Subjectively interesting motifs in time series

This paper introduces an approach to find motifs in time series that are emph{subjectively interesting}. That is, the aim is to find motifs that are surprising given an informative background distribution, which may for example correspond to the prior knowledge of a user of the tool. We quantify this surprisal using information theory, and more particularly the FORSIED framework. The resulting interestingness function according to which motifs are ranked is then subjective in the statistical sense, enabling us to find subsequence patterns (i.e., motifs and outliers) that are more truly interesting. Although finding the best motif appears intractable, we develop relaxations and a branch-and-bound approach that is implemented in a constraint programming solver. As shown in experiments on synthetic data and two real-world data sets this enables us to mine interesting patterns in small or mid-sized time series.