Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams)

no code implementations • 22 Jul 2022 • Mathieu Pont, Jules Vidal, Julien Tierny

We show the utility of our contributions by extending to merge trees two typical PCA applications.

Dimensionality Reduction

Wasserstein Distances, Geodesics and Barycenters of Merge Trees

1 code implementation • 16 Jul 2021 • Mathieu Pont, Jules Vidal, Julie Delon, Julien Tierny

We extend recent work on the edit distance [106] and introduce a new metric, called the Wasserstein distance between merge trees, which is purposely designed to enable efficient computations of geodesics and barycenters.