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Dynamic time warping ($\texttt{DTW}$) is one of the most used distancefunctions to compare time series, e.$\,$g. in nearest neighbor classifiers.Yet, fast state of the art algorithms only compare 1-dimensional time seriesefficiently. One of these state of the art algorithms uses a lower bound($\texttt{LB}_\texttt{Keogh}$) introduced by E. Keogh to prune $\texttt{DTW}$computations. We introduce $\texttt{LB}_\texttt{Box}$ as a canonical extensionto $\texttt{LB}_\texttt{Keogh}$ on multi-dimensional time series. We evaluateits performance conceptually and experimentally and show that an alternative to$\texttt{LB}_\texttt{Box}$ is necessary for multi-dimensional time series. Wealso propose a new algorithm for the dog-keeper distance ($\texttt{DK}$) whichis an alternative distance function to $\texttt{DTW}$ and show that itoutperforms $\texttt{DTW}$ with $\texttt{LB}_\texttt{Box}$ by more than oneorder of magnitude on multi-dimensional time series.

An Analytical Approach to Improving Time Warping on Multidimensional Time Series