Constructing approximate informative basis of association rules

Abstract

In the study of discovering association rules, it is regarded as an important task to reduce the number of generated rules without loss of any information about the significant rules. From this point of view, Bastide, et al. have proposed to generate only non-redundant rules [2]. Although the number of generated rules can be reduced drastically by taking the redundancy into account, many rules are often still generated. In this paper, we try to propose a method for reducing the number of the generated rules by extending the original framework. For this purpose, we introduce a notion of approximate generator and consider an approximate redundancy. According to our new notion of redundancy, many non-redundant rules in the original sense are judged redundant and invisible to users. This achieves the reduction of generated rules. Furthermore, it is shown that any redundant rule can be easily reconstructed from our non-redundant rule with its approximate support and confidence. The maximum errors of these values can be evaluated by a user-defined parameter. We present an algorithm for constructing a set of non-redundant rules, called an approximate informative basis. The completeness and weak-soundness of the basis are theoretically shown. Any significant rule can be reconstructed from the basis and any rule reconstructed from the basis is (approximately) significant. Some experimental results show an effectiveness of our method as well.