Set pattern discovery from binary relations has been extensively studied during the last decade. In particular, many complete and efficient algorithms for frequent closed set mining 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, for example, when adding the time dimension to the popular objects × features binary case. The generality of the task (no assumption being made on the relation arity or on the size of its attribute domains) makes it computationally challenging. We introduce an algorithm called Data-Peeler. From an n-ary relation, it extracts all closed n-sets satisfying given piecewise (anti) monotonic constraints. This new class of constraints generalizes both monotonic and antimonotonic constraints. 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 to efficiently enforce the closeness property. The relevance of the extracted closed n-sets is assessed on real-life 3-and 4-ary relations. Beyond natural 3-or 4-ary relations, expanding a relation with an additional attribute can help in enforcing rather abstract constraints such as the robustness with respect to binarization. Furthermore, a collection of closed n-sets is shown to be an excellent starting point to compute a tiling of the dataset.

@article{cerf2009closed, author = {Cerf, Loïc and Besson, Jérémy and Robardet, Céline and Boulicaut, Jean-François}, title = {Closed patterns meet n-ary relations}, journal = {ACM Transactions on Knowledge Discovery from Data}, publisher = {ACM}, address = {New York, NY, USA}, year = {2009}, volume = {3}, number = {1}, pages = {1--36}, doi = {10.1145/1497577.1497580}, issn = {1556-4681}, keywords = {ol_web2.0, trias, mode, three, fca, triadic}, abstract = {Set pattern discovery from binary relations has been extensively studied during the last decade. In particular, many complete and efficient algorithms for frequent closed set mining 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, for example, when adding the time dimension to the popular objects × features binary case. The generality of the task (no assumption being made on the relation arity or on the size of its attribute domains) makes it computationally challenging. We introduce an algorithm called Data-Peeler. From an n-ary relation, it extracts all closed n-sets satisfying given piecewise (anti) monotonic constraints. This new class of constraints generalizes both monotonic and antimonotonic constraints. 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 to efficiently enforce the closeness property. The relevance of the extracted closed n-sets is assessed on real-life 3-and 4-ary relations. Beyond natural 3-or 4-ary relations, expanding a relation with an additional attribute can help in enforcing rather abstract constraints such as the robustness with respect to binarization. Furthermore, a collection of closed n-sets is shown to be an excellent starting point to compute a tiling of the dataset.} }

%0 = article %A = Cerf, Loïc and Besson, Jérémy and Robardet, Céline and Boulicaut, Jean-François %C = New York, NY, USA %D = 2009 %I = ACM %T = Closed patterns meet n-ary relations

Set pattern discovery from binary relations has been extensively 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 binary case. The generality of the task — no assumption being made on the relation arity or on the size of its attribute domains — makes it computationally challenging. We introduce an algorithm called Data-Peeler. From a n-ary relation, it extracts all closed n-sets satisfying given piecewise (anti)-monotonic constraints. This new class of constraints generalizes both monotonic and anti-monotonic constraints. 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.

@inproceedings{cerf2008datapeeler, author = {Cerf, Loïc and Besson, Jérémy and Robardet, Céline and Boulicaut, Jean-Francois}, title = {Data-Peeler: Constraint-based Closed Pattern Mining in n-ary Relations}, booktitle = {Proc. SIAM International Conference on Data Mining SDM'08}, year = {2008}, pages = {37--48}, url = {http://www.siam.org/proceedings/datamining/2008/dm08_04_Cerf.pdf}, keywords = {ol_web2.0, trias, mode, three, fca, triadic}, abstract = {Set pattern discovery from binary relations has been extensively 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 binary case. The generality of the task — no assumption being made on the relation arity or on the size of its attribute domains — makes it computationally challenging. We introduce an algorithm called Data-Peeler. From a n-ary relation, it extracts all closed n-sets satisfying given piecewise (anti)-monotonic constraints. This new class of constraints generalizes both monotonic and anti-monotonic constraints. 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.} }

%0 = inproceedings %A = Cerf, Loïc and Besson, Jérémy and Robardet, Céline and Boulicaut, Jean-Francois %B = Proc. SIAM International Conference on Data Mining SDM'08 %D = 2008 %T = Data-Peeler: Constraint-based Closed Pattern Mining in n-ary Relations %U = http://www.siam.org/proceedings/datamining/2008/dm08_04_Cerf.pdf