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\subsection{Dataset}  \subsubsection{Description}  We used a dataset already used in the ACM DEBS 2013 Grand Challenge \cite{Mutschler_2013}, a competition of soccer analysis.  This dataset has been collected by the Real-Time Locating System deployed on a football field of the Nuremberg Stadium in Germany. Data originates from sensors located near For research purpose it is useful to split  the players' shoes (1 sensor per leg) and project  inthe ball (1 sensor). The goal keeper is equipped with  two additional sensors, one part. Thus  ateach hand. The sensors in the players' shoes and hands produce data with 200Hz frequency, while the sensor in the ball produces data with 2000Hz frequency. The total data rate reaches roughly 15.000 position events per second. Every position event describes position of a given sensor in a three-dimensional coordinate system.  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 moment  we defined a trajectory as a set of ordered x and y-axis positions and accelerations regularly distributed in time.   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 deal  with a frequency of 25 Hz which correspond to the best frequency we could have if we were extracting directly from the videos extraction  of the players' trajectories in  soccer match. As each players is equipped with several sensor we combine their data to have one videos  and only one trajectory per player or ball.  Sometimes some data have been missed, we cope with this problem interpolating data so clustering players' trajectories  as to maintain synchronization between the two  different trajectories.  When a player goes out of the field we can't neither treat it as usual with positions out of the field because it would be non sense nor stop extracting the data because it would break the continuity of extracted player's position. Whereas the displacement of a player going and fetching the ball out of the field is non sense, the paths of other players at this while bring relevant information. Thus in problem. For  this case purpose  we just consider that the outside player remain at the last read position on the field with used  a null acceleration. soccer players' trajectories dataset.