Evaluation of the capability of multilayer perceptron using total curvature of hypersurface: in the output-space

A multilayer perceptron (MLP)can be regarded as the mapping from the input layer to the output layer. From this point of view, MLP learning is a process of searching the "optimal" mapping from the input space to the output space. However, the meaning of optimality and features of the generalization have not been made clear in various application areas such as pattern recognition. In this paper the authors propose a new procedure for evaluating the capability of MLP and show that the "total curvature" of the hypersurface spanned by the output vectors of a MLP is an efficient measure of the capability. The authors justify the procedure by simulation experiments to evaluate the capability of several kinds of MLP using total curvature as the evaluation functional.