Mining partially periodic event patterns with unknown periods

Periodic behavior is common in real-world applications. However, in many cases, periodicities are partial in that they are present only intermittently. Herein, we study such intermittent patterns, which we refer to as p-patterns. Our formulation of p-patterns takes into account imprecise time information (e.g., due to unsynchronized clocks in distributed environments), noisy data (e.g., due to extraneous events), and shifts in phase and/or periods. We structure mining for p-patterns as two sub-tasks: (1) finding the periods of p-patterns and (2) mining temporal associations. For (2), a level-wise algorithm is used. For (1), we develop a novel approach based on a chi-squared test, and study its performance in the presence of noise. Further, we develop two algorithms for mining p-patterns based on the order in which the aforementioned sub-tasks are performed: the period-first algorithm and the association-first algorithm. Our results show that the association-first algorithm has a higher tolerance to noise; the period-first algorithm is more computationally efficient and provides flexibility as to the specification of support levels. In addition, we apply the period-first algorithm to mining data collected from two production computer networks, a process that led to several actionable insights.