Vector Quantization for Arbitrary Distance Function Estimation

| In this paper we apply the concepts of Vector Quantization (VQ) for the determination 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. To render the problem interesting, non-trivial 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-t criteria, we have utilized VQ principles to rst adaptively polarize the nodes into sub-regions. Subsequently, the parameters characterizing the sub-regions are learnt by using a variety of methods (including, for academic purposes a VQ strategy in the meta-domain). The algorithms have been rigorously tested for the actual road-travel distances involving cities in T urkiye. The results obtained are not only conclusive, but also the best currently available from any single or hybrid strategy.