Towards fault-tolerant formal concept analysis

Given Boolean data sets which record properties of objects, Formal Concept Analysis is a well-known approach for knowledge discovery. Recent application domains, e.g., for very large data sets, have motivated new algorithms which can perform constraint-based mining of formal concepts (i.e., closed sets on both dimensions which are associated by the Galois connection and satisfy some user-defined constraints). In this paper, we consider a major limit of these approaches when considering noisy data sets. This is indeed the case of Boolean gene expression data analysis where objects denote biological experiments and attributes denote gene expression properties. In this type of intrinsically noisy data, the Galois association is so strong that the number of extracted formal concepts explodes. We formalize the computation of the so-called δ-bi-sets as an alternative for capturing strong associations between sets of objects and sets of properties. Based on a previous work on approximate condensed representations of frequent sets by means of δ-free itemsets, we get an efficient technique which can be applied on large data sets. An experimental validation on both synthetic and real data is given. It confirms the added-value of our approach w.r.t. formal concept discovery, i.e., the extraction of smaller collections of relevant associations.