Arbitrary distance function estimation using discrete vector quantization

This paper develops a method by which the general philosophies of vector quantization (VQ) and discretized automata learning can be incorporated for the computation 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 inter-node arbitrary “distances” have to be estimated. Unlike traditional operations research methods, which use parametric functional estimators, we have utilized discretized VQ principles to first adaptively polarize the nodes into sub-regions. Subsequently, the parameters characterizing the sub-regions are learnt by using a variety of methods. The algorithms have been rigorously tested for the actual road-travel distances involving cities in Turkiye and the results obtained are conclusive. Indeed, from the point of view of both speed and accuracy, these present results are the best currently available from any single or hybrid strategy