document: Mining closed episodes with simultaneous events Sequential pattern discovery is a well-studied field in data mining . Episodes are sequential patterns describing events that often occur in the vicinity of each other . Episodes can impose restrictions to the order of the events , which makes them a versatile technique for describing complex patterns in the sequence . Most of the research on episodes deals with special cases such as serial , parallel , and injective episodes , while discovering general episodes is understudied . In this paper we extend the definition of an episode in order to be able to represent cases where events often occur simultaneously . We present an efficient and novel miner for discovering frequent and closed general episodes . Such a task presents unique challenges . Firstly , we can not define closure based on frequency . We solve this by computing a more conservative closure that we use to reduce the search space and discover the closed episodes as a postprocessing step . Secondly , episodes are traditionally presented as directed acyclic graphs . We argue that this representation has drawbacks leading to redundancy in the output . We solve these drawbacks by defining a subset relationship in such a way that allows us to remove the redundant episodes . We demonstrate the efficiency of our algorithm and the need for using closed episodes empirically on synthetic and real-world datasets .
doc_bio_tags: O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O