TDA (version 1.9.1)

wasserstein: 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)

Value

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

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).

Author

Jisu Kim and Fabrizio Lecci

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.

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)