learn_bipartite_graph_nie {finbipartite}

Laplacian matrix of a k-component bipartite graph via Nie's method Computes the Laplacian matrix of a bipartite graph on the basis of an observed similarity matrix.

Description

Laplacian matrix of a k-component bipartite graph via Nie's method

Computes the Laplacian matrix of a bipartite graph on the basis of an observed similarity matrix.

Usage

learn_bipartite_graph_nie(
  S,
  r,
  q,
  k,
  learning_rate = 1e-04,
  eta = 1,
  maxiter = 1000,
  reltol = 1e-06,
  verbose = TRUE,
  record_objective = FALSE
)

Arguments

S

a p x p similarity matrix, where p is the number of nodes in the graph.

r

number of nodes in the objects set.

q

number of nodes in the classes set.

k

number of components of the graph.

learning_rate

gradient descent parameter.

eta

rank constraint hyperparameter.

maxiter

maximum number of iterations.

reltol

relative tolerance as a convergence criteria.

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

obj_fun

objective function value per iteration

References

Feiping Nie, Xiaoqian Wang, Cheng Deng, Heng Huang. "Learning A Structured Optimal Bipartite Graph for Co-Clustering". Advances in Neural Information Processing Systems (NIPS 2017)

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))
S <- cov(X)
bipartite_graph <- learn_bipartite_graph_nie(S = S,
                                             r = r,
                                             q = q,
                                             k = 1,
                                             learning_rate = 5e-1,
                                             eta = 0,
                                             verbose=FALSE)