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Furthermore this dataset provides both positions and accelerations, which are the data we were looking for.  \subsubsection{Extraction of data}  For our experiments we used only data during a restricted period of several minutes beginning at arbitrary time of the play. Computationnaly we defined a trajectory as a set of ordered x and y-axis positions and accelerations regularly distributed in time. \verb|class trajectory:    def __init__(self):  """  initialization of a trajectory  """  self.id = ""  self.nbstep = 0 #nombre de pas  self.pos = [] #vecteur des positions  self.acc = [] #vecteur des accelerations  self.date = [] #dates associees aux positions et acceleration  self.datepred = 0. #sert seulement au chargementdes donnees  self.xpred = 0.   self.ypred = 0.  self.accxpred = 0.   self.accypred = 0.|  Furthermore we will handle a set of synchronized trajectories. This synchronization is highly important since we will used it when we will approximate the joint probability distribution of positions or accelerations of two players. Data are read and extracted with a frequency of 25 Hz which correspond to the best frequency we could have if we were extracting directly from the videos of the soccer match. As each players is equipped with several sensor we combine their data to have one and only one trajectory per player or ball.  Sometimes some data have been missed, we cope with this problem interpolating data so as to maintain synchronization between the different trajectories.