The Potential for Application of GMDH to Fuzzy Classification of Satellite Image Based on Comparison with Neural Network

Abstract

Fuzzy classification the authors have proposed is a new type of satellite image classification method which assumes each classification class to be a fuzzy set. With this both the possibility that a pixel may belong to more than one class and the possibility that a pixel may belong to none of the classes can be theoretically treated by the fuzzy set operations. The most important task to realize the fuzzy classification is the estimation of the membership function for each class. In the previous studies the applicability of neural network (NN) has been verified. However, NN is not necessarily satisfactory method in operational aspect because it needs a lot of trials in order to identify the appropriate network structure. This paper discusses the potential for the application of GMDH (Group Method of Data Handling) as an alternative to NN. An attention is mainly focused on the mathematical model structure of GMDH in comparison with NN. It is shown that the structure of GMDH is equivalent to that of a simplified NN in which the connection weights between some neurons are assumed to be zero. It means that the accuracy of estimation of membership functions by GMDH is theoretically lower than that of NN. On the other hand, GMDH aims to represent the complex I/O system by the recursive applications of simple regression analysis, and consequently GMDH is expected to be superior to NN in the operational aspect. Such a trade-off between high accuracy and operational easiness is demonstrated through the practical application. This paper concludes that GMDH can be an alternative to NN in fuzzy classification of satellite image.