# Mining Closed Strict Episodes

## TL;DR

This paper introduces a new class of strict episodes for sequential pattern mining, along with an efficient algorithm to discover closed episodes, enhancing the ability to find meaningful patterns in sequential data.

## Contribution

It defines strict episodes and a closure operator to enable efficient mining of closed episodes, extending existing pattern mining frameworks to sequential data.

## Key findings

- The proposed algorithm efficiently mines closed episodes in practice.
- Strict episodes facilitate defining subset relationships for episodes.
- Empirical results demonstrate the algorithm's effectiveness and scalability.

## Abstract

Discovering patterns in a sequence is an important aspect of data mining. One popular choice of such patterns are episodes, patterns in sequential data describing events that often occur in the vicinity of each other. Episodes also enforce in which order the events are allowed to occur. In this work we introduce a technique for discovering closed episodes. Adopting existing approaches for discovering traditional patterns, such as closed itemsets, to episodes is not straightforward. First of all, we cannot define a unique closure based on frequency because an episode may have several closed superepisodes. Moreover, to define a closedness concept for episodes we need a subset relationship between episodes, which is not trivial to define. We approach these problems by introducing strict episodes. We argue that this class is general enough, and at the same time we are able to define a natural subset relationship within it and use it efficiently. In order to mine closed episodes we define an auxiliary closure operator. We show that this closure satisfies the needed properties so that we can use the existing framework for mining closed patterns. Discovering the true closed episodes can be done as a post-processing step. We combine these observations into an efficient mining algorithm and demonstrate empirically its performance in practice.