The Wasserstein metric between #PersistenceDiagrams can be easily extended to #MergeTrees by restricting the set of candidate assignments to partial isomorphisms 👇
https://arxiv.org/abs/2207.10960

Available in the #TopologyToolKit!

#TopologicalDataAnalysis #DataScience #Visualization

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

Need to analyze a collection of datasets based on their #MergeTrees?
Check out our new approach for Principal Geodesic Analysis in the Wasserstein metric space of #MergeTrees, with applications to dimension reduction 👇
https://arxiv.org/abs/2207.10960

#TopologicalDataAnalysis #Visualization #DataScience

Funded by the European Research Council (ERC) (project TORI, https://erc-tori.github.io/)

#mergetrees describe the connectivity of landscape: imagine how after the deluge first mountain tops appear, then get connected by a revealed mountain pass and so on. If one tracks the connected components of the land masses, one gets merge trees. Folks in #tda use them a lot.

Turns out one can add them (but not subtract, pretty much like natural numbers). They form a commutative monoid (with unity).

Are they useful, in compositionality or elsewhere?

details:https://ymb.web.illinois.edu/2022/12/17/merge-tree-monoid/