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The computation of the distance of two time series is time-consuming for anyelastic distance function that accounts for misalignments. Among thosefunctions, DTW is the most prominent. However, a recent extensive evaluationhas shown that the move-split merge (MSM) metric is superior to DTW regardingthe analytical accuracy of the 1-NN classifier. Unfortunately, the running timeof the standard dynamic programming algorithm for MSM distance computation is$\Omega(n^2)$, where $n$ is the length of the longest time series. In thispaper, we provide approaches to reducing the cost of MSM distance computationsby using lower and upper bounds for early pruning paths in the underlyingdynamic programming table. For the case of one time series being a constant, wepresent a linear-time algorithm. In addition, we propose new linear-timeheuristics and adapt heuristics known from DTW to computing the MSM distance.One heuristic employs the metric property of MSM and the previously introducedlinear-time algorithm. Our experimental studies demonstrate substantialspeed-ups in our approaches compared to previous MSM algorithms. In particular,the running time for MSM is faster than a state-of-the-art DTW distancecomputation for a majority of the popular UCR data sets.

Exact and Heuristic Approaches to Speeding Up the MSM Time Series Distance Computation