learn_heavy_tail_kcomp_bipartite_graph {finbipartite}

Laplacian matrix of a k-component bipartite graph with heavy-tailed data Computes the Laplacian matrix of a k-component bipartite graph on the basis of an observed data matrix whose distribution is assumed to be Student-t.

Description

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

Computes the Laplacian matrix of a k-component bipartite graph on the basis of an observed data matrix whose distribution is assumed to be Student-t.

Usage

learn_heavy_tail_kcomp_bipartite_graph(
  X,
  r,
  q,
  k,
  nu = 2.001,
  rho = 1,
  learning_rate = 1e-04,
  maxiter = 1000,
  reltol = 1e-05,
  init = "default",
  verbose = TRUE,
  record_objective = FALSE
)

Arguments

X

a n x p data matrix, where p is the number of nodes in the graph and n is the number of observations.

r

number of nodes in the objects set.

q

number of nodes in the classes set.

k

number of components of the graph.

nu

degrees of freedom of the Student-t distribution.

rho

ADMM hyperparameter.

learning_rate

gradient descent parameter.

maxiter

maximum number of iterations.

reltol

relative tolerance as a convergence criteria.

init

string denoting how to compute the initial graph or a r x q matrix with initial graph weights.

verbose

whether or not to show a progress bar during the iterations.

record_objective

whether or not to record the objective function value during iterations.

Value

A list containing possibly the following elements:

laplacian

estimated Laplacian matrix

adjacency

estimated adjacency matrix

B

estimated graph weights matrix

maxiter

number of iterations taken to reach convergence

convergence

boolean flag to indicate whether or not the optimization converged

dual_residual

dual residual value per iteration

primal_residual

primal residual value per iteration

aug_lag

augmented Lagrangian value per iteration

rho_seq

constraint relaxation hyperparameter value per iteration

elapsed_time

time taken per iteration until convergence is reached

Examples

library(finbipartite)
library(igraph)
set.seed(42)
r <- 50
q <- 5
p <- r + q

bipartite <- sample_bipartite(r, q, type="Gnp", p = 1, directed=FALSE)
# randomly assign edge weights to connected nodes
E(bipartite)$weight <- 1
Lw <- as.matrix(laplacian_matrix(bipartite))
B <- -Lw[1:r, (r+1):p]
B[,] <- runif(length(B))
B <- B / rowSums(B)
# utils functions
from_B_to_laplacian <- function(B) {
  A <- from_B_to_adjacency(B)
  return(diag(rowSums(A)) - A)
}

from_B_to_adjacency <- function(B) {
  r <- nrow(B)
  q <- ncol(B)
  zeros_rxr <- matrix(0, r, r)
  zeros_qxq <- matrix(0, q, q)
  return(rbind(cbind(zeros_rxr, B), cbind(t(B), zeros_qxq)))
}
Ltrue <- from_B_to_laplacian(B)
X <- MASS::mvrnorm(100*p, rep(0, p), MASS::ginv(Ltrue))
bipartite_graph <- learn_heavy_tail_kcomp_bipartite_graph(X = X,
                                                          r = r,
                                                          q = q,
                                                          k = 1,
                                                          nu = 1e2,
                                                          verbose=FALSE)