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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. The Mutual Infomation of this distribution will be the lynchpin of our similarity measure for trajectories.  \subsubsection{Entropy}  Shannon introduced the entropy to be a measure of the quantity of information of a random variable. Let $X: P \rightarrow E$ be a random variable with $E$ a discrete probability space.  The entropy of $X$ is defined as:  $ S(X) = \sum_{x in E}P_{X}(x)*log(P_{X}(x))$    The entropy has three interpretations:   \begin{itemize}  \item the amount of information of a random variable (or of an event)  \item the uncertainty about the outcome of a random variable (or of an event)  \item the dispersion of the probability law of a random variable (or of the probabilities with which the events take place)  \end{itemize}    Let $X: P \rightarrow E$ be a random variable with $E$ a discrete probability space.  The entropy of $X$ is defined as:  $ S(X) = \sum_{x in E}P_{X}(x)*log(P_{X}(x))$      \subsection{MI-based metric for trajectories}