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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 trajectories field of trajectories' clustering the most competitive and widely used metrics are LCSS and DTW (but their computationally cost is much higher).  rely not on space positions but also on time and euclidian distance failed to take this parameter into account efficiently. Thus it accounts for the euclidian-based to be ineffective for the clustering of trajectories. Furthermore only discrete trajectories are available in the form of array which can be of different sizes with different time discretization or with different speed.