Vector quantization for arbitrary distance function estimation

In this article we apply the concepts of vector quantization for the evaluation of arbitrary distance functions – a problem which has important applications in logistics and location analysis. The input to our problem is the set of coordinates of a large number of nodes whose internode arbitrary ‘distances’ have to be estimated. To render the problem interesting, nontrivial and realistic, we assume that the explicit form of this distance function is both unknown and uncomputable. Unlike traditional operations research methods, which compute aggregate parameters of functional estimators according to certain goodness-of-fit criteria, we have utilized vector quantization principles to first adaptively polarize the nodes into subregions. Subsequently, the parameters characterizing the subregions are learned by using a variety of methods (including, for academic purposes a vector quantization strategy in the metadomain). The algorithms have been rigorously tested for the actual road-travel distances involving cities in Turkey. The results obtained are not only conclusive, but also the best currently available from any single or hybrid strategy.