Multi-way Time Series Join on Multi-length Patterns

This paper introduces a new pattern mining task that considers aligning or joining a set of time series based on an arbitrary number of subsequences (i.e., patterns) with arbitrary lengths. Joining multiple time series along common patterns can be pivotal in clustering and summarizing large time series datasets. An exact algorithm to join hundreds of time series based on multi-length patterns is impractical due to the high computational costs. This paper proposes a fast algorithm named MultiPAL to join multiple time series at interactive speed to summarize large time series datasets. The algorithm exploits Matrix Profiles of the individual time series to enable a greedy search over possible joins. The algorithm is orders of magnitude faster than the exact solution and can utilize hundreds of Matrix Profiles. We evaluate our algorithm for sequential mining on data from various real-world domains, including power management and bioacoustics monitoring.