pssk {LOMAR}

pssk

Description

Compute the persistence scale-space kernel on persistence diagrams. Reference: Jan Reininghaus, Stefan Huber, Ulrich Bauer, and Roland Kwitt. A stable multi-scale kernel for topological machine learning. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pages 4741–4748, 2015.

Usage

pssk(Dg1 = NULL, Dg2 = NULL, sigma = NULL, dimensions = NULL)

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

sigma

kernel bandwidth

dimensions

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

Value

kernel 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 <- pssk(Dg1 = D1, Dg2 = D2, sigma = 1)