---
title: "Hypercuboid-Formation Behaviour of Two Learning Algorithms"
authors:
  - "Chris Thornton"
doi: ""
url: "https://ijcai.org/proceedings/1987/62"
pdf: "https://ijcai.org/proceedings/1987/0062.pdf"
venue: "Proceedings of the Tenth International Joint Conference on Artificial Intelligence"
year: 1987
pages: "301-302"
track: "Knowledge Acquisition"
keywords:
---

# Hypercuboid-Formation Behaviour of Two Learning Algorithms

Chris Thornton

*Proceedings of the Tenth International Joint Conference on Artificial Intelligence*, pages 301-302.

## Abstract

Bundy. Silver and Plummer (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 diseusses 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.