Manuscript_files/20190129_Iris_experiments_R1.R
In hiendn/StoEMMIX: What the package does (short line)
#################################################################
## Iris1 ##
#################################################################
# Load libraries
library('MixSim')
library('mclust')
# Load source files for minibatch EM algorithms
source('https://raw.githubusercontent.com/hiendn/StoEMMIX/master/Manuscript_files/20190128_main_functions.R')
# Set memory limit
Sys.setenv('R_MAX_VSIZE'=10000000000000)
# Load in Iris data
data("iris", package = "datasets")
## Extract various required variables
# Get dimensions
d <- ncol(iris) - 1
# Get species label
id <- as.integer(iris[, 5])
# Get the number of subpopulations
g <- max(id)
## Estimate mixture model parameters
# Proportions
Pi <- prop.table(tabulate(id))
# Mean vectors
Mu <- t(sapply(1:g, function(k){ colMeans(iris[id == k, -5]) }))
# Covariance matrices
Sigma <- sapply(1:g, function(k){ var(iris[id == k, -5]) })
# Set the dimension of the covariance array
dim(Sigma) <- c(d, d, g)
# True matrix
True_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
True_matrix[ii,] <- c(Pi[ii],Mu[ii,],Sigma[,,ii][upper.tri(Sigma[,,ii],diag = T)])
}
## Setup parameters
# Number of observations to simulation
NN <- 10^6
# Set the number repetitions
Rep <- 100
# Number of components to fit
Groups <- 3
# Set a random seed
set.seed(20190129)
# Construct a matrix to store the results
Results <- matrix(NA,100,9)
Timing <- matrix(NA,100,5)
ARI_results <- matrix(NA,100,9)
SE_results <- matrix(NA,100,9)
# Conduct simulation study
for (rr in 1:Rep) {
# Simulate data
Pre_data <- simdataset(NN,Pi,Mu,Sigma)
IDs <- Pre_data$id
Data <- Pre_data$X
# Randomly generate labels for initialization
Samp <- sample(1:Groups,NN,replace = T)
# Initialize parameters
msEst <- mstep(modelName = "VVV", data = Data, z = unmap(Samp))
# Run batch EM algorithm
Tick <- proc.time()[3]
MC <- em('VVV', data=Data, parameters = msEst$parameters, control = emControl(eps=0,tol=0,itmax=10))
Timing[rr,1] <- proc.time()[3]-Tick
# Get likelihood value for batch EM algorithm
Results[rr,1] <- MC$loglik
# Get parameter estimates
MC_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
MC_matrix[ii,] <- c(MC$parameters$pro[ii],
t(MC$parameters$mean)[ii,],
MC$parameters$variance$sigma[,,ii][upper.tri(MC$parameters$variance$sigma[,,ii],diag = T)])
}
SE_results[rr,1] <- sum(apply((as.matrix(dist(rbind(MC_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI
ARI_results[rr,1] <- adjustedRandIndex(IDs,apply(MC$z,1,which.max))
# Run minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/10000,Groups,0.6,1-10^-10,10000)
Results[rr,2] <- Sto$`reg_log-likelihood`
Results[rr,3] <- Sto$`pol_log-likelihood`
Timing[rr,2] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,2] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,2] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,3] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,3] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/20000,Groups,0.6,1-10^-10,20000)
Results[rr,4] <- Sto$`reg_log-likelihood`
Results[rr,5] <- Sto$`pol_log-likelihood`
Timing[rr,3] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,4] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,4] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,5] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,5] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/10000,Groups,0.6,1-10^-10,10000,
1000,1000,1000)
Results[rr,6] <- Sto$`reg_log-likelihood`
Results[rr,7] <- Sto$`pol_log-likelihood`
Timing[rr,4] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,6] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,6] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,7] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,7] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/20000,Groups,0.6,1-10^-10,20000,
1000,1000,1000)
Results[rr,8] <- Sto$`reg_log-likelihood`
Results[rr,9] <- Sto$`pol_log-likelihood`
Timing[rr,5] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,8] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,8] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,9] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,9] <- adjustedRandIndex(IDs,unlist(Cluster))
# Save and print outputs
# save(Results,file='./Iris1.rdata')
print(c(rr,Results[rr,]))
save(Timing,file='./Iris1timing.rdata')
save(ARI_results,file='./Iris1ARI.rdata')
save(SE_results,file='./Iris1SE.rdata')
print(c(rr,Timing[rr,]))
print(c(rr,ARI_results[rr,]))
print(c(rr,SE_results[rr,]))
# Also sink results to a text file
# sink('./Iris1.txt',append = TRUE)
# cat(ii,Results[ii,],'\n')
# sink()
sink('./Iris1timing.txt',append = TRUE)
cat(rr,Timing[rr,],'\n')
sink()
sink('./Iris1ARI.txt',append = TRUE)
cat(rr,ARI_results[rr,],'\n')
sink()
sink('./Iris1SE.txt',append = TRUE)
cat(rr,SE_results[rr,],'\n')
