Distance induction in first order logic

Abstract

A distance on the problem domain allows one to tackle some typical goals of machine learning, e.g. classification or conceptual clustering, via robust data analysis algorithms (e.g. k-nearest neighbors or k-means). A method for building a distance on first-order logic domains is presented in this paper. The distance is constructed from examples expressed as definite or constrained clauses, via a two-step process: a set of d hypotheses is first learnt from the training examples. These hypotheses serve as new descriptors of the problem domain Λh: they induce a mapping π from, Ch onto the space of integers INd. The distance between any two examples E and F is finally defined as the Euclidean distance between π(E) and π(F). The granularity of this hypothesis-driven distance (HDD) is controlled via the user-supplied parameter d. The relevance of a HDD is evaluated from the predictive accuracy of the k-NN classifier based on this distance. Preliminary experiments demonstrate the potentialities of distance induction, in terms of predictive accuracy, computational cost, and tolerance to noise.