bottleneck {TDA}

Bottleneck distance between two persistence diagrams

Description

The function bottleneck computes the bottleneck distance between two persistence diagrams.

Usage

bottleneck(Diag1, Diag2, 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.

dimension

an integer or a vector specifying the dimension of the features used to compute the bottleneck distance. 0 for connected components, 1 for loops, 2 for voids and so on. The default value is 1 (loops). The default value is 1.

Details

The bottleneck distance between two diagrams is the cost of the optimal matching between points of the two diagrams. Note that all the diagonal points are included in the persistence diagrams when computing the optimal matching. When a vector is given for dimension, then maximum among bottleneck distances using each element in dimension is returned. The function bottleneck is an R wrapper of the function "bottleneck_distance" in the C++ library Dionysus. See references.

Value

The function bottleneck returns the value of the bottleneck 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

wasserstein, 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)

bottleneckDist <- bottleneck(Diag1[["diagram"]], Diag2[["diagram"]],
                             dimension = 1)
print(bottleneckDist)