A new generic basis of "factual" and "implicative" association rules

The extremely large number of association rules that can be drawn from – even reasonably sized datasets, bootstrapped the development of more acute techniques or methods to reduce the size of the reported rule sets. In this context, the battery of results provided by the Formal Concept Analysis (FCA) allowed one to define “irreducible” nuclei of association rule subset better known as generic bases. From such a condensed and reduced size set of association rules, it is possible to infer all association rules commonly via an adequate axiomatic system. In this paper, we introduce a novel informative generic basis of association rules, conveying two types of knowledge: “factual” and “implicative”. We also present a valid and complete axiomatic system allowing one to infer the set of all association rules. Results of the experiments carried out on real-life datasets have shown important profits in terms of compactness of the introduced generic basis.