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, triadic, trias, three, mode, fca}, 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, triadic, trias, three, mode, fca}, 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

@article{cattuto2007networkb, author = {Cattuto, Ciro and Schmitz, Christoph and Baldassarri, Andrea and Servedio, Vito D. P. and Loreto, Vittorio and Hotho, Andreas and Grahl, Miranda and Stumme, Gerd}, title = {Network Properties of Folksonomies}, editor = {Hoche, Susanne and Nürnberger, Andreas and Flach, Jürgen}, journal = {AI Communications Journal, Special Issue on ``Network Analysis in Natural Sciences and Engineering''}, publisher = {IOS Press}, year = {2007}, volume = {20}, number = {4}, pages = {245-262}, url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2007/cattuto2007network.pdf}, issn = {0921-7126}, keywords = {2007, semantics, emergent, folksonomy, tagorapub, folksonomies, l3s, network, itegpub, fca} }

%0 = article %A = Cattuto, Ciro and Schmitz, Christoph and Baldassarri, Andrea and Servedio, Vito D. P. and Loreto, Vittorio and Hotho, Andreas and Grahl, Miranda and Stumme, Gerd %D = 2007 %I = IOS Press %T = Network Properties of Folksonomies %U = http://www.kde.cs.uni-kassel.de/stumme/papers/2007/cattuto2007network.pdf

BibSonomy is a web-based social resource sharing system which allows users to organise and share bookmarks and publications in a collaborative manner. In this paper we present the system, followed by a description of the insights in the structure of its bibliographic data that we gained by applying techniques we developed in the area of Formal Concept Analysis.

@inproceedings{jaeschke2007analysis, author = {Jäschke, Robert and Hotho, Andreas and Schmitz, Christoph and Stumme, Gerd}, title = {Analysis of the Publication Sharing Behaviour in BibSonomy}, editor = {Priss, U. and Polovina, S. and Hill, R.}, booktitle = {Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007)}, series = {Lecture Notes in Artificial Intelligence}, publisher = {Springer-Verlag}, address = {Berlin, Heidelberg}, year = {2007}, volume = {4604}, pages = {283--295}, isbn = {3-540-73680-8}, keywords = {2007, analysis, bibsonomy, bookmarking, fca, folksonomy, iccs, l3s, ol_web2.0, social, trias, widely_related, emergentsemantics_evidence}, abstract = {BibSonomy is a web-based social resource sharing system which allows users to organise and share bookmarks and publications in a collaborative manner. In this paper we present the system, followed by a description of the insights in the structure of its bibliographic data that we gained by applying techniques we developed in the area of Formal Concept Analysis.} }

%0 = inproceedings %A = Jäschke, Robert and Hotho, Andreas and Schmitz, Christoph and Stumme, Gerd %B = Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007) %C = Berlin, Heidelberg %D = 2007 %I = Springer-Verlag %T = Analysis of the Publication Sharing Behaviour in BibSonomy

Social bookmark tools are rapidly emerging on the Web. In suchsystems users are setting up lightweight conceptual structurescalled folksonomies. The reason for their immediate success is thefact that no specific skills are needed for participating. In thispaper we specify a formal model for folksonomies and briefly describe our own system BibSonomy, which allows for sharing both bookmarksand publication references in a kind of personal library.

@inproceedings{hotho2006bibsonomy, author = {Hotho, Andreas and Jäschke, Robert and Schmitz, Christoph and Stumme, Gerd}, title = {BibSonomy: A Social Bookmark and Publication Sharing System}, editor = {de Moor, Aldo and Polovina, Simon and Delugach, Harry}, booktitle = {Proceedings of the First Conceptual Structures Tool Interoperability Workshop at the 14th International Conference on Conceptual Structures}, publisher = {Aalborg Universitetsforlag}, address = {Aalborg}, year = {2006}, pages = {87-102}, url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2006/hotho2006bibsonomy.pdf}, isbn = {87-7307-769-0}, keywords = {2006, bookmarking, social, nepomuk, bibsonomy, OntologyHandbook, FCA, folksonomy, tagorapub, iccs, l3s}, abstract = {Social bookmark tools are rapidly emerging on the Web. In suchsystems users are setting up lightweight conceptual structurescalled folksonomies. The reason for their immediate success is thefact that no specific skills are needed for participating. In thispaper we specify a formal model for folksonomies and briefly describe our own system BibSonomy, which allows for sharing both bookmarksand publication references in a kind of personal library.} }

%0 = inproceedings %A = Hotho, Andreas and Jäschke, Robert and Schmitz, Christoph and Stumme, Gerd %B = Proceedings of the First Conceptual Structures Tool Interoperability Workshop at the 14th International Conference on Conceptual Structures %C = Aalborg %D = 2006 %I = Aalborg Universitetsforlag %T = BibSonomy: A Social Bookmark and Publication Sharing System %U = http://www.kde.cs.uni-kassel.de/stumme/papers/2006/hotho2006bibsonomy.pdf

In this paper, we present the foundations for mining frequent tri-concepts, which extend the notion of closed itemsets to three-dimensional data to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution as well as experimental results on a large real-world example.

@inproceedings{jaeschke2006trias, author = {Jäschke, Robert and Hotho, Andreas and Schmitz, Christoph and Ganter, Bernhard and Stumme, Gerd}, title = {TRIAS - An Algorithm for Mining Iceberg Tri-Lattices}, booktitle = {Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06)}, publisher = {IEEE Computer Society}, address = {Hong Kong}, year = {2006}, pages = {907-911}, url = {http://www.kde.cs.uni-kassel.de/jaeschke/paper/jaeschke06trias.pdf}, doi = {http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.162}, isbn = {0-7695-2701-9}, keywords = {12, 2006, algorithm, fca, iccs_example, l3s, ol_web2.0, trias, trias_example, methods_concepts}, abstract = {In this paper, we present the foundations for mining frequent tri-concepts, which extend the notion of closed itemsets to three-dimensional data to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution as well as experimental results on a large real-world example.} }

%0 = inproceedings %A = Jäschke, Robert and Hotho, Andreas and Schmitz, Christoph and Ganter, Bernhard and Stumme, Gerd %B = Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06) %C = Hong Kong %D = 2006 %I = IEEE Computer Society %T = TRIAS - An Algorithm for Mining Iceberg Tri-Lattices %U = http://www.kde.cs.uni-kassel.de/jaeschke/paper/jaeschke06trias.pdf

@article{cimiano_hotho_staab_2005, author = {Cimiano, P. and Hotho, A. and Staab, S.}, title = {Learning Concept Hierarchies from Text Corpora using Formal Concept Analysis}, journal = {Journal of Artificial Intelligence Research}, year = {2005}, volume = {24}, number = {1}, pages = {305-339}, url = {http://ontology.csse.uwa.edu.au/reference/browse_paper.php?pid=233281549}, keywords = {fca, ol_web2.0, ontology_learning, taxonomy_learning} }

%0 = article %A = Cimiano, P. and Hotho, A. and Staab, S. %D = 2005 %T = Learning Concept Hierarchies from Text Corpora using Formal Concept Analysis %U = http://ontology.csse.uwa.edu.au/reference/browse_paper.php?pid=233281549