Mining succinct systems of minimal generators of formal concepts

Abstract

Formal concept analysis has become an active field of study for data analysis and knowledge discovery. A formal concept C is determined by its extent (the set of objects that fall under C) and its intent (the set of properties or attributes covered by C). The intent for C, also called a closed itemset, is the maximum set of attributes that characterize C. The minimal generators for C are the minimal subsets of C's intent which can similarly characterize C. This paper introduces the succinct system of minimal generators (SSMG) as a minimal representation of the minimal generators of all concepts, and gives an efficient algorithm for mining SSMGs. The SSMGs are useful for revealing the equivalence relationship among the minimal generators, which may be important for medical and other scientific discovery; and for revealing the extent-based semantic equivalence among associations. The SSMGs are also useful for losslessly reducing the size of the representation of all minimal generators, similar to the way that closed itemsets are useful for losslessly reducing the size of the representation of all frequent itemsets. The removal of redudancies will help human users to grasp the structure and information in the concepts. © Springer-Verlag Berlin Heidelberg 2005.