Learning Hybrid Concept Descriptions

Most symbolic learning methods are concerned with learning concept descriptions in the form of a decision tree or a set of rules expressed in terms of the originally given attributes. For some practical problems, these methods are inadequate because they cannot learn conditions that require counting of some object properties. Such problems occur, for example, in engineering, economy, medicine and software engineering. This paper describes a method for learning hybrid descriptions that combine logic-type and arithmetic-type properties. The presented method builds hybrid descriptions in the form of conditional counting rules, which are logic-type (DNF) expressions with counting conditions (expressing a relationship involving a count of some object properties). The method employs a constructive induction approach in which the learning system performs two intertwined searches: one—for the most appropriate knowledge representation space, and second—for the "best " hypothesis in the space. The first search is done by determining maximum symmetry classes of binary attributes in the initial DNF-type hypotheses, and extending the initial representation space by counting attributes that correspond to these symmetry classes. The search for the "best" hypothesis in so extended representation space is done by a standard AQ inductive rule learning program. It our experiments, the proposed method learned simple and accurate concept descriptions when conventional learning methods failed.