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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), their computationally cost is much higher though. 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.  rely not on space positions but also on time and euclidian distance failed to take this parameter into account efficiently.