An analytical comparison of some rule-learning programs
Artificial Intelligence
Learning Patterns in Multidimensional Space Using Interval Algebra
AIMSA '02 Proceedings of the 10th International Conference on Artificial Intelligence: Methodology, Systems, and Applications
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Bundy. Silver and Plummet (1985) provide an analysis of the Focussing algorithm and the Classification algorithm in the case where the description space consists of a set of relation trees. This paper discusses an extension to their analysis in which the description space is construed as a geometric space. Under this construal the behaviour of both the Focussing algorithm and the Classification algorithm is analysed in terms of the construction of hypercuboids. This analysis leads to a number of observations: (i) that a distinction can be made between a strong and a weak version of the disjunctive-concept problem; (ii) that certain solutions to the disjunctive-concept problem can be shown to exploit what are, in effect, distance functions over the description space and (iii). that the Classification algorithm is only capable of learning a subset of the possible disjunctive concepts in any given domain.