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Pairwise Wasserstein Distances Along Projection Directions Between Several Empirical Distributions

Source: R/sliced_wasserstein.R
compute_all_distances.Rd

This function computes the squared 2-Wasserstein distances between the projections of several empirical directions along specified projection directions. The projection directions can optionally be transformed by means of a linear map. The functions can output the squared distances along each projection direction, or the squared distances averaged over projection directions.

Usage

compute_all_distances(
  distributions,
  thetas,
  A = NULL,
  verbose = TRUE,
  keep_projections = TRUE
)

Arguments

distributions

A list of matrices representing empirical distributions.

thetas

A matrix, each row of which represents a projection direction.

A

Optionally, a matrix used to transform each projection direction.

verbose

If TRUE, show progress.

keep_projections

If TRUE, the distance matrix for each projection direction is output. If FALSE, the distance matrices for the different projection directions are averaged.

Value

If keep_projections = TRUE, a list of squared-distance matrices, one for each projection direction; otherwise, a matrix with the averaged squared distances.

Examples

M1 <- matrix(rnorm(50), ncol = 5)
M2 <- matrix(rnorm(150), ncol = 5)
M3 <- matrix(rnorm(250), ncol = 5)
# Sliced Wasserstein:
my_directions <- generate_directions(20, 5)
compute_all_distances(list(M1, M2, M3), my_directions,
  keep_projections = FALSE, verbose = FALSE)
#>           [,1]      [,2]      [,3]
#> [1,] 0.0000000 0.2662411 0.2123149
#> [2,] 0.2662411 0.0000000 0.2030276
#> [3,] 0.2123149 0.2030276 0.0000000
# Marginal Wasserstein distances:
marginal_wass <- compute_all_distances(list(M1, M2, M3), diag(1, 5),
  keep_projections = TRUE, verbose = FALSE)
marginal_wass[[3]] # along third dimension
#>           [,1]       [,2]       [,3]
#> [1,] 0.0000000 0.11677560 0.15943208
#> [2,] 0.1167756 0.00000000 0.05865423
#> [3,] 0.1594321 0.05865423 0.00000000
# Reweight projection directions
A <- diag(c(4, 0.5, 3, 2, 1))
shear_wass <- compute_all_distances(list(M1, M2, M3), diag(1, 5), A = A,
  keep_projections = TRUE, verbose = FALSE)
shear_wass[[3]]
#>          [,1]      [,2]      [,3]
#> [1,] 0.000000 1.0509804 1.4348888
#> [2,] 1.050980 0.0000000 0.5278881
#> [3,] 1.434889 0.5278881 0.0000000