sink()
}
#################################################################
## Iris2 ##
#################################################################
# Load libraries
library('MixSim')
library('mclust')
# Load source files for minibatch EM algorithms
source('https://raw.githubusercontent.com/hiendn/StoEMMIX/master/Manuscript_files/20190128_main_functions.R')
# Set memory limit
Sys.setenv('R_MAX_VSIZE'=10000000000000)
# Load in Iris data
data("iris", package = "datasets")
## Extract various required variables
# Get dimensions
d <- ncol(iris) - 1
# Get species label
id <- as.integer(iris[, 5])
# Get the number of subpopulations
g <- max(id)
## Estimate mixture model parameters
# Proportions
Pi <- prop.table(tabulate(id))
# Mean vectors
Mu <- t(sapply(1:g, function(k){ colMeans(iris[id == k, -5]) }))
# Covariance matrices
Sigma <- sapply(1:g, function(k){ var(iris[id == k, -5]) })
# Set the dimension of the covariance array
dim(Sigma) <- c(d, d, g)
# True matrix
True_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
True_matrix[ii,] <- c(Pi[ii],Mu[ii,],Sigma[,,ii][upper.tri(Sigma[,,ii],diag = T)])
}
## Setup parameters
# Number of observations to simulation
NN <- 10^7
# Set the number repetitions
Rep <- 100
# Number of components to fit
Groups <- 3
# Set a random seed
set.seed(20190129)
# Construct a matrix to store the results
Results <- matrix(NA,100,9)
Timing <- matrix(NA,100,5)
ARI_results <- matrix(NA,100,9)
SE_results <- matrix(NA,100,9)
# Conduct simulation study
for (rr in 1:Rep) {
# Simulate data
Pre_data <- simdataset(NN,Pi,Mu,Sigma)
IDs <- Pre_data$id
Data <- Pre_data$X
# Randomly generate labels for initialization
Samp <- sample(1:Groups,NN,replace = T)
# Initialize parameters
msEst <- mstep(modelName = "VVV", data = Data, z = unmap(Samp))
# Run batch EM algorithm
Tick <- proc.time()[3]
MC <- em('VVV', data=Data, parameters = msEst$parameters, control = emControl(eps=0,tol=0,itmax=10))
Timing[rr,1] <- proc.time()[3]-Tick
# Get likelihood value for batch EM algorithm
Results[rr,1] <- MC$loglik
# Get parameter estimates
MC_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
MC_matrix[ii,] <- c(MC$parameters$pro[ii],
t(MC$parameters$mean)[ii,],
MC$parameters$variance$sigma[,,ii][upper.tri(MC$parameters$variance$sigma[,,ii],diag = T)])
}
SE_results[rr,1] <- sum(apply((as.matrix(dist(rbind(MC_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI
ARI_results[rr,1] <- adjustedRandIndex(IDs,apply(MC$z,1,which.max))
# Run minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/100000,Groups,0.6,1-10^-10,100000)
Results[rr,2] <- Sto$`reg_log-likelihood`
Results[rr,3] <- Sto$`pol_log-likelihood`
Timing[rr,2] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,2] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,2] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,3] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,3] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/200000,Groups,0.6,1-10^-10,200000)
Results[rr,4] <- Sto$`reg_log-likelihood`
Results[rr,5] <- Sto$`pol_log-likelihood`
Timing[rr,3] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,4] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,4] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,5] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,5] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/100000,Groups,0.6,1-10^-10,100000,
1000,1000,1000)
Results[rr,6] <- Sto$`reg_log-likelihood`
Results[rr,7] <- Sto$`pol_log-likelihood`
Timing[rr,4] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,6] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,6] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,7] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,7] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/200000,Groups,0.6,1-10^-10,200000,
1000,1000,1000)
Results[rr,8] <- Sto$`reg_log-likelihood`
Results[rr,9] <- Sto$`pol_log-likelihood`
Timing[rr,5] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,8] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,8] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,9] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,9] <- adjustedRandIndex(IDs,unlist(Cluster))
# Save and print outputs
# save(Results,file='./Iris2.rdata')
print(c(rr,Results[rr,]))
save(Timing,file='./Iris2timing.rdata')
save(ARI_results,file='./Iris2ARI.rdata')
save(SE_results,file='./Iris2SE.rdata')
print(c(rr,Timing[rr,]))
print(c(rr,ARI_results[rr,]))
print(c(rr,SE_results[rr,]))
# Also sink results to a text file
# sink('./Iris2.txt',append = TRUE)
# cat(ii,Results[ii,],'\n')
# sink()
sink('./Iris2timing.txt',append = TRUE)
cat(rr,Timing[rr,],'\n')
sink()
sink('./Iris2ARI.txt',append = TRUE)
cat(rr,ARI_results[rr,],'\n')
sink()
sink('./Iris2SE.txt',append = TRUE)
cat(rr,SE_results[rr,],'\n')
sink()
}
hiendn/StoEMMIX documentation built on Sept. 9, 2019, 6:07 a.m.
