Bottleneck distance between persistence diagrams

The largest displacement of the best matching between two persistence diagrams, where a point may also match the diagonal. Essential classes are matched only to essential classes; a dimension whose essential counts differ is Inf apart.

Usage

hg_bottleneck(d1, d2, dimension = NULL, tol = .Machine$double.eps^0.5)

Arguments

d1, d2

hg_homology() results, or data.frames with columns dimension, birth, death.

dimension

Integer vector of dimensions to compare. NULL compares every dimension present in either diagram.

tol

Tolerance of the binary search. Default .Machine$double.eps^0.5.

Value

A named numeric vector, one distance per dimension, named "dim_<k>".

References

Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. (2007). Stability of persistence diagrams. Discrete & Computational Geometry, 37, 103–120. doi:10.1007/s00454-006-1276-5

Edelsbrunner, H., & Harer, J. (2010). Computational Topology: An Introduction. American Mathematical Society.

See also

hg_wasserstein()

Examples

d1 <- data.frame(dimension = 0L, birth = 0, death = 2)
d2 <- data.frame(dimension = 0L, birth = 0, death = 3)
hg_bottleneck(d1, d2)
#> dim_0 
#>     1