Hema Rao Madala and Alexey G. Ivakhnenko
Inductive Learning Algorithms for Complex System ModelingContents
Chapter 1. Introduction
SYSTEMS AND CYBERNETICS 1
1.1 Definitions 2
1.2 Model and simulation 4
1.3 Concept of black box 5
2 SELF-ORGANIZATION MODELING 6
2.1 Neural approach 6
2.2 Inductive approach 7
INDUCTIVE LEARNING METHODS 9
3.1 Principal shortcoming in model development 10
3.2 Principle of self-organization 11
3.3 Basic technique 11
3.4 Selection criteria or objective functions 12
3.5 Heuristics used in problem-solving 17
Chapter 2. Inductive Learning GMDH Algorithms
1 SELF-ORGANIZATION METHOD 27
1.1 Basic iterative algorithm 28
2 NETWORK STRUCTURES 30
2.1 Multilayer algorithm 30
2.2 Combinatorial algorithm 32
2.3 Recursive scheme for faster combinatorial sorting 35
2.4 Multilayered structures using combinatorial setup 38
2.5 Selectional-combinatorial multilayer algorithm 38
2.6 Multilayer algorithm with propagating residuals
(front propagation algorithm) 41
2.7 Harmonic Algorithm 42
2.8 New algorithms 44
3 LONG-TERM QUANTITATIVE PREDICTIONS 51
3.1 Autocorrelation functions 51
3.2 Correlation interval as a measure of predictability 53
3.3 Principal characteristics for predictions 60
4 DIALOGUE LANGUAGE GENERALIZATION 63
4.1 Regular (subjective) system analysis 64
4.2 Multilevel (objective) analysis 65
4.3 Multilevel algorithm 65
Chapter 3.Noise Immunity and Convergence
1 ANALOGY WITH INFORMATION THEORY 75
1.1 Basic concepts of information and self-organization theories 77
1.2 Shannon's second theorem 79
1.3 Law of conservation of redundancy 81
1.4 Model complexity versus transmission band 82
2 CLASSIFICATION AND ANALYSIS OF CRITERIA 83
2.1 Accuracy criteria 84
2.2 Consistent criteria 85
2.3 Combined criteria 86
2.4 Correlational criteria 86
2.5 Relationships among the criteria 87
3 IMPROVEMENT OF NOISE IMMUNITY 89
3.1 Minimum-bias criterion as a special case 90
3.2 Single and multicriterion analysis 93
4 ASYMPTOTIC PROPERTIES OF CRITERIA 98
4.1 Noise immunity of modeling on a finite sample 99
4.2 Asymptotic properties of the external criteria 102
4.3 Calculation of locus of the minima 105
5 BALANCE CRITERION OF PREDICTIONS 108
5.1 Noise immunity of the balance criterion 111
6 CONVERGENCE OF ALGORITHMS 118
6.1 Canonical formulation 118
6.2 Internal convergence 120
Chapter 4. Physical Fields and Modeling
1 FINITE-DIFFERENCE PATTERN SCHEMES 126
1.1 Ecosystem modeling 128
2 COMPARATIVE STUDIES 133
2.1 Double sorting 135
2.2 Example - pollution studies 137
3 CYCLIC PROCESSES 143
3.1 Model formulations 146
3.2 Realization of prediction balance 151
3.3 Example - Modeling of tea crop productions 153
3.4 Example - Modeling of maximum applicable frequency (MAP) 159
Chapter 5. Clusterization and Recognition
1 SELF-ORGANIZATION MODELING AND CLUSTERING 165
2 METHODS OF SELF-ORGANIZATION CLUSTERING 177
2.1 Objective clustering - case of unsupervised learning 178
2.2 Objective clustering - case of supervised learning 180
2.3 Unimodality - "criterion-clustering complexity" 188
3 OBJECTIVE COMPUTER CLUSTERING ALGORITHM 194
4 LEVELS OF DISCRETIZATION AND BALANCE CRITERION 202
5 FORECASTING METHODS OF ANALOGUES 207
5.1 Group analogues for process forecasting 211
5.2 Group analogues for event forecasting 217
Chapter 6. Applications
1 FIELD OF APPLICATION 225
2 WEATHER MODELING 227
2.1 Prediction balance with time- and space-averaging 227
2.2 Finite difference schemes 230
2.3 Two fundamental inductive algorithms 233
2.4 Problem of long-range forecasting 234
2.5 Improving the limit of predictability 235
2.6 Alternate approaches to weather modeling 238
3 ECOLOGICAL SYSTEM STUDIES 247
3.1 Example - ecosystem modeling 248
3.2 Example - ecosystem modeling using rank correlations 253
4 MODELING OF ECONOMICAL SYSTEM 256
4.1 Examples - modeling of British and US economies 257
5 AGRICULTURAL SYSTEM STUDIES 270
5.1 Winter wheat modeling using partial summation functions 272
6 MODELING OF SOLAR ACTIVITY 279
Chapter 7. Inductive and Deductive Networks
1 SELF-ORGANIZATION MECHANISM IN THE GMDH NETWORKS 285
1.1 Some concepts, definitions, and tools 287
2 NETWORK TECHNIQUES 291
2.1 Inductive technique 291
2.2 Adaline 292
2.3 Back Propogation 293
2.4 Self-organization boolean logic 295
3 GENERALIZATION 296
3.1 Bounded with transformations 297
3.2 Bounded with objective functions 298
4 COMPARISON AND SIMULATION RESULTS 300
Chapter 8. Basic Algorithms and Program Listings
1 COMPUTATIONAL ASPECTS OF MULTILAYERED GMDH ALGORITHM 311
1.1 Program listing 313
1.2 Sample output 323
2 COMPUTATIONAL ASPECTS OF COMBINATORIAL ALGORITHM 326
2.1 Program listing 327
2.2 Sample outputs 336
3 COMPUTATIONAL ASPECTS OF HARMONICAL ALGORITHM 339
3.1 Program listing 341
3.2 Sample output 353
Epilogue 357
Bibliography 359
Index 365
From abstract:
Inductive Learning Algorithms for Complex Systems Modeling is a professional monograph that surveys new types of learning algorithms for modeling complex scientific systems in science and engineering. The book features discussions of GMDH algorithm development, structure, and behavior; comprehensive coverage of all types of algorithms useful for this subject; and applications of various modeling activities (e.g., environmental systems, noise immunity, economic systems, clusterization, and neural networks). It presents recent studies on clusterization and recognition problems, and it includes listings of algorithms in FORTRAN that can be run directly on PCs.
Inductive Learning Algorithms for Complex Systems Modeling will be a valuable reference for graduate students, research workers, and scientists in app lied mathematics, statistics, computer science, and systems science disciplines. The book will also benefit engineers and scientists from applied fields such as environmental studies, oceanographic modeling, weather forecasting, air and water pollution studies, economics, hydrology, agriculture, fisheries, and time series evaluations.
Features:
• Discusses GMDH self-organising algorithm development, structure, and behavior
• Presents comprehensive coverage of algorithms useful for complex systems modeling
• Includes recent studies on clusterization and recognition problems
• Provides listings of algorithms in FORTRAN that can be run directly on PCs.