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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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