pf.kernel: Persistence Fisher Kernel (PFK)

In kernelTDA: Statistical Learning with Kernel for Persistence Diagrams

Description

Computes the Persistence Fisher Kernel (PFK) between persistence diagrams.

Usage

pf.kernel(d1, d2 = NULL, h, dimension, sigma)

Arguments

d1	A persistence diagram (matrix with 3 col where the first one is the dimension, the second is the birth-time and the third is the death-time) or a list of diagrams.
d2	A persistence diagram (matrix with 3 col where the first one is the dimension, the second is the birth-time and the third is the death-time).
h	bandwidth of the PFK.
dimension	The dimension of the topological feature (0 for connected components, 1 for cycles etc)
sigma	standard deviation of the base Gaussian Kernel.

Value

If d1 is a list of Persistence Diagrams, this function returns a matrix whose (i,j) entry is the PFK computed in (d1[[i]], d2[[j]]), otherwise it returns the value for the PFK computed in (d1, d2).

Author(s)

Tullia Padellini

References

\insertRef

le2018persistencekernelTDA

Examples

diag1 <- matrix(c(1,1,1,0,2,3,2,2.5,4), ncol = 3, byrow = FALSE)
diag2 <- matrix(c(1,1,0,1,1,2), ncol = 3, byrow = FALSE)
pf.kernel(d1 = diag1, d2 = diag2, h = 1, dimension = 1, sigma = 1)

kernelTDA documentation built on April 19, 2020, 3:56 p.m.