Neural Network Learning to Discover Laws Ruling Noisy Empirical Data

Improvement in learning effectiveness of special neural networks (SNN) aiding the process of finding out hidden rules governing a given empirical data set is the topic of discussion in this paper. The SNN's are based on the 1/(.) type reciprocal functions, used as activation ones. The functions are located mainly in hidden layer and input nodes of the network. This is a specific characteristic of our SNN's. The SNN structure is simpler compared with other networks applied for solving similar problems [1-15]. Previous attempts to train such networks have not led do fully satisfactory results [16], [17]. One of the main reasons for that is noise encountered in the considered discrete empirical date. In this paper, a new methodology of the SNN training is presented. The proposed approach relies on introducing to the learning technique suitably prepared knowledge base in order to cope with the problem of adverse influence of noise on the training effects. In this way it is possible, for example, to eliminate from the learning process some unwanted rises of the SNN weights if it is assumed that the symbolic law description of a given data set, to be determined, has a monotonically-decreasing-function form. Results of learning with and without the use of the knowledge base are compared and superiority of the proposed approach over the previously presented ones is shown. The presented description and achieved results are restricted, for simplicity reasons, to one-dimensional relationship.