.- 10.3 A Simple Principle of Holographic Associative Memory.- 10.4 Addressing in Holographic Memories.- 10.5 Recent Advances of Optical Associative Memories.- Bibliography on Pattern Recognition.- References.