On Using “Stochastic Learning on the Line” to Design Novel Distance Estimation Methods

Abstract

In this paper, we consider the problem of Distance Estimation (DE) when the inputs are the x and y coordinates of the points under consideration. The aim of the problem is to yield an accurate value for the real (road) distance between the points specified by the latter coordinates. This problem has, typically, been tackled by utilizing parametric functions called Distance Estimation Functions (DEFs). The parameters are learned from the training data (i.e., the true road distances) between a subset of the points under consideration. We propose to use Learning Automata (LA)-based strategies to solve the problem. In particular, we resort to the Adaptive Tertiary Search (ATS) strategy, proposed by Oommen et al., to affect the learning. By utilizing the information provided in the coordinates of the nodes and the true distances from this subset, we propose a scheme to estimate the inter-nodal distances. In this regard, we use the ATS strategy to calculate the best parameters for the DEF. Traditionally, the parameters of the DEF are determined by minimizing an appropriate “Goodness-of-Fit” (GoF) function. As opposed to this, the ATS uses the current estimate of the distances, the feedback from the Environment, and the set of known distances, to determine the unknown parameters of the DEF. While the GoF functions can be used to show that the results are competitive, our research shows that they are rather not necessary to compute the parameters themselves. The results that we have obtained using artificial and real-life datasets demonstrate the power of the scheme, and also validate our hypothesis that we can completely move away from the GoF-based paradigm that has been used for four decades, demonstrating that our scheme is novel and pioneering.

The second author gratefully acknowledges the partial support of NSERC, the Natural Sciences and Engineering Council of Canada.