FWpoint.regularization: Modified Fermat-Weber point numerical solver for ultrametrics

In TML: Tropical Geometry Tools for Machine Learning

Modified Fermat-Weber point numerical solver for ultrametrics

Description

Returns a modified Fermat-Weber point of N points using a gradient based numerical method This method is appropriate for points coming from ultrametrics. The algorithm tries to find a point that minimizes the sum of tropical distances from the samples, but also also tries to find a point that is as close as possible to the space of ultrametrics. The tradeoff between these two objectives is controlled by the penalty parameter. If penalty=0, the method is identical to FWpoint_numerical; it finds the Fermat-Weber point, which may not be an ultrametric. If penalty is very large, the algorithm is trying to find the Fermat-Weber point in the space of ultrametrics.

Usage

FWpoint.num.w.reg(datamatrix, penalty = 0)

Arguments

datamatrix	matrix of dimension N*e, where N is the number of observations which lie in R^e
penalty	positive real number; the regularization rate

Value

vector; Fermat-Weber point approximation

Author(s)

Georgios Aliatimis [e-mail]

References

Aliatimis, Georgios, Ruriko Yoshida, Burak Boyaci and James A. Grant (2023). Tropical Logistic Regression on Space of Phylogenetic Trees

Examples

D = matrix(c(0,0,0,0,2,5,0,3,1),3,3,TRUE)
FWpoint.num.w.reg(D,1e4) # (0,2,5/3) not ultrametric
FWpoint.num.w.reg(D,1e4) # (0,5/3,5/3) ultrametric

TML documentation built on Sept. 11, 2024, 6:19 p.m.