Finding Local Groupings of Time Series

Collections of time series can be grouped over time both globally, over their whole time span, as well as locally, over several common time ranges, depending on the similarity patterns they share. In addition, local groupings can be persistent over time, defining associations of local groupings. In this paper, we introduce Z-Grouping, a novel framework for finding local groupings and their associations. Our solution converts time series to a set of event label channels by applying a temporal abstraction function and finds local groupings of maximized time span and time series instance members. A grouping-instance matrix structure is also exploited to detect associations of contiguous local groupings sharing common member instances. Finally, the validity of each local grouping is assessed against predefined global groupings. We demonstrate the ability of Z-Grouping to find local groupings without size constraints on time ranges on a synthetic dataset, three real-world datasets, and 128 UCR datasets, against four competitors.