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Another crucial point is that a reliable similarity measure for our problem should take into account the time parameter.  \subsection{Mutual Information: definition and properties}  Mutual Information is widely used for instance for registration of medical images as it is depicted in \cite{Pluim_2003}. The main idea is to introduced a feature space (or a joint probability) of the two trajectories we want to compare and to evaluate the quantity of "information" shared by the two trajectories based on this feature space. This quantity is calculate with Mutual Information.   In our case the feature space will be the distribution of the couple of positions of 2 players' trajectories during a window of time during a few minutes. Thus it corresponds to a 4 dimension distribution. And we will used Mutual Infomation of this distribution as the lynchpin of our similarity measure for trajectories.  \subsection{MI-based metric for trajectories}