Keanu Sisouk

Keanu Sisouk

Wasserstein Dictionaries of Persistence Diagrams


27 octobre 2023    
15h30 - 16h30

Salle du Conseil, Espace Turing
45 rue des Saints-Pères, Paris, 75006

Type d’évènement

We introduce a multi-scale gradient descent approach for the efficient resolution of the corresponding minimization problem, which interleaves the optimization of the barycenter weights with the optimization of the atom diagrams. Our approach leverages the analytic expressions for the gradient of both sub-problems to ensure fast iterations and it additionally exploits shared-memory parallelism. Extensive experiments on public ensembles demonstrate the efficiency of our approach, with Wasserstein dictionary computations in the orders of minutes for the largest examples. We show the utility of our contributions in two applications. First, we apply Wassserstein dictionaries to data reduction and reliably compress persistence diagrams by concisely representing them with their weights in the dictionary. Second, we present a dimensionality reduction framework based on a Wasserstein dictionary defined with a small number of atoms and encode the dictionary as a low dimensional simplex embedded in a visual space.

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