learn_kcomp_heavytail_graph: Laplacian matrix of a k-component graph with heavy-tailed data
Computes the Laplacian matrix of a graph on the basis of an observed data matrix, where we assume the data to be Student-t distributed.

Description

Laplacian matrix of a k-component graph with heavy-tailed data

Computes the Laplacian matrix of a graph on the basis of an observed data matrix, where we assume the data to be Student-t distributed.

Usage

learn_kcomp_heavytail_graph(
  X,
  k = 1,
  heavy_type = "gaussian",
  nu = NULL,
  w0 = "naive",
  d = 1,
  beta = 1e-08,
  update_beta = TRUE,
  early_stopping = FALSE,
  rho = 1,
  update_rho = FALSE,
  maxiter = 10000,
  reltol = 1e-05,
  verbose = TRUE,
  record_objective = FALSE
)

Value

A list containing possibly the following elements:

laplacian: estimated Laplacian matrix
adjacency: estimated adjacency matrix
theta: estimated Laplacian matrix slack variable
maxiter: number of iterations taken to reach convergence
convergence: boolean flag to indicate whether or not the optimization conv erged
beta_seq: sequence of values taken by the hyperparameter beta until convergence
primal_lap_residual: primal residual for the Laplacian matrix per iteratio n
primal_deg_residual: primal residual for the degree vector per iteration
dual_residual: dual residual per iteration
lagrangian: Lagrangian value per iteration
elapsed_time: Time taken to reach convergence

Arguments

X: an n x p data matrix, where n is the number of observations and p is the number of nodes in the graph.
k: the number of components of the graph.
heavy_type: a string which selects the statistical distribution of the data . Valid values are "gaussian" or "student".
nu: the degrees of freedom of the Student-t distribution. Must be a real number greater than 2.
w0: initial vector of graph weights. Either a vector of length p(p-1)/2 or a string indicating the method to compute an initial value.
d: the nodes' degrees. Either a vector or a single value.
beta: hyperparameter that controls the regularization to obtain a k-component graph
update_beta: whether to update beta during the optimization.
early_stopping: whether to stop the iterations as soon as the rank constraint is satisfied.
rho: constraint relaxation hyperparameter.
update_rho: whether or not to update rho during the optimization.
maxiter: maximum number of iterations.
reltol: relative tolerance as a convergence criteria.
verbose: whether to show a progress bar during the iterations.
record_objective: whether to record the objective function per iteration.