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Gromov-Wasserstein Distance

Source: R/all_generic.R, R/gromov_wasserstein.R
gromov_wasserstein.Rd

Generic function for computing Gromov-Wasserstein distance between domains

Usage

gromov_wasserstein(data, ...)

# S3 method for class 'hyperdesign'
gromov_wasserstein(
  data,
  epsilon = 0.1,
  metric = c("euclidean", "maximum", "manhattan", "canberra", "binary", "minkowski"),
  init = "uniform",
  max_iter = 100,
  tol = 1e-09,
  verbose = FALSE,
  marginals = NULL,
  scale = c("per_domain", "global", "none"),
  inner_max_iter = 30,
  inner_tol = 1e-09,
  dist_chunk_size = 1000,
  ...
)

# Default S3 method
gromov_wasserstein(data, ...)

Arguments

data

The input data (typically a hyperdesign object)

...

Additional arguments passed to methods:

  • epsilon: Entropic regularization parameter (default: 0.1)

  • metric: Distance metric for within-domain distances (default: "euclidean")

  • init: Initialization method: "uniform" (default), "random", or initial transport plans

  • max_iter: Maximum iterations for optimization (default: 100)

  • tol: Convergence tolerance (default: 1e-9)

  • verbose: Print convergence information (default: FALSE)

  • marginals: Optional list of marginal distributions

  • scale: How to scale distance matrices (default: "per_domain")

  • inner_max_iter: Maximum iterations for inner Sinkhorn loop (default: 30)

  • inner_tol: Convergence tolerance for inner Sinkhorn iterations (default: 1e-9)

  • dist_chunk_size: Chunk size for memory-efficient distance computation (default: 1000)

epsilon

Entropic regularization parameter. Default: 0.1

metric

Distance metric for within-domain distances. Default: "euclidean"

init

Initialization method: "uniform" or "random". Default: "uniform"

max_iter

Maximum iterations for outer loop. Default: 100

tol

Convergence tolerance for outer loop. Default: 1e-9

verbose

Print convergence information. Default: FALSE

marginals

Optional list of marginal distributions per domain

scale

Scaling strategy: "per_domain", "global", or "none". Default: "per_domain"

inner_max_iter

Maximum Sinkhorn iterations. Default: 30

inner_tol

Sinkhorn convergence tolerance. Default: 1e-9

dist_chunk_size

Chunk size for distance computation. Default: 1000

Value

A `gromov_wasserstein` object containing transport plans, pairwise distances, convergence status, and domain metadata. See `gromov_wasserstein.hyperdesign` for full details.

Examples

# \donttest{
set.seed(1)
X1 <- matrix(rnorm(30), 10, 3)
X2 <- matrix(rnorm(30), 10, 3)
library(multidesign)
md1 <- multidesign(X1, data.frame(id = 1:10))
md2 <- multidesign(X2, data.frame(id = 1:10))
hd <- hyperdesign(list(d1 = md1, d2 = md2))
result <- gromov_wasserstein(hd, epsilon = 0.5, max_iter = 10)
# }