NegPSpan: efficient extraction of negative sequential patterns with embedding constraints Mining frequent sequential patterns consists in extracting recurrent behaviors, modeled as patterns, in a big sequence dataset. Such patterns inform about which events are frequently observed in sequences, i.e. what does really happen. Sometimes, knowing that some specific event does not happen is more informative than extracting a lot of observed events. Negative sequential patterns (NSP) formulate recurrent behaviors by patterns containing both observed events and absent events. Few approaches have been proposed to mine such NSPs. In addition, the syntax and semantics of NSPs differ in the different methods which makes it difficult to compare them. This article provides a unified framework for the formulation of the syntax and the semantics of NSPs. Then, we introduce a new algorithm, NegPSpan, that extracts NSPs using a PrefixSpan depthfirst scheme and enabling maxgap constraints that other approaches do not take into account. The formal framework allows for highlighting the differences between the proposed approach wrt to the methods from the literature, especially wrt the state of the art approach eNSP. Intensive experiments on synthetic and real datasets show that NegPSpan can extract meaningful NSPs and that it can process bigger datasets than eNSP thanks to significantly lower memory requirements and better computation times.

Matrix Profile XV: Exploiting Time Series Consensus Motifs to Find Structure in Time Series Sets In recent years the data mining community has largely coalesced around the idea that many problems in time series analytics essentially reduce to finding and then reasoning about repeated structure in time series. Existing tools can find conserved structure within a single time series (motifs) and between pairs of time series (joins). However, to date there are no tools to find repeated structure in sets of time series, an idea we call time series consensus motifs in recognition of their similarity to their discrete analogs in DNA strings. In this work we introduce a definition of time series consensus motifs and a scalable algorithm to discover them in large data collections. We further show that given this new primitive, we can solve multiple higherlevel problems in time series data mining. We demonstrate the utility of our ideas with case studies in diverse domains.