Principles of neural spatial interaction modelling

The focus of this paper is on the neural network approach to modelling origin-destination flows across geographic space. The novelty about neural spatial interaction models lies in their ability to model non-linear processes between spatial flows and their determinants, with few ' if any ' a priori assumptions of the data generating process. The paper draws attention to models based on the theory of feedforward networks with a single hidden layer, and discusses some important issues that are central for successful application development. The scope is limited to feedforward neural spatial interaction models that have gained increasing attention in recent years. It is argued that failures in applications can usually be attributed to inadequate learning and/or inadequate complexity of the network model. Parameter estimation and a suitably chosen number of hidden units are, thus, of crucial importance for the success of real world applications. The paper views network learning as an optimization problem, describes various learning procedures, provides insights into current best practice to optimize complexity and suggests the use of the bootstrap pairs approach to evaluate the model's generalization performance.