TY - JOUR AU - Cerf, Loïc AU - Besson, Jérémy AU - Robardet, Céline AU - Boulicaut, Jean-François T1 - Closed patterns meet n-ary relations JO - ACM Transactions on Knowledge Discovery from Data PY - 2009/ VL - 3 IS - 1 SP - 1 EP - 36 UR - DO - 10.1145/1497577.1497580 KW - ol_web2.0 KW - triadic KW - trias KW - three KW - mode KW - fca L1 - SN - N1 - N1 - AB - 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. ER - TY - JOUR AU - Cerf, Loïc AU - Besson, Jérémy AU - Robardet, Céline AU - Boulicaut, Jean-François T1 - Closed patterns meet n-ary relations JO - ACM Transactions on Knowledge Discovery from Data PY - 2009/ VL - 3 IS - 1 SP - 1 EP - 36 UR - DO - 10.1145/1497577.1497580 KW - fca KW - mode KW - ol_tut2010 KW - three KW - triadic KW - trias L1 - SN - N1 - N1 - AB - 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. ER - TY - CONF AU - Cerf, Loïc AU - Besson, Jérémy AU - Robardet, Céline AU - Boulicaut, Jean-Francois A2 - T1 - Data-Peeler: Constraint-based Closed Pattern Mining in n-ary Relations T2 - Proc. SIAM International Conference on Data Mining SDM'08 PB - C1 - PY - 2008/04 CY - VL - IS - SP - 37 EP - 48 UR - http://www.siam.org/proceedings/datamining/2008/dm08_04_Cerf.pdf DO - KW - ol_web2.0 KW - triadic KW - trias KW - three KW - mode KW - fca L1 - SN - N1 - N1 - AB - 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. ER - TY - CONF AU - Cerf, Loïc AU - Besson, Jérémy AU - Robardet, Céline AU - Boulicaut, Jean-Francois A2 - T1 - Data-Peeler: Constraint-based Closed Pattern Mining in n-ary Relations T2 - Proc. SIAM International Conference on Data Mining SDM'08 PB - C1 - PY - 2008/04 CY - VL - IS - SP - 37 EP - 48 UR - http://www.siam.org/proceedings/datamining/2008/dm08_04_Cerf.pdf DO - KW - fca KW - mode KW - ol_tut2010 KW - three KW - triadic KW - trias L1 - SN - N1 - N1 - AB - 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. ER - TY - JOUR AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd T1 - Discovering Shared Conceptualizations in Folksonomies JO - Web Semantics: Science, Services and Agents on the World Wide Web PY - 2008/02 VL - 6 IS - 1 SP - 38 EP - 53 UR - http://www.sciencedirect.com/science/article/B758F-4R53WD4-1/2/ae56bd6e7132074272ca2035be13781b DO - 10.1016/j.websem.2007.11.004 KW - 2008 KW - analysis KW - concept KW - folksonomy KW - formal KW - l3s KW - ol_web2.0 KW - tagging KW - trias KW - wp5 KW - methods_concepts KW - emergentsemantics_evidence L1 - SN - N1 - N1 - AB - Social bookmarking tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualizations are not formalized, but rather implicit. We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualizations. Our approach extends the data mining task of discovering all closed itemsets to three-dimensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples. ER - TY - JOUR AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd T1 - Discovering Shared Conceptualizations in Folksonomies JO - Web Semantics: Science, Services and Agents on the World Wide Web PY - 2008/02 VL - 6 IS - 1 SP - 38 EP - 53 UR - http://www.kde.cs.uni-kassel.de/pub/pdf/jaeschke2008discovering.pdf DO - 10.1016/j.websem.2007.11.004 KW - 2008 KW - analysis KW - concept KW - fca KW - folksonomy KW - formal KW - l3s KW - myown KW - ol_tut2010 KW - tagging KW - top KW - trias L1 - SN - N1 - N1 - AB - Social bookmarking tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualizations are not formalized, but rather implicit. We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualizations. Our approach extends the data mining task of discovering all closed itemsets to three-dimensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples. ER - TY - JOUR AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd T1 - Discovering shared conceptualizations in folksonomies JO - Web Semant. PY - 2008/ VL - 6 IS - 1 SP - 38 EP - 53 UR - http://portal.acm.org/citation.cfm?id=1346701 DO - http://dx.doi.org/10.1016/j.websem.2007.11.004 KW - analysis KW - concept KW - fca KW - formal KW - myown KW - ontologyhandbook KW - trias L1 - SN - N1 - Publications of Gerd Stumme N1 - AB - Social bookmarking tools are rapidly emerging on the Web. In such systems users are setting up lightweight conceptual structures called folksonomies. Unlike ontologies, shared conceptualizations are not formalized, but rather implicit. We present a new data mining task, the mining of all frequent tri-concepts, together with an efficient algorithm, for discovering these implicit shared conceptualizations. Our approach extends the data mining task of discovering all closed itemsets to three-dimensional data structures to allow for mining folksonomies. We provide a formal definition of the problem, and present an efficient algorithm for its solution. Finally, we show the applicability of our approach on three large real-world examples. