Neural Network Modelling of Constrained Spatial Interaction Flows

Abstract

A novel modular product unit neural network architecture is presented to model singly
constrained spatial interaction flows. Modularity is seen as decomposition on the
computational level. The network is composed of two processing layers. The first layer
is implemented as a layer of functionally independent modules with identical
topologies. Each module is a feedforward network with two inputs, H hidden product
units and terminates with a single summation unit. The collective outputs of these
modules constitute the input to the second processing layer consisting of output units
that perform the flow prediction. The efficacy of the model approach is demonstrated
for the origin constrained case of spatial interaction using Austrian interregional
telecommunication traffic data. The model requires a global search procedure for
parameter estimation, such as the Alopex procedure. A benchmark comparison against
the standard origin constrained gravity model and the two-stage neural network
approach, suggested by Openshaw (1998), illustrates the superiority of the proposed
model in terms of generalisation performance measured by ARV and SRMSE.

Keywords: Origin constrained or destination constrained spatial interaction, neural
spatial interaction model, product unit network, Alopex procedure, benchmark
performance tests

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