huge.generator: Data generator

In huge: High-Dimensional Undirected Graph Estimation

Description

Implements the data generation from multivariate normal distributions with different graph structures, including "random", "hub", "cluster", "band" and "scale-free".

Usage

huge.generator(
  n = 200,
  d = 50,
  graph = "random",
  v = NULL,
  u = NULL,
  g = NULL,
  prob = NULL,
  vis = FALSE,
  verbose = TRUE
)

Arguments

n	The number of observations (sample size). The default value is 200.
d	The number of variables (dimension). The default value is 50.
graph	The graph structure with 4 options: "random", "hub", "cluster", "band" and "scale-free".
v	The off-diagonal elements of the precision matrix, controlling the magnitude of partial correlations with u. The default value is 0.3.
u	A positive number being added to the diagonal elements of the precision matrix, to control the magnitude of partial correlations. The default value is 0.1.
g	For "cluster" or "hub" graph, g is the number of hubs or clusters in the graph. The default value is about d/20 if d >= 40 and 2 if d < 40. For "band" graph, g is the bandwidth and the default value is 1. NOT applicable to "random" graph.
prob	For "random" graph, it is the probability that a pair of nodes has an edge. The default value is 3/d. For "cluster" graph, it is the probability that a pair of nodes has an edge in each cluster. The default value is 6*g/d if d/g <= 30 and 0.3 if d/g > 30. NOT applicable to "hub" or "band" graphs.
vis	Visualize the adjacency matrix of the true graph structure, the graph pattern, the covariance matrix and the empirical covariance matrix. The default value is FALSE
verbose	If verbose = FALSE, tracing information printing is disabled. The default value is TRUE.

Details

Given the adjacency matrix theta, the graph patterns are generated as below:

(I) "random": Each pair of off-diagonal elements are randomly set theta[i,j]=theta[j,i]=1 for i!=j with probability prob, and 0 other wise. It results in about d*(d-1)*prob/2 edges in the graph.

(II)"hub":The row/columns are evenly partitioned into g disjoint groups. Each group is associated with a "center" row i in that group. Each pair of off-diagonal elements are set theta[i,j]=theta[j,i]=1 for i!=j if j also belongs to the same group as i and 0 otherwise. It results in d - g edges in the graph.

(III)"cluster":The row/columns are evenly partitioned into g disjoint groups. Each pair of off-diagonal elements are set theta[i,j]=theta[j,i]=1 for i!=j with the probability probif both i and j belong to the same group, and 0 other wise. It results in about g*(d/g)*(d/g-1)*prob/2 edges in the graph.

(IV)"band": The off-diagonal elements are set to be theta[i,j]=1 if 1<=|i-j|<=g and 0 other wise. It results in (2d-1-g)*g/2 edges in the graph.

(V) "scale-free": The graph is generated using B-A algorithm. The initial graph has two connected nodes and each new node is connected to only one node in the existing graph with the probability proportional to the degree of the each node in the existing graph. It results in d edges in the graph.

The adjacency matrix theta has all diagonal elements equal to 0. To obtain a positive definite precision matrix, the smallest eigenvalue of theta*v (denoted by e) is computed. Then we set the precision matrix equal to theta*v+(|e|+0.1+u)I. The covariance matrix is then computed to generate multivariate normal data.

Value

An object with S3 class "sim" is returned:

data	The n by d matrix for the generated data
sigma	The covariance matrix for the generated data
omega	The precision matrix for the generated data
sigmahat	The empirical covariance matrix for the generated data
theta	The adjacency matrix of true graph structure (in sparse matrix representation) for the generated data

See Also

huge and huge-package

Examples

## band graph with bandwidth 3
L = huge.generator(graph = "band", g = 3)
plot(L)

## random sparse graph
L = huge.generator(vis = TRUE)

## random dense graph
L = huge.generator(prob = 0.5, vis = TRUE)

## hub graph with 6 hubs
L = huge.generator(graph = "hub", g = 6, vis = TRUE)

## hub graph with 8 clusters
L = huge.generator(graph = "cluster", g = 8, vis = TRUE)

## scale-free graphs
L = huge.generator(graph="scale-free", vis = TRUE)

Example output

Generating data from the multivariate normal distribution with the band graph structure....done.
Generating data from the multivariate normal distribution with the random graph structure....done.
Generating data from the multivariate normal distribution with the random graph structure....done.
Generating data from the multivariate normal distribution with the hub graph structure....done.
Generating data from the multivariate normal distribution with the cluster graph structure....done.
Generating data from the multivariate normal distribution with the scale-free graph structure....done.

huge documentation built on July 1, 2021, 1:06 a.m.