Data Peeler: Contraint-Based Closed Pattern Mining in n-ary Relations

Set pattern discovery from binary relations has been exten- sively studied during the last decade. In particular, many complete and efficient algorithms which extract frequent closed sets are now available. Generalizing such a task to n-ary relations (n � 2) appears as a timely challenge. It may be important for many applications, e.g., when adding the time dimension to the popular objects × features bi- nary case. The generality of the task — no assumption be- ing made on the relation arity or on the size of its attribute domains — makes it computationally challenging. We in- troduce an algorithm called Data-Peeler. From a n-ary relation, it extracts all closed n-sets satisfying given piece- wise (anti)-monotonic constraints. This new class of con- straints generalizes both monotonic and anti-monotonic con- straints. Considering the special case of ternary relations, Data-Peeler outperforms the state-of-the-art algorithms CubeMiner and Trias by orders of magnitude. These good performances must be granted to a new clever enumeration strategy allowing an efficient closeness checking. An original application on a real-life 4-ary relation is used to assess the relevancy of closed n-sets constraint-based mining.