TDA (version 1.3)

wasserstein: Wasserstein distance between two persistence diagrams

Description

This function 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. Default is 1.

dimension

an integer 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. Default is 1 (loops).

Value

• Returns the value of the Wasserstein distance between the two persistence diagrams.

Details

The Wasserstein distance between two diagrams is the cost of the optimal matching between points of the two diagrams. This function is an R wrapper of the function "wasserstein_distance" in the C++ library Dionysus. See references.

References

Dmitriy Morozov, "Dionysus, a C++ library for computing persistent homology". http://www.mrzv.org/software/dionysus/

Herbert Edelsbrunner and John Harer (2010), Computational topology: an introduction. American Mathematical Society.

See Also

bottleneck, ripsDiag, gridDiag, plot.diagram

Examples

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

DiagLim=5
maxdimension=1

Diag1=ripsDiag(XX1,maxdimension,DiagLim, printProgress=FALSE)$diagram
Diag2=ripsDiag(XX2,maxdimension,DiagLim, printProgress=FALSE)$diagram

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