A methodology for neural spatial interaction modeling

Manfred M. Fischer, Martin Reismann

Publication: Scientific journalJournal articlepeer-review

Abstract

This paper attempts to develop a mathematically rigid and unified framework for
neural spatial interaction modeling. Families of classical neural network models, but
also less classical ones such as product unit neural network ones are considered for the
cases of unconstrained and singly constrained spatial interaction flows. Current
practice appears to suffer from least squares and normality assumptions that ignore the
true integer nature of the flows and approximate a discrete-valued process by an
almost certainly misrepresentative continuous distribution. To overcome this deficiency
we suggest a more suitable estimation approach, maximum likelihood estimation under
more realistic distributional assumptions of Poisson processes, and utilize a global
search procedure, called Alopex, to solve the maximum likelihood estimation problem.
To identify the transition from underfitting to overfitting we split the data into training,
internal validation and test sets. The bootstrapping pairs approach with replacement is
adopted to combine the purity of data splitting with the power of a resampling
procedure to overcome the generally neglected issue of fixed data splitting and the
problem of scarce data. In addition, the approach has power to provide a better
statistical picture of the prediction variability, Finally, a benchmark comparison
against the classical gravity models illustrates the superiority of both, the
unconstrained and the origin constrained neural network model versions in terms of
generalization performance measured by Kullback and Leibler's information criterion.
Original languageEnglish
Pages (from-to)207 - 228
JournalGeographical Analysis. An International Journal of Theoretical Geography
Volume34
Issue number3
DOIs
Publication statusPublished - 2002

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