Neural Spatial Interaction Models: Network Training, Model Complexity and Generalization Performance
Spatial interaction models approximate mean interaction frequencies between origin and destination locations by using origin-specific, destination-specific and spatial separation information. The focus is on models that are based on the theory of feedforward neural networks. This contribution considers the functional form of neural spatial interaction models, including the specification of the activation functions, and discusses the problem of network training within a maximum likelihood framework that involves the solution of a non-linear optimization problem. This requires the evaluation of the log-likelihood function with respect to the network parameters. Overfitting is a problem that is likely to occur in neural spatial interaction models. To avoid this problem the contribution recommends controlling the model complexity either by regularization or by early stopping in network training. A bootstrapping pairs approach with replacement may be adopted to evaluate the generalization performance of the models.
KeywordsNeural spatial interaction models network training gradient based search model complexity regularization bootstrapping generalization performance
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