Mining Frequent Synchronous Patterns with a Graded Notion of Synchrony

Abstract

We present methods to find (significant) frequent synchronous patterns in event sequences, using a graded notion of synchrony that captures both the number of instances of a pattern as well as the precision of synchrony of its constituting events. Since transferring earlier work (using a binary notion of synchrony) poses certain problems, we opt for an efficient approximation scheme to compute the pattern support. Furthermore, we transfer methods for filtering for significant and removing induced patterns, which require adaptations. Finally, we demonstrate the effectiveness of our approach with experiments on a large number of data sets with injected synchronous patterns.

Mining Frequent Synchronous Patterns based on Item Cover Similarity

“…In the case of graded synchrony, however, we desire a synchrony operator that yields a degree of synchrony between 0 and 1. Such a synchrony operator is described in 9 , based on the notion of an influence map as it was introduced in 22 . An influence map describes the vicinity around an event in which synchrony with other events is expedient and can be defined formally as…”

“…With this notion we define that there is synchrony to some degree between events iff the influence maps of these events overlap, and that the area of the overlap measures the degree of synchrony, or formally, that the degree of synchrony is the integral over the minimum of the influence maps 9 . A synchrony operator σ w gives rise to the definition of a support operator s S ,w (I).…”

“…If the synchrony operator σ w is binary, this support is feasible, because there exists an efficient greedy algorithm that computes this support 3,20 . With a graded synchrony operator, however, this greedy algorithm is no longer guaranteed to find the optimal solution 9 , while the general problem of finding a maximum independent set is NP-complete 14 and even hard to approximate 12 , rendering general solution approaches inefficient.…”

“…A straightforward extension with a notion of graded synchrony requires to solve a maximum weight independent set problem, for which the greedy algorithm of the binary case no longer guarantees the optimal solution and which is NP-complete in the general case 14 . In order to avoid these complications, an efficient approximation scheme for the support was presented in 9 , based on an earlier conceptual approach using influence maps and their overlap 22 .…”

“…The remainder of this paper is structured as follows: Section 2 covers basic terminology and notation and reviews the graded notion of synchrony as it was introduced in 9 as well as influence map overlap support. Section 3 discusses Jaccard item set mining and transfers it to the continuous setting.…”