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Complex systems, such as airplanes, cars, or financial markets, producemultivariate time series data consisting of a large number of systemmeasurements over a period of time. Such data can be interpreted as a sequenceof states, where each state represents a prototype of system behavior. Animportant problem in this domain is to identify repeated sequences of states,known as motifs. Such motifs correspond to complex behaviors that capturecommon sequences of state transitions. For example, in automotive data, a motifof "making a turn" might manifest as a sequence of states: slowing down,turning the wheel, and then speeding back up. However, discovering these motifsis challenging, because the individual states and state assignments areunknown, have different durations, and need to be jointly learned from thenoisy time series. Here we develop motif-aware state assignment (MASA), amethod to discover common motifs in noisy time series data and leverage thosemotifs to more robustly assign states to measurements. We formulate the problemof motif discovery as a large optimization problem, which we solve using anexpectation-maximization type approach. MASA performs well in the presence ofnoise in the input data and is scalable to very large datasets. Experiments onsynthetic data show that MASA outperforms state-of-the-art baselines by up to38.2%, and two case studies demonstrate how our approach discovers insightfulmotifs in the presence of noise in real-world time series data.

MASA: Motif-Aware State Assignment in Noisy Time Series Data