Second-Order and Nonsmooth Training Methods for Fuzzy Neural Networks
Buch in deiner Nähe kaufen
Beschreibung
Fuzzy neural networks are a way to combine fuzzy systems and neural networks. By this combination we hope to integrate the robustness of fuzzy systems with the learning methods. In this book two methods for training are developed and their numerical properties are discussed in detail.
The first algorithm is based on second-order methods developed in the field of nonlinear optimization. A direct application of these methods is inefficient because of the large number of weights in fuzzy neural networks. By exploiting the specific structure of neural networks the computational cost could be drastically reduced, while the advantages of these methods can be retained. The convergence properties of this algorithm are investigated in deatil by methods taken from the field of optimization.
The second algorithm deals with the properties of fuzzy membership functions. Many of the commonly used membership functions are not continuously differentiable, they are nonsmooth. However, almost all of the training algorithms are based on the assumption that the functions are smooth and consequently they fail for fuzzy neural networks. Therefore, an algorithm for training of nonsmooth fuzzy neural networks is proposed and it is shown by numerical examples and by theoretical investigations, that the algorithm converges, whereas standard training methods fail.
A charcter recognition problem from the field of image processing is used as a test-bed for evaluating all of the algorithms.
Autor*in
Christian Eitzinger