2009/03/01 by Loïc Cerf, Jérémy Besson, Céline Robardet +1 · 1 citation
Computer Science · Mathematics · #Data Mining Algorithms and Applications #Rough Sets and Fuzzy Logic #Data Management and Algorithms #Arity #Binary relation #Computer science #Relation (database) #Closeness #Closed set #Monotonic function #Theoretical computer science #Mathematics #Piecewise #Algorithm #Data mining #Discrete mathematics
paper · doi:10.1145/1497577.1497580
openalex publication_date 2009/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
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.