Lucas Fidon edited In_this_project_we_adopted__.tex  almost 8 years ago

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In this project, we adopted the clustering algorithm described in \cite{NIPS2008_3478}. This method relies on the notion of stabilities of a data point introduced in \cite{NIPS2008_3478}. Depending on the whole set of distances distances,  each data point is more or less liable to be a cluster center. Those distances can be penalized so that a point that was a good candidate to be a center becomes a  poor one. The more a data point has to be penalized, the more stable he is. Therefore, the stability of a data point measures how much a data point need to be penalized such that it can no longer be 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 metric since the single input of the algorithm is distance matrix. This trait is essential for our case since it allows us to built a relevant metric for trajectories linked to the dependencies between the player trajectories through 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 clusters. The amount of clusters can be adjusted by a penalization constant which affect the selection of new cluster centers: the higher this constant the less clusters it tends to find.