Discovering the key structure of a database is one of the main goals of data mining. In pattern set mining we do so by discovering a small set of patterns that together describe the data well. The richer the class of patterns we consider, and the more powerful our description language, the better we will be able to summarise the data. In this paper we propose , a novel greedy MDL-based method for summarising sequential data using rich patterns that are allowed to interleave. Experiments show is orders of magnitude faster than the state of the art, results in better models, as well as discovers meaningful semantics in the form patterns that identify multiple choices of values.
Discovering sequential patterns is an active research topic. Traditionally there was a focus on mining frequent sequential patterns, with different definitions of how to count occurrences @cite_22 @cite_8 @cite_11 . Mining general patterns, patterns where the order of events are specified by a DAG is surprisingly hard. Even testing whether a sequence contains a pattern is NP-complete @cite_19 . Consequently, research has focused on mining subclasses of episodes, such as, episodes with unique labels @cite_16 @cite_12 , strict episodes @cite_21 , and injective episodes @cite_16 .
@cite_22 @cite_8 @cite_21 @cite_19 @cite_16 @cite_12 @cite_11
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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. 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. Sequential pattern mining is an important problem in data mining. State of the art techniques for mining sequential patterns, such as frequent subsequences, are often based on the pattern-growth approach, which recursively projects conditional databases. Explicitly creating database projections is thought to be a major computational bottleneck, but we will show in this paper that it can be beneficial when the appropriate data structure is used. Our technique uses a canonical directed acyclic graph as the sequence database representation, which can be represented as a binary decision diagram (BDD). In this paper, we introduce a new type of BDD, namely a sequence BDD (SeqBDD), and show how it can be used for efficiently mining frequent subsequences. A novel feature of the SeqBDD is its ability to share results between similar intermediate computations and avoid redundant computation. We perform an experimental study to compare the SeqBDD technique with existing pattern growth techniques, that are based on other data structures such as prefix trees. Our results show that a SeqBDD can be half as large as a prefix tree, especially when many similar sequences exist. In terms of mining time, it can be substantially more efficient when the support is low, the number of patterns is large, or the input sequences are long and highly similar. Sequential pattern mining under various constraints is a challenging data mining task. The paper provides a generic framework based on constraint programming to discover sequence patterns defined by constraints on local patterns (e.g., Gap, regular expressions) or constraints on patterns involving combination of local patterns such as relevant subgroups and top-k patterns. This framework enables the user to mine in a declarative way both kinds of patterns. The solving step is done by exploiting the machinery of Constraint Programming. For complex patterns involving combination of local patterns, we improve the mining step by using dynamic CSP. Finally, we present two case studies in biomedical information extraction and stylistic analysis in linguistics.