Interpolation and extrapolation: Comparison of definitions and survey of algorithms for convex and concave hulls

Abstract

Any data based method is vulnerable to the problem of extrapolation, nonetheless there exists no unified theory on handling it. The main topic of this publication is to point out the differences in definitions of extrapolation and related methods. There are many different interpretations of extrapolation and a multitude of methods and algorithms, which address the problem of extrapolation detection in different fields of study. We examine popular definitions of extrapolation, compare them to each other and list related literature and methods. It becomes apparent, that the opinions what extrapolation is and how to handle it, differ greatly from each other. We categorize existing literature and give guidelines to choose an appropriate definition of extrapolation for a present problem. We also present hull algorithms, from classic approaches to recent advances. The presented guidelines and categorized literature enables the reader to categorize a present problem, inspect relevant literature and apply suitable methods and algorithms to solve a problem, which is affected by extrapolation.