Boolean Matrix Decomposition by Formal Concept Sampling

Finding interesting patterns is a classical problem in data mining. Boolean matrix decomposition is nowadays a standard tool that can find a set of patterns-also called factors-in Boolean data that explain the data well. We describe and experimentally evaluate a probabilistic algorithm for Boolean matrix decomposition problem. The algorithm is derived from GreCon algorithm which uses formal concepts-maximal rectangles or tiles-as factors in order to find a decomposition. We change the core of GreCon by substituting a sampling procedure for a deterministic computation of suitable formal concepts. This allows us to alleviate the greedy nature of GreCon, creates a possibility to bypass some of the its pitfalls and to preserve its features, e.g. an ability to explain the entire data.