Inductive Learning Algorithms for Complex Systems Modeling

H.R. Madala

• Publisher: CRC Press
• Year: 2019
• Print ISBN: 9781315894393
• eBook ISBN: 9781351090391
• Topic: Computer Science
• Subtopic: Programming Algorithms
• Index: Computer Science

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 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 IBM-compatible PCs. Inductive Learning Algorithms for Complex Systems Modeling will be a valuable reference for graduate students, research workers, and scientists in applied 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.

Chapter 1

Introduction

1 Systems and Cybernetics

Civilization is rapidly becoming very dependent on large-scale systems of men, machines, and environment. Because such systems are often unpredictable, we must rapidly develop a more sophisticated understanding of them to prevent serious consequences. Very often the ability of the system to carry out its function (or alternatively, its catastrophically failing to function) is a property of the system as a whole and not of any particular component. The single most important rule in the management of large scale systems is that one must account for the entire system—the sum of all the parts. This most likely involves the discipline of “differential games.” It is reasonable to predict that cybernetic methods will be relevant to the solution of the greatest problems that face man today.

Cybernetics is the science of communication and control in machines and living creatures [133]. Nature employs the best cybernetic systems that can be conceived. In the neurological domain of living beings, the ecological balance involving environmental feedback, the control of planetary movements, or the regulation of the temparature of the human body, the cybernetic systems of nature are fascinating in their accuracy and efficiency. They are cohesive, self-regulating and stable systems; yet they do have the remarkable adaptability to change and the inherent capacity to use experience of feedback to aid the learning process.

Sustained performance of any system requires regulation and control. In complicated machinery the principles of servomechanism and feedback control have long been in effective use. The control principles in cybernetics are the error-actuated feedback and homeostasis. Take the case of a person driving a car. He keeps to the desired position on the road by constantly checking the deviation through visual comparison. He then corrects the error by making compensating movements of the steering wheel. Error sensing and feedback are both achieved by the driver’s brain which coordinates his sight and muscular action. Homeostasis is the self-adjusting property that all living organisms possess and that makes use of feedback from the environment to adjust metabolism to changing environmental conditions. Keeping the temperature of the human body constant is a good example of homeostasia.

The application of cybernetics to an environmental situation is much more involved than the servomechanism actuating “feedback correction.” The number of variables activating in the system are plentiful. The variables behave in stochastic manner and interactive relationships among them are very complex. Examples of such systems in nature are meteorological and environmental systems, agricultural crops, river flows, demographic systems, pollution, and so on. According to complexity of interactions with various influences in nature, these are called cybernetical systems. Changes take place in a slow and steady manner, and any suddenness of change cannot be easily perceived. If these systems are not studied continuously by using sophisticated techniques and if predictions of changes are not allowed to accumulate, sooner or later the situation is bound to get out of hand.

The tasks of engineering cybernetics (self-organization modeling, identification, optimal control, pattern recognition, etc.) require development of special theories which, although look different, have many things in common. The commonality among theories that form the basis of complex problem-solving has increased, indicating the maturity of cybernetics as a branch of science [37]. This leads to a common theory of self-organization modeling that is a combination of the deductive and inductive methods and allows one to solve complex problems. The mathematical foundations of such a common theory might be the approach that utilizes the black box concept as a study of input and output, the neural approach that utilizes the concept of threshold logic and connectionism, the inductive approach that utilizes the concept of inductive mechanism for maintaining the composite control of the system, the probabilistic approach that utilizes multiplicative functions of the hierarchical theory of statistical decisions, and Gödel’s mathematical logic approach (incompleteness theorem) that utilizes the principle of “external complement” as a selection criterion.

The following are definitions of terms that are commonly used in cybernetic literature and the concept of black box.

1.1 Definitions

1. A system is a collection of interacting, divers...

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• 1 Introduction
• 2 Inductive Learning Algorithms
• 3 Noise Immunity and Convergence
• 4 Physical Fields and Modeling
• 5 Clusterization and Recognition
• 6 Applications
• 7 Inductive and Deductive Networks
• 8 Basic Algorithms and Program Listings
• Epilogue
• Bibliography
• Index