An Analytical Approach to Improving Time Warping on Multidimensional Time Series
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Dynamic time warping (DTW) is one of the most used distance functions to compare time series, e. g. in nearest neighbor classifiers. Yet, fast state of the art algorithms only compare 1-dimensional time series efficiently. One of these state of the art algorithms uses a lower bound (LB_Keogh) introduced by E. Keogh to prune DTW computations. We introduce LB_Box as a canonical extension to LB_Keogh on multi-dimensional time series. We evaluate its performance conceptually and experimentally and show that an alternative to LB_Box is necessary for multi-dimensional time series. We also propose a new algorithm for the dog-keeper distance (DK) which is an alternative distance function to DTW and show that it outperforms DTW with LB_Box by more than one order of magnitude on multi-dimensional time series.
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