TR-96-17: Discrete Vector Quantization for Arbitrary Distance Function Estimation

There are currently many vastly dierent areas of research involving adaptive learning. Two of these are the ones which concern neural networks and learning automata. 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. The latter is 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 use optimized 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 (including, for academic purposes a VQ strategy in the meta-domain). After an initial training phase, a system which achieves distance estimation attempts to yield an estimate of any node-pair distance without actually deriving an explicit form for the unknown function. The algorithms have been rigorously tested for the actual road-travel distances involving cities in Turkiye and the results obtained are conclusive. Indeed, these present results are the best currently available from any single or hybrid strategy.

TR-96-17.pdf