Constraint-Based Mining of Episode Rules and Optimal Window Sizes

Abstract

Episode rules are patterns that can be extracted from a large event sequence, to suggest to experts possible dependencies among occurrences of event types. The corresponding mining approaches have been designed to find rules under a temporal constraint that specifies the maximum elapsed time between the first and the last event of the occurrences of the patterns (i.e., a window size constraint). In some applications the appropriate window size is not known, and furthermore, this size is not the same for different rules. To cope with this class of applications, it has been recently proposed in [2] to specifying the maximal elapsed time between two events (i.e., a maximum gap constraint) instead of a window size constraint. Unfortunately, we show that the algorithm proposed to handle the maximum gap constraint is not complete. In this paper we present a sound and complete algorithm to mine episode rules under the maximum gap constraint, and propose to find, for each rule, the window size corresponding to a local maximum of confidence. We show that the extraction can be efficiently performed in practice on real and synthetic datasets. Finally the experiments show that the notion of local maximum of confidence is significant in practice, since no local maximum are found in random datasets, while they can be found in real ones. This research is partially funded by the European Commission IST Programme -Accompanying Measures, AEGIS project (IST-2000-26450).

MARBLES: Mining Association Rules Buried in Long Event Sequences

“…Méger and Rigotti [15] propose a method for mining association rules of the form X ⇒ Y , such that X and Y are both serial episodes, and X is a prefix of Y . Cule et al [8] introduce an alternative interestingness measure for episodes, combining frequency with the cohesion of an episode.…”

Extracting Trees of Quantitative Serial Episodes

“…One remaining problem to be solved is to build the occurrence list of the episode under consideration (as the list L e for α → e). Fortunately, several approaches to extract episodes, or closely related patterns like sequential patterns, are based on the use of such occurrence lists (e.g., [8,11,14]), providing the information needed to update the duration lists D i . The basic idea is that if we store in a list L the locations (positions in the data sequence) of the occurrences of a pattern α, then for an event type e, we can use 3 L to build the list L e of occurrences of α → e. Notice that the expansion is made using occurrences of e that are not necessarily contiguous to the last elements of the occurrences of α.…”

“…It should be noticed that these choices made for the part that extracts the episodes (i.e., using occurrence lists together with a depth-first strategy) correspond to a typical approach used to mine serial episodes under the minimal occurrence semantics, similar for instance to the one used in [11].…”

“…The need of quantitative temporal information in patterns over event sequences has been pointed in recent works in the data mining literature [13,3,12,4,6,11].…”

“…Episodes have natural applications into several domains, including for instance the analysis of business time series [2], medical data [10], geophysical data [11] and also alarm log analysis for network monitoring (especially in telecommunications) [5]. However, in many applications episodes clearly show some limitations, due to the fact that the information provided by the is-followedby relation is not always enough to properly characterize the phenomena at hand.…”