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).
Furthermore if this method comes to be proved efficient, its scope will strongly depends of its computational complexity. The current problem is polynomial however we don’t know yet whether there is an universal “good” choice of \(C_{penalty}\) - probably not. We don’t know neither if which method will be used to extract the players trajectories in the soccer videos. Therefore, it is well nigh impossible to estimate the efficiency that could be reach by a complete algorithm resolving our problem.
Entropie is wide spread in a large amount of research fields, therefore we can think of Mutual Inforamtion as a very general concept. Thus this clustering method should be easily scalable to other types of trajectories. Especially I hope we will be able to use it for biomedical image analyses, for example to detect pattern in video of cells growth. Knowing that it is already possible to track cells efficiently \cite{Kostelec_2015} it is possibly appropriate for the analysis of those trajectories.