Characterization of concept lattices for ordered contexts

The discovery of frequent sequential patterns in an ordered collection of data, such as sequential databases or time-series data, is an important issue in several contexts. In this paper, we employ formal concept analysis to develop the notion of closure for these sequential patterns and to characterize the concept lattice of the ordered contexts. The proposed concept lattice will serve as a model for the patterns extracted in the context of sequential databases by a recent algorithm (CloSpan, cite{Clospan}). Finally, we will show how we can also use our model to derive other kind of structured patterns, like the closed set of episodes in the context of time-series data cite{Toivonen}. So, the convenient transformation of the sequential patterns in the concepts of the lattice will give rise to the most representative set of parallel and serial closed episodes.