English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper presents a computational framework for the Wassersteinauto-encoding of merge trees (MT-WAE), a novel extension of the classicalauto-encoder neural network architecture to the Wasserstein metric space ofmerge trees. In contrast to traditional auto-encoders which operate onvectorized data, our formulation explicitly manipulates merge trees on theirassociated metric space at each layer of the network, resulting in superioraccuracy and interpretability. Our novel neural network approach can beinterpreted as a non-linear generalization of previous linear attempts [79] atmerge tree encoding. It also trivially extends to persistence diagrams.Extensive experiments on public ensembles demonstrate the efficiency of ouralgorithms, with MT-WAE computations in the orders of minutes on average. Weshow the utility of our contributions in two applications adapted from previouswork on merge tree encoding [79]. First, we apply MT-WAE to merge treecompression, by concisely representing them with their coordinates in the finallayer of our auto-encoder. Second, we document an application to dimensionalityreduction, by exploiting the latent space of our auto-encoder, for the visualanalysis of ensemble data. We illustrate the versatility of our framework byintroducing two penalty terms, to help preserve in the latent space both theWasserstein distances between merge trees, as well as their clusters. In bothapplications, quantitative experiments assess the relevance of our framework.Finally, we provide a C++ implementation that can be used for reproducibility.

Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams)