Efficient Mining of Closed Flock Patterns from Large Trajectory Data

In this paper, we study the closed pattern mining problem for a class of spatio-temporal patterns, called closed (k, r)-flock patterns in trajectory databases. A (k, r)-flock pattern (Gudmundsson and van Kreveld, 2006) represents a set of moving objects traveling close each other within radius r during time period of length k. Based on the notion of the envelope for a flock pattern, we introduce the class of closed flock patterns, which is a maximally dense pattern obtained by adding new objects as long as the shape does not change. Then, as a main result, we present a polynomial delay and space mining algorithm that finds all closed (k, r)-flock patterns with specified radius and more than one entities appearing in an input trajectory database. This algorithm is designed based on depth-first search over the tree-shaped search space for all closed flock patterns appearing in an input database. We also show theoretical analysis of some properties including compactness of closed flock patterns.