Journal of Geographical Systems

, Volume 4, Issue 3, pp 287–299 | Cite as

Learning in neural spatial interaction models: A statistical perspective

  • Manfred M. Fischer


 In this paper we view learning as an unconstrained non-linear minimization problem in which the objective function is defined by the negative log-likelihood function and the search space by the parameter space of an origin constrained product unit neural spatial interaction model. We consider Alopex based global search, as opposed to local search based upon backpropagation of gradient descents, each in combination with the bootstrapping pairs approach to solve the maximum likelihood learning problem. Interregional telecommunication traffic flow data from Austria are used as test bed for comparing the performance of the two learning procedures. The study illustrates the superiority of Alopex based global search, measured in terms of Kullback and Leibler's information criterion.

Key words: Maximum likelihood learning, local search, global search, backpropagation of gradient descents, Alopex procedure, origin constrained neural spatial interaction model 
JEL Classification: C45, C51 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Manfred M. Fischer
    • 1
  1. 1.Department of Economic Geography and Geoinformatics, Vienna University of Economics and Business Administration, Rossauer Laende 23/1, A-1090 Vienna, Austria (e-mail:

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