During this talk, we will focus on the problem of testing the equality of metric measure spaces (mm-spaces) up to an isomorphism (a measure-preserving isometry), giving samples on these spaces. For this purpose, we introduce a new shape signature, the distance-to-a-measure signature, which is a probability measure on R+ built from the mm-space of interest. To reach our goal, we use bootstrap methods, involving Wasserstein metrics.
Distance to a measure to compare samples of points
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Claire Brécheteau
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