  Complex systems, such as airplanes, cars, or financial markets, produce
multivariate time series data consisting of a large number of system
measurements over a period of time. Such data can be interpreted as a sequence
of states, where each state represents a prototype of system behavior. An
important problem in this domain is to identify repeated sequences of states,
known as motifs. Such motifs correspond to complex behaviors that capture
common sequences of state transitions. For example, in automotive data, a motif
of "making a turn" might manifest as a sequence of states: slowing down,
turning the wheel, and then speeding back up. However, discovering these motifs
is challenging, because the individual states and state assignments are
unknown, have different durations, and need to be jointly learned from the
noisy time series. Here we develop motif-aware state assignment (MASA), a
method to discover common motifs in noisy time series data and leverage those
motifs to more robustly assign states to measurements. We formulate the problem
of motif discovery as a large optimization problem, which we solve using an
expectation-maximization type approach. MASA performs well in the presence of
noise in the input data and is scalable to very large datasets. Experiments on
synthetic data show that MASA outperforms state-of-the-art baselines by up to
38.2%, and two case studies demonstrate how our approach discovers insightful
motifs in the presence of noise in real-world time series data.
