### Hypercuboid-formation behaviour of two learning algorithms

Christopher Thornton

Bundy et al (1985) have provided an analytical comparison of a number of rule-learning programs including the Focussing algorithm and the Classification algorithm. They analyse the behaviour of these algorithms in the case where the description space consists of a set of relation trees. However, it is possible to add some interesting footnotes to their analysis if we take the step of re-construing the description space as a geometrical 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 there is at least one, novel generalisation of the Focussing algorithm, (ii) that a heuristic-based strategy for coping with the disjunctive-concept problem will, in general, involve the exploitation of a valid metric over the description space and (iii) that the class of disjunctive rules (or concepts) which can be constructed by the Classification algorithm (Hunt et al, 1966) is characterised by some quite specific geometrical constraints.

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