learn_combinatorial_graph_laplacian: Learn the Combinatorial Graph Laplacian from data Learns a...

In spectralGraphTopology: Learning Graphs from Data via Spectral Constraints

Learn the Combinatorial Graph Laplacian from data Learns a graph Laplacian matrix using the Combinatorial Graph Laplacian (CGL) algorithm proposed by Egilmez et. al. (2017)

Description

Learn the Combinatorial Graph Laplacian from data

Learns a graph Laplacian matrix using the Combinatorial Graph Laplacian (CGL) algorithm proposed by Egilmez et. al. (2017)

Usage

learn_combinatorial_graph_laplacian(
  S,
  A_mask = NULL,
  alpha = 0,
  reltol = 1e-05,
  max_cycle = 10000,
  regtype = 1,
  record_objective = FALSE,
  verbose = TRUE
)

Arguments

S	sample covariance matrix
A_mask	binary adjacency matrix of the graph
alpha	L1-norm regularization hyperparameter
reltol	minimum relative error considered for the stopping criteri
max_cycle	maximum number of cycles
regtype	type of L1-norm regularization. If reg_type == 1, then all elements of the Laplacian matrix will be regularized. If reg_type == 2, only the off-diagonal elements will be regularized
record_objective	whether or not to record the objective function value at every iteration. Default is FALSE
verbose	if TRUE, then a progress bar will be displayed in the console. Default is TRUE

Value

A list containing possibly the following elements

laplacian	estimated Laplacian Matrix
elapsed_time	elapsed time recorded at every iteration
frod_norm	relative Frobenius norm between consecutive estimates of the Laplacian matrix
convergence	whether or not the algorithm has converged within the tolerance and max number of iterations
obj_fun	objective function value at every iteration, in case record_objective = TRUE

References

H. E. Egilmez, E. Pavez and A. Ortega, "Graph Learning From Data Under Laplacian and Structural Constraints", in IEEE Journal of Selected Topics in Signal Processing, vol. 11, no. 6, pp. 825-841, Sept. 2017. Original MATLAB source code is available at: https://github.com/STAC-USC/Graph_Learning

spectralGraphTopology documentation built on March 18, 2022, 7:35 p.m.