TDA (version 1.0)

bottleneck: Bottleneck distance between two persistence diagrams

Description

This function computes the bottleneck distance between two persistence diagrams

Usage

bottleneck(Diag1, Diag2, dimension)

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 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.

Value

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

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. This function is an R wrapper of the function "bottleneck_distance" in the C++ library Dionysus. See references.

References

http://www.mrzv.org/software/dionysus/

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

See Also

ripsDiag, gridDiag, plot.diagram

Examples

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

DiagLim=5
maxdimension=1

Diag1=ripsDiag(XX1,maxdimension,DiagLim, printStatus=FALSE)
Diag2=ripsDiag(XX2,maxdimension,DiagLim, printStatus=FALSE)

bottleneckDist=bottleneck(Diag1, Diag2, dimension=1)
print(bottleneckDist)