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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' trajectory  clustering the most competitive and widely used similarity measures metrics  are \textbf{LCSS} (Longuest Common Subsequence) and \textbf{DTW} (Dynamic Time Warping). Indeed they are more adapted to the available  discrete trajectories in the form of array which can be of different sizes with different time discretization or with different speed that are available. speed.  The computationally costs cost  of LCSS and DTW are much higher though. However what we are looking for is a similarity measure metric  which is high when two trajectories depend "depend"  on each other whereas LCSS and DTW-based similarities 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 player of his team 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 2 players' two player  trajectories will almost always remain remote from each other during the match and so will get a poor low  LCSS and DTW similarities. 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 similarity measure metric  for our problem should takeinto account  the time parameter. parameter into account.