Abstract
The objective of this paper is to evaluate the usefulness of the weighted l p norm as a distance measure when axis rotation is included to obtain the best fit. We compare the weighted l p and Euclidean norms in an empirical study of 18 major country and city road networks. A substantial improvement in accuracy is obtained with the weighted l p norm for networks with a significant component of rectangular travel. We show that the weighted l p norm, and by inference other multi-parameter distance estimators, are justified in practice provided the reference axes are oriented properly to model the directional bias inherent in the network.
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