  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 cannot 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.