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Stumme, Gerd A2 - Priss, U. A2 - Polovina, S. A2 - Hill, R. T1 - Analysis of the Publication Sharing Behaviour in BibSonomy T2 - Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007) PB - Springer-Verlag C1 - Berlin, Heidelberg PY - 2007/07 CY - VL - 4604 IS - SP - 283 EP - 295 UR - DO - KW - 2007 KW - BibSonomy KW - bibsonomy KW - bookmarking KW - fca KW - folksonomy KW - iccs KW - itegpub KW - l3s KW - myown KW - publication KW - sharing KW - social KW - trias L1 - SN - 3-540-73680-8 N1 - N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Stumme, Gerd A2 - Priss, U. A2 - Polovina, S. A2 - Hill, R. T1 - Analysis of the Publication Sharing Behaviour in BibSonomy T2 - Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007) PB - Springer-Verlag C1 - Berlin, Heidelberg PY - 2007/07 CY - VL - 4604 IS - SP - 283 EP - 295 UR - DO - KW - 2007 KW - analysis KW - bibsonomy KW - bookmarking KW - fca KW - folksonomy KW - iccs KW - l3s KW - ol_web2.0 KW - social KW - trias KW - widely_related KW - emergentsemantics_evidence L1 - SN - 3-540-73680-8 N1 - N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Stumme, Gerd A2 - Priss, U. A2 - Polovina, S. A2 - Hill, R. T1 - Analysis of the Publication Sharing Behaviour in BibSonomy T2 - Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007) PB - Springer-Verlag C1 - Berlin, Heidelberg PY - 2007/07 CY - VL - 4604 IS - SP - 283 EP - 295 UR - DO - KW - 2007 KW - analysis KW - bibsonomy KW - bookmarking KW - dfg KW - fca KW - folksonomy KW - iccs KW - social KW - trias L1 - SN - N1 - Antrag dfg Literatur N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Stumme, Gerd A2 - T1 - Analysis of the Publication Sharing Behaviour in BibSonomy T2 - Proceedings of the 15th International Conference on Conceptual Structures PB - C1 - Sheffield, England PY - 2007/07 CY - VL - 4604 IS - SP - EP - UR - DO - KW - 2007 KW - bibsonomy KW - fca KW - iccs KW - myown KW - trias L1 - SN - N1 - N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Stumme, Gerd A2 - Priss, U. A2 - Polovina, S. A2 - Hill, R. T1 - Analysis of the Publication Sharing Behaviour in BibSonomy T2 - Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007) PB - Springer-Verlag C1 - Berlin, Heidelberg PY - 2007/07 CY - VL - 4604 IS - SP - 283 EP - 295 UR - DO - KW - 2007 KW - analysis KW - bibsonomy KW - bookmarking KW - fca KW - folksonomy KW - iccs KW - l3s KW - myown KW - ol_tut2010 KW - social KW - trias L1 - SN - 3-540-73680-8 N1 - N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Stumme, Gerd A2 - Priss, U. A2 - Polovina, S. A2 - Hill, R. T1 - Analysis of the Publication Sharing Behaviour in BibSonomy T2 - Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007) PB - Springer-Verlag C1 - Berlin, Heidelberg PY - 2007/07 CY - VL - 4604 IS - SP - 283 EP - 295 UR - DO - KW - 2007 KW - BibSonomy KW - bibsonomy KW - bookmarking KW - fca KW - folksonomy KW - iccs KW - itegpub KW - l3s KW - myown KW - publication KW - sharing KW - social KW - trias L1 - SN - 3-540-73680-8 N1 - N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd A2 - T1 - TRIAS - An Algorithm for Mining Iceberg Tri-Lattices T2 - Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06) PB - IEEE Computer Society C1 - Hong Kong PY - 2006/12 CY - VL - IS - SP - 907 EP - 911 UR - http://www.kde.cs.uni-kassel.de/stumme/papers/2006/jaeschke2006trias.pdf DO - http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.162 KW - 2006 KW - FCA KW - OntologyHandbook KW - algorithm KW - analysis KW - concept KW - fca KW - folksonomies KW - folksonomy KW - formal KW - iceberg KW - itegpub KW - lattices KW - myown KW - nepomuk KW - tagging KW - tri KW - triadic KW - trias L1 - SN - 0-7695-2701-9 N1 - N1 - AB - ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd A2 - T1 - TRIAS - An Algorithm for Mining Iceberg Tri-Lattices T2 - Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06) PB - IEEE Computer Society C1 - Hong Kong PY - 2006/12 CY - VL - IS - SP - 907 EP - 911 UR - http://www.kde.cs.uni-kassel.de/jaeschke/paper/jaeschke06trias.pdf DO - http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.162 KW - 12 KW - 2006 KW - algorithm KW - fca KW - iccs_example KW - l3s KW - ol_web2.0 KW - trias KW - trias_example KW - methods_concepts L1 - SN - 0-7695-2701-9 N1 - N1 - AB - 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd A2 - T1 - TRIAS - An Algorithm for Mining Iceberg Tri-Lattices T2 - ICDM '06: Proceedings of the Sixth International Conference on Data Mining PB - IEEE Computer Society C1 - Washington, DC, USA PY - 2006/ CY - VL - IS - SP - 907 EP - 911 UR - http://www.kde.cs.uni-kassel.de/pub/pdf/jaeschke2006trias.pdf DO - 10.1109/ICDM.2006.162 KW - 2006 KW - fca KW - iceberg KW - myown KW - ol_tut2010 KW - triadic KW - trias L1 - SN - 0-7695-2701-9 N1 - N1 - AB - 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 folk-sonomies. 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. ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd A2 - T1 - TRIAS - An Algorithm for Mining Iceberg Tri-Lattices T2 - Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06) PB - IEEE Computer Society C1 - Hong Kong PY - 2006/12 CY - VL - IS - SP - 907 EP - 911 UR - http://www.kde.cs.uni-kassel.de/stumme/papers/2006/jaeschke2006trias.pdf DO - http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.162 KW - 2006 KW - FCA KW - OntologyHandbook KW - algorithm KW - analysis KW - concept KW - fca KW - folksonomies KW - folksonomy KW - formal KW - iceberg KW - itegpub KW - lattices KW - myown KW - nepomuk KW - tagging KW - tri KW - triadic KW - trias L1 - SN - 0-7695-2701-9 N1 - N1 - AB - ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd A2 - T1 - TRIAS - An Algorithm for Mining Iceberg Tri-Lattices T2 - Proc. 6th ICDM conference PB - C1 - Hong Kong PY - 2006/12 CY - VL - IS - SP - EP - UR - DO - http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.162 KW - 2006 KW - fca KW - kdubiq KW - mining KW - myown KW - sosbuch KW - summerschool KW - trias L1 - SN - 0-7695-2701-9 N1 - N1 - AB - ER - TY - CONF AU - Jäschke, Robert AU - Hotho, Andreas AU - Schmitz, Christoph AU - Ganter, Bernhard AU - Stumme, Gerd A2 - T1 - TRIAS - An Algorithm for Mining Iceberg Tri-Lattices T2 - Proceedings of the 6th IEEE International Conference on Data Mining (ICDM 06) PB - IEEE Computer Society C1 - Hong Kong PY - 2006/12 CY - VL - IS - SP - 907 EP - 911 UR - http://www.kde.cs.uni-kassel.de/pub/pdf/jaeschke2006trias.pdf DO - http://doi.ieeecomputersociety.org/10.1109/ICDM.2006.162 KW - 12 KW - 2006 KW - algorithm KW - fca KW - iccs_example KW - l3s KW - myown KW - ol_tut2010 KW - trias KW - trias_example L1 - SN - 0-7695-2701-9 N1 - N1 - AB - ER - TY - JOUR AU - Lehmann, Fritz AU - Wille, Rudolf T1 - A triadic approach to formal concept analysis JO - Conceptual Structures: Applications, Implementation and Theory PY - 1995/ VL - IS - SP - 32 EP - 43 UR - http://dx.doi.org/10.1007/3-540-60161-9_27 DO - KW - analysis KW - concept KW - fca KW - formal KW - triadic KW - trias L1 - SN - N1 - SpringerLink - Book Chapter N1 - AB - Formal Concept Analysis, developed during the last fifteen years, has been based on the dyadic understanding of a concept constituted by its extension and its intension. The pragmatic philosophy of Charles S. Peirce with his three universal categories, and experiences in data analysis, have suggested a triadic approach to Formal Concept Analysis. This approach starts with the primitive notion of a triadic context defined as a quadruple (G, M, B, Y) where G, M, and B are sets and Y is a ternary relation between G, M, and B, i.e. Y G×M×B; the elements of G, M, and B are called objects, attributes, and conditions, respectively, and (g, m,b) Y is read: the object g has the attribute m under (or according to) the condition b. A triadic concept of a triadic context (G, M, B, Y) is defined as a triple (A ER -