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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 trajectory clustering the most competitive and widely used metrics are \textbf{LCSS} (Longuest Common Subsequence) and \textbf{DTW} (Dynamic Time Warping). Warping)\cite{Zhang_Zhang_2006}.  Indeed they are more adapted to the available discrete trajectories in the form of array arrays  which can be of different sizes with different time discretization or with different speed. The computationally cost of LCSS and DTW are much higher though. However what we are looking for is a metric which is high when two trajectories "depend" on each other whereas LCSS and DTW-based metrics are high when two trajectories are close to each other in the same time. For instance if a player always goes to the middle of the field when another one 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 two player trajectories will almost always remain remote from each other during the match and so will get a low LCSS and DTW distance. 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 metric for our problem should take the time parameter into account.