A Methodology for Neural Spatial Interaction Modeling

Abstract

A methodology for neural spatial interaction modeling

Principles of Neural Spatial Interaction Modeling

“…An example of a powerful global search procedure is Alopex, a correlationbased method for solving the maximum likelihood problem. The reader interested in details of the procedure is referred to Fischer and Reismann (2002b).…”

“…The standard approach for assessing the generalization performance of a neural spatial interaction model is data splitting (see, for example, Fischer and Reismann, 2002b). This method simulates learning and generalization by partitioning the total data set, say M U ={(x u , y u ) with u=1, ..., U}, into three separate subsets: a training [insample] set M U1 ={(x u1 , y u1 ) with u1=1, ..., U1}, an internal validation set M U2 ={(x u2 , y u2 ) with u2=1, ..., U2} and a testing [out-of-sample] set M U3 ={(x u3 , y u3 ) with u3=1, ..., U3}.…”

Learning in neural spatial interaction models: A statistical perspective

“…It is evident that the choice of the loss function plays a crucial role in the determination of the optimal parameterŵ . We follow Fischer and Reismann (2002b) to specify an appropriate loss function. Hereby, we assume that the objective is to find that neural spatial interaction model which is the most likely explanation of the observed data set (Rumelhart et al, 1995).…”

Spatial Econometric Methods for Modeling Origin Destination Flows

“…The subject of spatial interaction modeling has a long and distinguished history that has led to the emergence of three major schools of analytical thought: the macroscopic school based upon a statistical equilibrium approach (see Wilson 1967;Roy 2004), the microscopic school based on a choice-theoretic approach (see Smith 1975;Sen and Smith 1995), and the geocomputational school based upon the neural network approach that processes spatial interaction models as universal function approximators (see Fischer 2002;Fischer and Reismann 2002). In these schools there is a deep-seated view that spatial interaction implies movement of entities, and that this has little to do with spatial association (Getis 1991).…”