deletions | additions       diff --git a/We_used_the_clustering_algorithm__.tex b/We_used_the_clustering_algorithm__.tex  index 6f0f3be..9a656d3 100644  --- a/We_used_the_clustering_algorithm__.tex  +++ b/We_used_the_clustering_algorithm__.tex 
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We In this project, we have  used the clustering algorithm described in \cite{NIPS2008_3478}. It is based This method rely  on the introduced a  notion of stabilities of a data point. point also introduced in \cite{NIPS2008_3478}.  The stability of a data point measure how much we need to penalize that point such that it can no longer be chosen as a center in an optimal solution of the problem. Thanks to a measure of this stability this algorithm managed to cluster data points based on an arbitrary matrix of distances, which is metric since  the single input required by of  the algorithm. algorithm is the matrix of distances of the data points.  This quality is essential for our case since it allows us to built a relevant metric for trajectories linked to the dependencies of between  thedistribution of  players' position trajectories  throw the time. We will described in more details the metrics used in the next part. Furthermore this algorithm is little sensitive to noise and initialization besides it selects automatically the number of cluster that can be adjusted by a penalization constant which affect the selection of new cluster's centers: the higher this constant the less clusters it tends to find.  \subsection{Metrics for trajectories}