Constraint-Based Mining of Episode Rules and Optimal Window Sizes

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.