A unified view of the apriori-based algorithms for frequent episode discovery

Frequent episode discovery framework is a popular framework in temporal data mining with many applications. Over the years, many different notions of frequencies of episodes have been proposed along with different algorithms for episode discovery. In this paper, we present a unified view of all the apriori-based discovery methods for serial episodes under these different notions of frequencies. Specifically, we present a unified view of the various frequency counting algorithms. We propose a generic counting algorithm such that all current algorithms are special cases of it. This unified view allows one to gain insights into different frequencies, and we present quantitative relationships among different frequencies. Our unified view also helps in obtaining correctness proofs for various counting algorithms as we show here. It also aids in understanding and obtaining the anti-monotonicity properties satisfied by the various frequencies, the properties exploited by the candidate generation step of any apriori-based method. We also point out how our unified view of counting helps to consider generalization of the algorithm to count episodes with general partial orders.