echet Means and Statistics on Vineyards

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [20], Mileyko and his collaborators made the rst study of the properties of the Fr echet mean in ( Dp;Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fr echet mean of a nite

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