GMDH - Methodology and Implementation in C

Contents
Preface
Organization of the Chapters
Intended Audience
Resources for Readers
About the Editor
List of Contributors
1. Introduction
1.1 Historical Background of GMDH
1.2 Basic GMDH Algorithm
1.2.1 External criteria
1.3 GMDH-Type Neural Networks
1.4 Classification of GMDH Algorithms
1.4.1 Parametric GMDH algorithms
1.4.1.1 Multilayer GMDH
1.4.1.2 Combinatorial GMDH
1.4.1.3 Objective system analysis
1.4.2 Non-parametric GMDH algorithms
1.4.2.1 Objective cluster analysis (OCA)
1.4.2.2 Analogue complexing (AC)
1.4.2.3 Pointing finger clusterization algorithm
1.5 Rationale for GMDH in C Language
1.6 Available Public Software
1.7 Recent Developments
1.8 Conclusions
References
2. GMDH Multilayered Iterative Algorithm (MIA)
2.1 Multilayered Iterative Algorithm (MIA) Networks
2.1.1 GMDH layers
2.1.2 GMDH nodes
2.1.3 GMDH connections
2.1.4 GMDH network
2.1.5 Regularized model selection
2.1.6 GMDH algorithm
2.2 Computer Code for GMDH-MIA
2.2.1 Compute a tree of quadratic polynomials
2.2.2 Evaluate the Ivakhnenko polynomial using the tree of polynomials generated
2.2.3 Compute the coefficients in the Ivakhnenko polynomial using the same tree of polynomials generated
2.2.4 Main program
2.3 Examples
2.3.1 Example 1
2.3.2 Example 2
2.4 Summary
References
3. GMDH Multilayered Algorithm Using Prior Information
3.1 Introduction
3.2 Criterion Correction Algorithm
3.3 C++ Implementation
3.3.1 Building sources
3.4 Example
3.5 Conclusion
References
4. Combinatorial (COMBI) Algorithm
4.1 The COMBI Algorithm
4.2 Usage of the “Structure of Functions”
4.3 Gradual Increase of Complexity
4.4 Implementation
4.5 Output Post-Processing
4.6 Output Interpretation
4.7 Predictive Model
4.8 Summary
References
5. GMDH Harmonic Algorithm
5.1 Introduction
5.2 Polynomial Harmonic Approximation
5.2.1 Polynomial, harmonic and hybrid terms
5.2.2 Hybrid function approximation
5.2.3 Need for hybrid modelling
5.3 GMDH Harmonic
5.3.1 Calculation of the non-multiple frequencies
5.3.2 Isolation of significant harmonics
5.3.3 Computing of the harmonics
Appendix A. Derivation of the trigonometric equations
A.1 System of equations for the weighting coefficients
A.2 Algebraic equation for the frequencies
A.3 The normal trigonometric equation
References
6. GMDH-Based Modified Polynomial Neural Network Algorithm
6.1 Modified Polynomial Neural Network
6.2 Description of the Program of MPNN Calculation
6.2.1 The software framework (GMDH)
6.2.2 Object-oriented architecture of the software framework
6.2.3 Description of the program graphic interface
6.2.4 Description of the basic functions of the data processing interface
6.3 The GMDH PNN Application in Solving the Problem of an Autonomous Mobile Robot (AMR) Control
6.3.1 The review of GMDH applications in robotics
6.3.2 The application of MPNN for controlling the autonomous mobile robot
6.4 Application of MPNN for the Control of the Autonomous Cranberry Harvester
6.4.1 General project description
6.4.2 Formalization of the cranberry harvester control problem
6.4.3 Experiment results
6.4.3.1 Results of experiments of obstacle recognition
6.4.3.2 The results of experiments on the prediction of the distribution of the extreme component derivative of the objective function
6.4.3.3 The experiment results of AMR movement control
6.4.3.4 The results of group prediction based on the formation of independent local data samples for the regions with the common boundary
6.5 Conclusion
References
7. GMDH-Clustering
7.1 Quality Criteria for GMDH-Clustering
7.1.1 Introduction
7.1.2 Problem statement
7.1.3 Measures of similarity
7.1.4 Selection of informative attributes and the search for the best clusterization: common approach to the classification of methods
7.1.5 Criteria for the evaluation of clusterization quality
7.1.6 Objective clusterization
7.2 Computer Code for GMDH-Clustering Quality Criteria
7.3 Examples
7.3.1 Example 1
7.3.2 Example 2
7.4 Conclusion
References
8. Multiagent Clustering Algorithm
8.1 Introduction
8.2 Honey Bee Swarm
8.3 Clustering based on the Multiagent Approach
8.4 Computer Code for Multiagent Clustering
8.4.1 Moving of agents
8.4.2 Natural selection
8.4.3 Evaluation of the conditions for objects in different cells
8.4.4 Main program: beeClustering
8.5 Examples
8.5.1 Example 1: Synthetic data
8.5.2 Example 2: Real-world problem
8.6 Conclusion
References
9. Analogue Complexing Algorithm
9.1 General Introduction to Analogue Usage in Task Solutions
9.2 Analogue Complexing
9.2.1 First case: The analogue complexing GMDH algorithm
9.2.1.1 Computer code for a simple analogue complexing algorithm example with distance calculation in Euclidean space
9.2.2 Second case: Method of long-range prognosis for the air temperature over a period of ten days using robust inductive models and analogue principle (example)
9.2.2.1 Introduction
9.2.2.2 Polynomial harmonic basis of inductive prognostic models
9.2.2.3 Accuracy estimation of the long-range prognosis of the average air temperature for a period of ten days
9.2.2.4 Research of the prognosis accuracy for the average air temperature during January 2003 to December 2007 with a half-year lead-time
9.2.2.5 Example of the long-range prognosis for the average air temperature of a ten-day period and its accuracy
9.2.2.6 Research of teaching data quantity on the prognosis accuracy of the average air temperature for a ten-day period
9.2.2.7 Summary of the example
9.3 Summary
References
10. GMDH-Type Neural Network and Genetic Algorithm
10.1 Introduction
10.2 Background of the GMDH-type Neural Network and Genetic Algorithm
10.3 Description of the Genome Representation of the GMDH-GA Procedure
10.4 GMDH-GA for Modeling the Tool wear Problem
10.5 Stock Price Prediction Using the GMDH-type Neural Network
10.6 Summary
References
Index