learn_combinatorial_graph_laplacian {spectralGraphTopology}

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