Improving Analogical Extrapolation Using Case Pair Competence

Abstract

An analogical proportion is a quaternary relation that is to be read “a is to b as c is to d”, verifying some symmetry and permutation properties. As can be seen, it involves a pair of pairs. Such a relation is at the basis of an approach to case-based reasoning called analogical extrapolation, which consists in retrieving three cases forming an analogical proportion with the target problem in the problem space and then in finding a solution to this problem by solving an analogical equation in the solution space. This paper studies how the notion of competence of pairs of source cases can be estimated and used in order to improve extrapolation. A preprocessing of the case base associates to each case pair a competence given by two scores: the support and the confidence of the case pair, computed on the basis of other case pairs forming an analogical proportion with it. An evaluation in a Boolean setting shows that using case pair competences improves significantly the result of the analogical extrapolation process.