An Approach to Modeling Domain-Wide Information, based on Limited Points' Data - Part I

摘要

Predicting values at data points in a specified region when only a few values are known is a perennial problem and many approaches have been developed in response. Interpolation schemes provide some success and are the most widely used among the approaches. However, none of those schemes incorporates historical aspects in their formulae. This study presents an approach to interpolation, which utilizes the historical relationships existing between the data points in a region of interest. By combining the historical relationships with the interpolation equations, an algorithm for making predictions over an entire domain area, where data is known only for some random parts of that area, is presented. A performance analysis of the algorithm indicates that even when provided with less than ten percent of the domain's data, the algorithm outperforms the other popular interpolation algorithms when more than fifty percent of the domain's data is provided to them.