PGGMBC {HeteroGGM}

Penalized GGM-based clustering.

Description

The main function of penalized Gaussian graphical model-based clustering with unconstrained covariance matrices.

Usage

PGGMBC(lambda, data, K, initial.selection="K-means", initialize, average=F,
              asymmetric=T, eps = 5e-2, maxiter=10,
              maxiter.AMA=5, local_appro=T, trace = F, penalty = "MCP")

Arguments

lambda

A list, the sequences of the tuning parameters (lambda1 and lambda2).

data

n * p matrix, the design matrix.

K

Int, a given number of subgroups.

initial.selection

The different initial values from two clustering methods, which can be selected from c("K-means","dbscan").

initialize

A given initial values, which should be given when initial.selection is not in c("K-means","dbscan").

average

The logical variable, whether to use averaging when integrating parameters that are identified as identical subgroups, the default setting is F, which means the estimated parameters for the subgroup with the largest sample size among the subgroups identified as identical subgroups is used as the final parameter for this subgroup.

asymmetric

The logical variable, symmetry of the precision matrices or not, the default setting is T.

eps

A float value, algorithm termination threshold.

maxiter

Int, maximum number of cycles of the ADMM algorithm.

maxiter.AMA

Int, maximum number of cycles of the AMA algorithm.

local_appro

The logical variable, whether to use local approximations when updating mean parameters, the default setting is T.

trace

The logical variable, whether or not to output the number of identified subgroups during the search for parameters.

penalty

The type of the penalty, which can be selected from c("MCP", "SCAD", "lasso").

Value

A list including all estimated parameters and the BIC values with all choices of given tuning parameters, and the selected optional parameters.

Author(s)

Mingyang Ren, Sanguo Zhang, Qingzhao Zhang, Shuangge Ma. Maintainer: Mingyang Ren <[e-mail]>.

References

Ren, M., Zhang S., Zhang Q. and Ma S. (2020). Gaussian Graphical Model-based Heterogeneity Analysis via Penalized Fusion. Biometrics, Published Online, https://doi.org/10.1111/biom.13426. Zhou, H., Pan, W., & Shen, X. (2009). Penalized model-based clustering with unconstrained covariance matrices. Electronic journal of statistics, 3, 1473.

Examples

######## Example 1: Generate simulation data and apply this method to analysis #######
n <- 200              # The sample size of each subgroup
p <- 20               # The dimension of the precision matrix
K <- 3               # The true number of subgroups
N <- rep(n,K)        # The sample sizes of K subgroups

################ The true parameters ################
mue <- 1.5
nonnum <- 4
mu01 <- c(rep(mue,nonnum),rep(-mue,nonnum),rep(0,p-2*nonnum))
mu02 <- c(rep(mue,2*nonnum),rep(0,p-2*nonnum))
mu03 <- c(rep(-mue,2*nonnum),rep(0,p-2*nonnum))

# Power law network
set.seed(2)
A.list <- Power.law.network(p,s=5,I2=c(1),I3=c(2))
Theta01 <- A.list$A1
Theta02 <- A.list$A2
Theta03 <- A.list$A3
sigma01 <- solve(Theta01)
sigma02 <- solve(Theta02)
sigma03 <- solve(Theta03)
Mu0.list <- list(mu01,mu02,mu03)
Sigma0.list <- list(sigma01,sigma02,sigma03)
Theta0.list <- list(Theta01,Theta02,Theta03)

################ Generating simulated data ################
whole.data <- generate.data(N,Mu0.list,Theta0.list,Sigma0.list)

################ The implementation and evaluation of competitors ################
lambda <- genelambda.obo(nlambda1=5,lambda1_max=0.5,lambda1_min=0.1,
                         nlambda2=15,lambda2_max=1.5,lambda2_min=0.1)
res <- PGGMBC(lambda, whole.data$data, K, initial.selection="K-means")
Theta_hat.list <- res$Theta_hat.list
Mu_hat.list <- res$Mu_hat.list
prob.list <- res$prob.list
L.mat.list <- res$L.mat.list
opt_num <- res$Opt_num
opt_Theta_hat <- Theta_hat.list[[opt_num]]
opt_Mu_hat <- Mu_hat.list[[opt_num]]
opt_L.mat <- L.mat.list[[opt_num]]
opt_prob <- prob.list[[opt_num]]

######## Example 2: Call the built-in simulation data set and analyze #######
data(example.data)
K <- 3
lambda <- genelambda.obo(nlambda1=5,lambda1_max=0.5,lambda1_min=0.1,
                         nlambda2=15,lambda2_max=1.5,lambda2_min=0.1)
res <- PGGMBC(lambda, example.data$data, K, initial.selection="K-means")
Theta_hat.list <- res$Theta_hat.list
opt_num <- res$Opt_num
opt_Theta_hat <- Theta_hat.list[[opt_num]]