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\section{Metrics for trajectories}  Most of the time the metrics used for clustering are based on euclidian metric. However in the field of trajectories' clustering the most competitive and widely used similarity measures are \textbf{LCSS} (Longuest Common Subsequence) and \textbf{DTW} (Dynamic Time Warping). Indeed they are more adapted to the discrete trajectories in the form of array which can be of different sizes with different time discretization or with different speed that are available. The computationally costs of LCSS and DTW are much higher though. However what we are looking for is a similarity measure which is high when two trajectories depend on each other whereas LCSS and DTW-based similarities are high when two trajectories are close to each other in the same time. For instance if a player always go goes  to the middle of the field when another player of his team go is going  to the adverse penalty spot they should be similar since there is a strong dependency between them. Yet in the previous example, the 2 players' trajectories will almost always remain remote from each other during the match and so will get a poor LCSS and DTW similarities. This is what motivates us for building a new similarity measure which will rely on this intuitive notion of "dependency" that need to be explicit.  Another crucial point is that a reliable similarity measure for our problem should take into account the time parameter.