learn_laplacian_pgd_connected: Learns sparse Laplacian matrix of a connected graph Learns a...

In mirca/sparseGraph: Estimating Graphs with Nonconvex, Sparse Promoting Regularizations

Learns sparse Laplacian matrix of a connected graph Learns a connected graph via non-convex, sparse promoting regularization functions such as MCP, SCAD, and re-weighted l1-norm.

Description

Learns sparse Laplacian matrix of a connected graph

Learns a connected graph via non-convex, sparse promoting regularization functions such as MCP, SCAD, and re-weighted l1-norm.

Usage

learn_laplacian_pgd_connected(
  S,
  w0 = "naive",
  alpha = 0,
  sparsity_type = "none",
  eps = 1e-04,
  gamma = 2.001,
  eta = 0.01,
  backtrack = TRUE,
  maxiter = 10000,
  reltol = 1e-05,
  verbose = TRUE
)

Arguments

S	a pxp sample covariance/correlation matrix, where p is the number of nodes of the graph
w0	initial estimate for the weight vector the graph or a string selecting an appropriate method. Available methods are: "qp": finds w0 that minimizes ||ginv(S) - L(w0)||_F, w0 >= 0; "naive": takes w0 as the negative of the off-diagonal elements of the pseudo inverse, setting to 0 any elements s.t. w0 < 0
alpha	hyperparameter to control the level of sparsiness of the estimated graph
sparsity_type	type of non-convex sparsity regularization. Available methods are: "mcp", "scad", "re-l1", and "none"
eps	hyperparameter for the re-weighted l1-norm
eta	learning rate
backtrack	whether to update the learning rate using backtrack line search
maxiter	maximum number of iterations
reltol	relative tolerance on the Frobenius norm of the estimated Laplacian matrix as a stopping criteria
verbose	whether or not to show a progress bar displaying the iterations

Value

A list containing possibly the following elements:

laplacian	the estimated Laplacian Matrix
adjacency	the estimated Adjacency Matrix
maxiter	number of iterations taken to converge
convergence	boolean flag to indicate whether or not the optimization converged
elapsed_time	elapsed time recorded at every iteration

Author(s)

Ze Vinicius, Jiaxi Ying, and Daniel Palomar

mirca/sparseGraph documentation built on Aug. 31, 2022, 4:20 p.m.