ws_dist: Compute the p-Wasserstein distance between two measures

In WSGeometry: Geometric Tools Based on Balanced/Unbalanced Optimal Transport

Description

This is essentially a wrapper function of transport. It has the advantage of allowing more general input objects, such as images or matrices, without the user having to manually convert these objects.

Usage

ws_dist(A, B, p = 2, sampling = FALSE, S = NULL, R = NULL)

Arguments

A	One of the following: A matrix, representing an image; A file name containing an image; A wpp-object.
B	One of the following: A matrix, representing an image; A file name containing an image; A wpp-object.
p	A positive real number specifying the power of the Wasserstein distance.
sampling	A boolean specifying whether a stochastic approximation (Sommerfeld et al., 2019) should be used to approximate the distance.
S	A positive integer specifying the number of samples drawn in the stochastic approximation.
R	The number of repetitions averaged over in the stochastic approximation.

Value

A number specifying the computed p-Wasserstein distance.

References

M Sommerfeld, J Schrieber, Y Zemel, and A Munk (2019). Optimal transport: Fast probabilistic approximations with exact solvers. Journal of Machine Learning Research 20(105):1–23.

Examples

P1<-transport::random32a$mass
P2<-transport::random32b$mass
P1<-P1/sum(P1)
P2<-P2/sum(P2)
ws_dist(P1,P2)

WSGeometry documentation built on Dec. 15, 2021, 1:08 a.m.