MASS: distance profile of a query over a time series

Given a long time series, the distance profile of a query time series computes distances between the query and every possible subsequence of a long time series. MASS (Mueen’s Algorithm for Similarity Search) is an algorithm to efficiently compute distance profile under z-normalized Euclidean distance (Mueen et al. in The fastest similarity search algorithm for time series subsequences under Euclidean distance. http://www.cs.unm.edu/~mueen/FastestSimilaritySearch.html, 2017). MASS is recognized as a useful tool in many data mining works. However, complete documentation of the increasingly efficient versions of the algorithm does not exist. In this paper, we formalize the notion of a distance profile, describe four versions of the MASS algorithm, show several extensions of distance profiles under various operating conditions, describe how MASS improves performances of existing data mining algorithms, and finally, show utility of MASS in domains including seismology, robotics and power grids.