Disjunctive Learning with a Soft-Clustering Method

Abstract

In the case of concept learning from positive and negative examples, it is rarely possible to find a unique discriminating conjunctive rule; in most cases, a disjunctive description is needed. This problem, known as disjunctive learning, is mainly solved by greedy methods, iteratively adding rules until all positive examples are covered. Each rule is determined by discriminating properties, where the discriminating power is computed from the learning set. Each rule defines a subconcept of concept to be learned with these methods. The final set of sub-concepts is then highly dependent from both the learning set and the learning method.

In this paper, we propose a different strategy: we first build clusters of similar examples thus defining subconcepts, and then we characterize each cluster by a unique conjunctive definition. The clustering method relies on a similarity measure designed for examples described in first order logic. The main particularity of our clustering method is to build “soft clusters”, i.e. allowing some objects to belong to different groups. Once clusters have been built, we learn first-order rules defining the clusters, using a general-to-specific method: each step consists in adding a literal that covers all examples of a group and rejects as many negative examples as possible.

This strategy limits some drawbacks of greedy algorithms and induces a strong reduction of the hypothesis space: for each group (subconcept), the search space is reduced to the set of rules that cover all the examples of the group and reject the negative examples of the concept.