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 work studies how the introduction of the entropic regularization term inunbalanced Optimal Transport (OT) models may alter their homogeneity withrespect to the input measures. We observe that in common settings (includingbalanced OT and unbalanced OT with Kullback-Leibler divergence to themarginals), although the optimal transport cost itself is not homogeneous,optimal transport plans and the so-called Sinkhorn divergences are indeedhomogeneous. However, homogeneity does not hold in more general UnbalancedRegularized Optimal Transport (UROT) models, for instance those using the TotalVariation as divergence to the marginals. We propose to modify the entropicregularization term to retrieve an UROT model that is homogeneous whilepreserving most properties of the standard UROT model. We showcase theimportance of using our Homogeneous UROT (HUROT) model when it comes toregularize Optimal Transport with Boundary, a transportation model involving aspatially varying divergence to the marginals for which the standard(inhomogeneous) UROT model would yield inappropriate behavior.

An Homogeneous Unbalanced Regularized Optimal Transport model with applications to Optimal Transport with Boundary