Data transformation: a semantically-based approach to function discovery

Abstract

This paper presents the method of data transformation for discovering numeric functions from their examples. Based on the idea of transformations between functions, this method can be viewed as a semantic counterpart to the more common approach of formula construction used in most previous discovery systems. Advantages of the new method include a flexible implementation through the design of transformation rules, and a sound basis for rigorous mathematical analysis to characterize what can be discovered. The method has been implemented in a discovery system called "LINUS," which can identify a wide range of functions: rational functions, quadratic relations, and many transcendental functions, as well as those that can be transformed to rational functions by combinations of differentiation, logarithm and function inverse operations.