shrink_into_CH: Identify the position of a point relative to the convex hull...

In ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks

Identify the position of a point relative to the convex hull of a set of points

Description

This function uses linear programming to find the value by which vector p needs to be scaled towards or away from vector m in order for p to be on the boundary of the convex hull of rows of M. If p is a matrix, a value that scales all rows of p into the convex hull of M is found.

Usage

shrink_into_CH(
  p,
  M,
  m = NULL,
  verbose = FALSE,
  ...,
  solver = c("glpk", "lpsolve")
)

Arguments

p	a d-dimensional vector or a matrix with d columns.
M	an n by d matrix. Each row of M is a d-dimensional vector.
m	a d-dimensional vector specifying the value towards which to shrink; must be in the interior of the convex hull of M, and defaults to its centroid (column means).
verbose	A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
...	arguments passed directly to linear program solver.
solver	a character string selecting which solver to use; by default, tries Rglpk's but falls back to lpSolveAPI's.

Value

Logical, telling whether p is (or all rows of p are) in the closed convex hull of the points in M.

The scaling factor described above is returned. shrink_into_CH() >= 1 indicates that all points in p are in the convex hull of M.

Note

This is a successor to the deprecated function is.inCH(), which was originally written for the "stepping" algorithm of Hummel et al (2012). See Krivitsky, Kuvelkar, and Hunter (2022) for detailed discussion of algorithms used in is.inCH() and shrink_into_CH().

References

https://www.cs.mcgill.ca/~fukuda/soft/polyfaq/node22.html

Hummel, R. M., Hunter, D. R., and Handcock, M. S. (2012), Improving Simulation-Based Algorithms for Fitting ERGMs, Journal of Computational and Graphical Statistics, 21: 920-939.

Krivitsky, P. N., Kuvelkar, A. R., and Hunter, D. R. (2022). Likelihood-based Inference for Exponential-Family Random Graph Models via Linear Programming. arXiv preprint arXiv:2202.03572. https://arxiv.org/abs/2202.03572

ergm documentation built on May 31, 2023, 8:04 p.m.