Time Series Join on Subsequence Correlation

We consider the problem of joining two long time series based on their most correlated segments. Two time series can be joined at any locations and for arbitrary length. Such join locations and length provide useful knowledge about the synchrony of the two time series and have applications in many domains including environmental monitoring, patient monitoring and power monitoring. However, join on correlation is a computationally expensive task, specially when the time series are large. The naive algorithm requires O(n(4)) computation where n is the length of the time series. We propose an algorithm, named Jocor, that uses two algorithmic techniques to tackle the complexity. First, the algorithm reuses the computation by caching sufficient statistics and second, the algorithm prunes unnecessary correlation computation by admissible heuristics. The algorithm runs orders of magnitude faster than the naive algorithm and enables us to join long time series as well as many small time series. We propose a variant of Jocor for fast approximation and an extension to a GPU-based parallel method to bring down the running-time to interactive level for analytics applications. We show three independent uses of time series join on correlation which are made possible by our algorithm.