Learning Algorithm of Neural Networks Based on the Concept of Possibility and Necessity

Abstract

In this paper, we propose two learning methods of neural networks for a two-group discriminant problem. One method corresponds to the possibility analysis and the other to the necessity analysis. The proposed methods are the same as the back-propagation algorithm except for the cost function. The cost function to be minimized in our methods is not the sum of squared errors but the weighted sum of squared errors. The value of weight relating to each data point varies in process of learning and depends on whether the data point belongs to group 1 or group 2. For example, if we consider the possibility of group 1, the weight relating to the data points in group 1 is constant but the weight of group 2 is gradually decreased in process of learning. On the other hand, if we consider the necessity of group 1, the weight relating to the data points in group 1 is gradually decreased but the weight of group 2 is constant.