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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 metrics similarity measures  are LCSS \textbf{LCSS} (Longuest Common Subsequence)  and DTW (but \textbf{DTW} (Dynamic Time Warping),  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 higher though. Indeed they are more adapted  tobe ineffective for  theclustering of trajectories. Furthermore only  discrete trajectoriesare available  in the form of array which can be of different sizes with different time discretization or with different speed. speed that are available.   rely not on space positions but also on time and euclidian distance failed to take this parameter into account efficiently.