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Pairwise distances within a set of persistence diagrams

Source: R/distances.R
pairwise-distances.Rd

This collection of functions computes the pairwise distance matrix between all pairs in a set of persistence diagrams of the same homology dimension. The diagrams must be represented as 2-column matrices. The first column of the matrix contains the birth times and the second column contains the death times of the points.

Usage

bottleneck_pairwise_distances(
  x,
  tol = sqrt(.Machine$double.eps),
  validate = TRUE,
  dimension = 0L,
  ncores = 1L
)

wasserstein_pairwise_distances(
  x,
  tol = sqrt(.Machine$double.eps),
  p = 1,
  validate = TRUE,
  dimension = 0L,
  ncores = 1L
)

kantorovich_pairwise_distances(
  x,
  tol = sqrt(.Machine$double.eps),
  p = 1,
  validate = TRUE,
  dimension = 0L,
  ncores = 1L
)

Arguments

x

A list of either 2-column matrices or objects of class persistence specifying the set of persistence diagrams.

tol

A numeric value specifying the relative error. Defaults to sqrt(.Machine$double.eps). For the Bottleneck distance, it can be set to 0.0 in which case the exact Bottleneck distance is computed, while an approximate Bottleneck distance is computed if tol > 0.0. For the Wasserstein distance, it must be strictly positive.

validate

A boolean value specifying whether to validate the input persistence diagrams. Defaults to TRUE. If FALSE, the function will not check if the input persistence diagrams are valid. This can be useful for performance reasons, but it is recommended to keep it TRUE for safety.

dimension

An integer value specifying the homology dimension for which to compute the distance. Defaults to 0L. This is only used if x and y are objects of class persistence.

ncores

An integer value specifying the number of cores to use for parallel computation. Defaults to 1L.

p

A numeric value specifying the power for the Wasserstein distance. Defaults to 1.0.

Value

An object of class 'dist' containing the pairwise distance matrix between the persistence diagrams.

Examples

spl <- persistence_sample[1:10]

# Extract the list of 2-column matrices for dimension 0 in the sample
x <- lapply(spl[1:10], function(x) x$pairs[[1]])

# Compute the pairwise Bottleneck distances
Db <- bottleneck_pairwise_distances(spl)
Db <- bottleneck_pairwise_distances(x)

# Compute the pairwise Wasserstein distances
Dw <- wasserstein_pairwise_distances(spl)
Dw <- wasserstein_pairwise_distances(x)