Artificial Neural Networks. A New Approach to Modelling Interregional Telecommunication Flows

During the last thirty years there has been much research effort in regional science devoted to modelling interactions over geographic space. Theoretical approaches for studying these phenomena have been modified considerably. This paper suggests a 'new modelling approach, based upon a general nested sigmoid neural network model. Its feasibility is illustrated in the context of modelling interregional telecommunication traffic in Austria and its performance is evaluated in comparison with the classical regression approach of the gravity type. The application of this neural network approach may be viewed as a three-stage process. The first stage refers to the identification of an appropriate network from the family of two-layered feedforward networks with 3 input nodes, one layer of (sigmoidal) intermediate nodes and one (sigmoidal) output node (logistic activation function). There is no general procedure to address this problem. We solved this issue experimentally. The input-output dimensions have been chosen in order to make the comparison with the gravity model as close as possible. The second stage involves the estimation of the network parameters of the selected neural network model. This is perlormed via the adaptive setting of the network parameters (training, estimation) by means of the application of a least mean squared error goal and the error back propagating technique, a recursive learning procedure using a gradient search to minimize the error goal. Particular emphasis is laid on the sensitivity of the network perlormance to the choice of the initial network parameters as well as on the problem of overlitting. The final stage of applying the neural network approach refers to the testing of the interregional teletraffic flows predicted. Prediction quality is analysed by means of two perlormance measures, average relative variance and the coefficient of determination, as well as by the use of residual analysis. The analysis shows that the neural network model approach outperlorms the classical regression approach to modelling telecommunication traffic in Austria.