deletions | additions       diff --git a/section_Conclusion_begin_itemize_item__.tex b/section_Conclusion_begin_itemize_item__.tex  index 3d05a82..6df4a0c 100644  --- a/section_Conclusion_begin_itemize_item__.tex  +++ b/section_Conclusion_begin_itemize_item__.tex 
...
\end{itemize}  Mutual Information of players position based metric has shown to give very encouraging results for automatic analysis of soccer players.  Indeed with a few tests only it has been possible to give concrete interpretations to the clusters provided by the algorithm.   Some further tests should be driven to understand why it works and why the mutual information of players acceleration based metric doesn't work.  More parameters could be considered using ACP to select the most relevant to improve the results.  The statements about the results remain too subjective though. It lacks an objective measure of the quality of the clusters.  I tried to use silhouette index, which is a common way to measure the quality of a clusters' set \cite{parisot:tel-00978520}. The silhouette index belongs to $[-1,1]$: it is close to $1$ if the cluster are perfectly separated to each other and close to $-1$ in the opposite case. However I always get values rather close to $0$ when I compute it to my results, which does not give much information since it is a very general index, and thus there is no telling whether it suits to our problem or not. Therefore, further step would consist in developing such an index designed for this problem and to compare the results with other cluster sets generated with state-of-the-art metrics (as LCSS or DTW for example).