Mining Constrained Cross-Graph Cliques in Dynamic Networks

Three algorithms — CubeMiner, Trias, and Data-Peeler — have been recently proposed to mine closed patterns in ternary relations, i.e., a generalization of the so-called formal concept extraction from binary relations. In this paper, we consider the specific context where a ternary relation denotes the value of a graph adjacency matrix (i. e., a Vertices × Vertices matrix) at different timestamps. We discuss the constraint-based extraction of patterns in such dynamic graphs. We formalize the concept of δ-contiguous closed 3-clique and we discuss the availability of a complete algorithm for mining them. It is based on a specialization of the enumeration strategy implemented in Data-Peeler. Indeed, the relevant cliques are specified by means of a conjunction of constraints which can be efficiently exploited. The added-value of our strategy for computing constrained clique patterns is assessed on a real dataset about a public bicycle renting system. The raw data encode the relationships between the renting stations during one year. The extracted δ-contiguous closed 3-cliques are shown to be consistent with our knowledge on the considered city. Löıc Cerf Université de Lyon, CNRS, INRIA INSA-Lyon, LIRIS Combining, UMR5205, F-69621, France e-mail: [email protected] Bao Tran Nhan Nguyen Université de Lyon, CNRS, INRIA INSA-Lyon, LIRIS Combining, UMR5205, F-69621, France e-mail: [email protected] Jean-François Boulicaut Université de Lyon, CNRS, INRIA INSA-Lyon, LIRIS Combining, UMR5205, F-69621, France e-mail: [email protected]