Adjacency Matrix from Precision Matrix

Convert a precision matrix to a partial-correlation-based adjacency matrix.

Usage

prec_to_adj(
  prec.mat,
  diag.zero = TRUE,
  absolute = FALSE,
  threshold = NULL,
  weighted = TRUE
)

Arguments

prec.mat

A numeric precision matrix.

diag.zero

A logical value (default = TRUE) specifying whether to set the diagonal entries of the adjacency matrix to 0. If diag.zero = FALSE, the diagonal entries are set to 1 for a weighted network. For an unweighted network (weighted = FALSE), the diagonal is always forced to 0 to avoid self-loops.

absolute

A logical value (default = FALSE) specifying whether to take the absolute values of the partial correlations.

threshold

A nonnegative numeric value (default = NULL) specifying the threshold for edge filtering. Entries with absolute values smaller than the threshold are set to 0.

weighted

A logical value (default = TRUE) specifying whether to return a weighted adjacency matrix. If weighted = FALSE, the matrix is a binary adjacency matrix with entries equal to 0 or 1.

Value

A numeric adjacency matrix with S3 class "adjmat".

Details

For a precision matrix \(\Omega\), the partial correlation between nodes \(i\) and \(j\) is computed as $$\rho_{ij} = - \frac{\Omega_{ij}}{\sqrt{\Omega_{ii}\Omega_{jj}}}.$$

Examples

library(grasps)

## reproducibility for everything
set.seed(1234)

## block-structured precision matrix based on SBM
sim <- gen_prec_sbm(p = 30, K = 3,
                    within.prob = 0.25, between.prob = 0.05,
                    weight.dists = list("gamma", "unif"),
                    weight.paras = list(c(shape = 20, rate = 10),
                                        c(min = 0, max = 5)),
                    cond.target = 100)
## ground truth visualization
plot(sim)


## n-by-p data matrix
library(MASS)
X <- mvrnorm(n = 20, mu = rep(0, 30), Sigma = sim$Sigma)

## precision matrix: adaptive lasso; BIC
prec <- grasps(X = X, membership = sim$membership, penalty = "adapt", crit = "BIC")

## precision matrix visualization
plot(prec)


## performance
performance(hatOmega = prec$hatOmega, Omega = sim$Omega)
#>      measure    value
#> 1   sparsity   0.8897
#> 2  Frobenius  24.9549
#> 3         KL   8.1014
#> 4  quadratic 114.8538
#> 5   spectral  13.4520
#> 6         TP  22.0000
#> 7         TN 361.0000
#> 8         FP  26.0000
#> 9         FN  26.0000
#> 10       TPR   0.4583
#> 11       FPR   0.0672
#> 12        F1   0.4583
#> 13       MCC   0.3911

## adjacency matrix: diagonal = 0; raw partial correlations;
##                   no thresholding; weighted network
adj <- prec_to_adj(prec$hatOmega,
                   diag.zero = TRUE, absolute = FALSE,
                   threshold = NULL, weighted = TRUE)

## adjacency matrix visualization
plot(adj)