Methodological Challenges in Neural Spatial Interaction Modelling: The Issue of Model Selection

Spatial interaction modelling is a well established field in geography and regional science. Since the pioneering work of Wilson (1970) on entropy maximization, however, there has been surprisingly little innovation in the design of spatial interaction models. The principal exceptions include the competing destinations version of Fotheringham (1983), the use of genetic algorithms to breed new forms of spatial interaction models, either directly (Openshaw 1988) or by genetic programming (Turton et al. 1997), and the design of neural spatial interaction interaction models (Fischer and Gopal 1994; Gopal and Fischer 1993; Openshaw 1993). Neural spatial models are termed neural in the sense that they are based on neural computational approaches, inspired by neuroscience. They are more closely related to spatial interaction models of the gravity type, and under commonly met conditions they can be viewed as a special class of general feedforward neural network models with a single hidden layer and sigmoidal transfer functions (see Fischer 1998). Rigorous mathematical proofs for the universality of such feedforward neural network models (see, among others, Hornik et al. 1989) establish the neural spatial interaction models as a powerful class of universal approximators for spatial interaction flow data.