LOMAR (version 0.5.0)

sliced_Wd: sliced_Wd

Description

Compute sliced Wasserstein distance or kernel. Reference: Mathieu Carriere, Marco Cuturi, and Steve Oudot. Sliced Wasserstein kernel for persistence diagrams. In Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 664–673, 2017.

Usage

sliced_Wd(Dg1, Dg2, M = 10, sigma = 1, dimensions = NULL, return.dist = FALSE)

Value

kernel or distance value

Arguments

Dg1

a persistence diagram as a n1 x 3 matrix where each row is a topological feature and the columns are dimension, birth and death of the feature.

Dg2

another persistence diagram as a n2 x 3 matrix

M

number of slices (default: 10)

sigma

kernel bandwidth (default: 1)

dimensions

vector of the dimensions of the topological features to consider, if NULL (default) use all available dimensions

return.dist

logical (default: FALSE). Whether to return the kernel or distance value.

Examples

D1 <- matrix(c(0,0,0,1,1,0,0,0,1.5, 3.5,2,2.5,3, 4, 6), ncol = 3, byrow = FALSE)
D2 <- matrix(c(0,0,1,1,0, 0, 1.2, 2, 1.4, 3.2,4.6,6.5), ncol = 3, byrow = FALSE)
K <- sliced_Wd(Dg1 = D1, Dg2 = D2, M = 10, sigma = 1, return.dist = TRUE)