SOFIA: How to Make FCA Polynomial?

In pattern mining, one of the most important problems is fighting exponential explosion of the set of patterns. A typical solution is generating only a part of all patterns satisfying some criteria. The most well-known criterion is support of a pattern, which has the monotonicity property allowing one to generate only frequent (highly supported) patterns. Many other useful criteria are not monotonic, which makes it difficult to generate best patterns efficiently. In this paper we introduce the notion of “generalized monotonicity” and Σοφια algorithm that allow to generate top patterns in polynomial time modulo basic operations, e.g., measure computation, for criteria that are not monotonic. This approach is applicable not only to itemsets, but to complex descriptions such as sequences, graphs, numbers or interval tuples, etc. In this paper we consider stability and Δ-measures which are not monotonic. In the experiments, we compute top best patterns w.r.t. these measures and obtain very promising results.