Estimating actual distances by norm functions: a comparison between the lk,p,θ-norm and the lb1,b2,θ-norm and a study about the selection of the data set

The aim of this paper is two-fold. First, the weighted lp-norm, which has proved to be an accurate distance predicting function and has been proposed by several authors as the most suitable predictor of distances, is compared through an empirical study with the l2b-norm, a function with the same number of parameters as the first one. The results show that neither distance function dominates the other. On the contrary, depending on the region considered either norm may be significantly better than the other. The second aim is to investigate how the selection of the data set representing the network of the region affects the ability of the distance predicting function for predicting distances, and to try to deduce how to obtain a suitable data set which adequately represents a given geographical region. Through another empirical study it is shown that the selection of the data set dramatically affects the accuracy of the predictions. To obtain a suitable data set it is important to choose a good sample size, and more importantly, the cities should be chosen so that they are distributed all over the region and represent the density of the cities in the region.