wasserstein: Wasserstein distance between two persistence diagrams

In TDA: Statistical Tools for Topological Data Analysis

Wasserstein distance between two persistence diagrams

Description

The function wasserstein computes the Wasserstein distance between two persistence diagrams.

Usage

  wasserstein(Diag1, Diag2, p = 1, dimension = 1)

Arguments

Diag1	an object of class diagram or a matrix (n by 3) that stores dimension, birth and death of n topological features.
Diag2	an object of class diagram or a matrix (m by 3) that stores dimension, birth and death of m topological features.
p	integer specifying the power to be used in the computation of the Wasserstein distance. The default value is 1.
dimension	an integer or a vector specifying the dimension of the features used to compute the wasserstein distance. 0 for connected components, 1 for loops, 2 for voids and so on. The default value is 1 (loops).

Details

The Wasserstein distance between two diagrams is the cost of the optimal matching between points of the two diagrams. When a vector is given for dimension, then maximum among bottleneck distances using each element in dimension is returned. This function is an R wrapper of the function "wasserstein_distance" in the C++ library Dionysus. See references.

Value

The function wasserstein returns the value of the Wasserstein distance between the two persistence diagrams.

Author(s)

Jisu Kim and Fabrizio Lecci

References

Morozov D (2007). "Dionysus, a C++ library for computing persistent homology". https://www.mrzv.org/software/dionysus/.

Edelsbrunner H, Harer J (2010). "Computational topology: an introduction." American Mathematical Society.

See Also

bottleneck, alphaComplexDiag, alphaComplexDiag, gridDiag, ripsDiag, plot.diagram

Examples

XX1 <- circleUnif(20)
XX2 <- circleUnif(20, r = 0.2)

DiagLim <- 5
maxdimension <- 1

Diag1 <- ripsDiag(XX1, maxdimension, DiagLim, printProgress = FALSE)
Diag2 <- ripsDiag(XX2, maxdimension, DiagLim, printProgress = FALSE)

wassersteinDist <- wasserstein(Diag1[["diagram"]], Diag2[["diagram"]], p = 1,
                               dimension = 1)
print(wassersteinDist)

TDA documentation built on Feb. 16, 2023, 6:35 p.m.