In this article we present a novel approach to rare sequence mining using pattern structures. Particularly, we are interested in mining closed sequences, a type of maximal sub-element which allows providing a succinct description of the patterns in a sequence database. We present and describe a sequence pattern structure model in which rare closed subsequences can be easily encoded. We also propose a discussion and characterization of the search space of closed sequences and, through the notion of sequence alignments, provide an intuitive implementation of a similarity operator for the sequence pattern structure based on directed acyclic graphs. Finally, we provide an experimental evaluation of our approach in comparison with state-of-the-art closed sequence mining algorithms showing that our approach can largely outperform them when dealing with large regions of the search space.
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