SupplementaryMaterial Anovelnotionofbarycenterforprobabilitydistributions basedonoptimalweakmasstransport

Figure 6: Example of pushforward measures constructed from barycentric projections for two measuresµandν intwodimensions(left)andonedimension(right). 1 We next illustrate the differences between the optimal barycentric map and a barycentric map constructed from an OT plan in the classical Kantorovich formulation in Eq.(1). We sampled r = 50 observationsXi and m = 60 observationsYi, each sets from a 2DGaussian.