Neural Network Modelling of Constrained Spatial Interaction Flows



1 Introduction

The subject of spatial interaction is fundamental to economic geography and regional
science. Spatial interaction models are used to facilitate the explanation and prediction
of human and economic interaction over geographic space. That there have been
relatively few papers in this area in recent years is merely a function of the hiatus that
followed a very active period of theory development. The 1960s and 1970s saw a huge
outpouring of both theoretical and empirical work. These were the heady days of
Stewart and Warntz, Stouffer, Isard, Wilson and Alonso. The empiricism that eminated
from their theoretical and methodological contributions filled regional science and
geographical journals. The lull came not so much because interest decreased, but
because very little in the way of novel theoretical insights. One exception was the
excitement over the work of Fotheringham on competing destinations in the early 1980s
when several new models were developed and new perspectives added (Fischer and
Getis 1999).

In more recent years, the major influence stems both from the emerging data-rich
environment and from technological innovations. The powerful and fast computing
environment now upon us has brought many scholars to spatial interaction theory once
again, either by utilising evolutionary computation to breed novel forms of spatial
interaction models (see Openshaw 1988; Turton, Openshaw and Diplock 1997) or
network-based approaches to spatial interaction (see, for example, Openshaw 1993,
1998, Fischer and Gopal 1994, Black 1995, Fischer, Hlavackova-Schindler and
Reismann 1999, Bergkvist 2000, Reggiani and Tritapepe 2000, Mozolin, Thill and
Usery 2000) leading to neural spatial interaction models. Neural spatial interaction
models are termed
neural in the sense that they have been inspired by neuroscience.
But they are more closely related to conventional spatial interaction of the gravity type
than they are to neurobiological models.

Interest in the recent past has largely focused on some crucuial issues in unconstrained
neural spatial interaction modelling (see, for example, Fischer, Hlavackova-Schindler,
and Reismann 1999, Fischer 2000). These models represent a rich and flexible family
of spatial interaction function approximators. But they may be of little practical value if
a priori information is available on accounting constraints on the predicted flows. The



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