Discovering Periodic Patterns in Irregular Time Series Finding (partial) periodic patterns in time series data is a challenging problem of great importance in many applications. Due to computational reasons, most previous studies in this area have focused on the efficient discovery of periodic patterns in regular time series data. Unfortunately, these studies have limited applicability because realworld data naturally exists as an irregular time series. This paper proposes a more flexible model of periodic pattern that may be present in irregular time series. Two measures, period and periodsupport, were employed to determine the interestingness of a pattern in a series. The former measure captures the interarrival times of a pattern in a series, while the latter captures the number of periodic occurrences of a pattern in a series. A novel tree structure, called Periodic Pattern tree (PPtree), has been introduced to record the irregular occurrences of items within the series. A patterngrowth algorithm has also been presented to find all periodic patterns from PPtree. Experimental results demonstrate that the proposed model can find useful information, and the algorithm is efficient.

Matrix Profile XIX: Time Series Semantic Motifs: A New Primitive for Finding HigherLevel Structure in Time Series Time series motifs are approximately repeated patterns in realvalued temporal data. They are used for exploratory data mining methods including clustering, classification, segmentation, and rule discovery. Their current definition is limited to finding literal or nearexact matches and is unable to discover higher level semantic structure. Consider a time series generated by an accelerometer on a smartwatch. This data offers the possibility of finding motifs in human behavior. One such example is the motif generated by a handshake. Under current motif definitions, a singlepump handshake would not match a threepump handshake, even though they are culturally and semantically equivalent events. In this work we generalize the definition of motifs to one which allows us to capture higher level semantic structure. We refer to these as time series semantic motifs. Surprisingly this increased expressiveness does not come at a great cost. Our algorithm SemanticMotifFinder takes approximately the same time as current stateoftheart motif discovery algorithms. Furthermore, we demonstrate the utility of our ideas on diverse datasets.