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#################################################################
## Iris1 ##
#################################################################
# Load libraries
library('MixSim')
library('mclust')
# Load source files for minibatch EM algorithms
source('https://raw.githubusercontent.com/hiendn/StoEMMIX/master/Manuscript_files/20190128_main_functions.R')
# Set memory limit
Sys.setenv('R_MAX_VSIZE'=10000000000000)
# Load in Iris data
data("iris", package = "datasets")
## Extract various required variables
# Get dimensions
d <- ncol(iris) - 1
# Get species label
id <- as.integer(iris[, 5])
# Get the number of subpopulations
g <- max(id)
## Estimate mixture model parameters
# Proportions
Pi <- prop.table(tabulate(id))
# Mean vectors
Mu <- t(sapply(1:g, function(k){ colMeans(iris[id == k, -5]) }))
# Covariance matrices
Sigma <- sapply(1:g, function(k){ var(iris[id == k, -5]) })
# Set the dimension of the covariance array
dim(Sigma) <- c(d, d, g)
# True matrix
True_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
True_matrix[ii,] <- c(Pi[ii],Mu[ii,],Sigma[,,ii][upper.tri(Sigma[,,ii],diag = T)])
}
## Setup parameters
# Number of observations to simulation
NN <- 10^6
# Set the number repetitions
Rep <- 100
# Number of components to fit
Groups <- 3
# Set a random seed
set.seed(20190129)
# Construct a matrix to store the results
Results <- matrix(NA,100,9)
Timing <- matrix(NA,100,5)
ARI_results <- matrix(NA,100,9)
SE_results <- matrix(NA,100,9)
# Conduct simulation study
for (rr in 1:Rep) {
# Simulate data
Pre_data <- simdataset(NN,Pi,Mu,Sigma)
IDs <- Pre_data$id
Data <- Pre_data$X
# Randomly generate labels for initialization
Samp <- sample(1:Groups,NN,replace = T)
# Initialize parameters
msEst <- mstep(modelName = "VVV", data = Data, z = unmap(Samp))
# Run batch EM algorithm
Tick <- proc.time()[3]
MC <- em('VVV', data=Data, parameters = msEst$parameters, control = emControl(eps=0,tol=0,itmax=10))
Timing[rr,1] <- proc.time()[3]-Tick
# Get likelihood value for batch EM algorithm
Results[rr,1] <- MC$loglik
# Get parameter estimates
MC_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
MC_matrix[ii,] <- c(MC$parameters$pro[ii],
t(MC$parameters$mean)[ii,],
MC$parameters$variance$sigma[,,ii][upper.tri(MC$parameters$variance$sigma[,,ii],diag = T)])
}
SE_results[rr,1] <- sum(apply((as.matrix(dist(rbind(MC_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI
ARI_results[rr,1] <- adjustedRandIndex(IDs,apply(MC$z,1,which.max))
# Run minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/10000,Groups,0.6,1-10^-10,10000)
Results[rr,2] <- Sto$`reg_log-likelihood`
Results[rr,3] <- Sto$`pol_log-likelihood`
Timing[rr,2] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,2] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,2] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,3] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,3] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/20000,Groups,0.6,1-10^-10,20000)
Results[rr,4] <- Sto$`reg_log-likelihood`
Results[rr,5] <- Sto$`pol_log-likelihood`
Timing[rr,3] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,4] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,4] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,5] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,5] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/10000,Groups,0.6,1-10^-10,10000,
1000,1000,1000)
Results[rr,6] <- Sto$`reg_log-likelihood`
Results[rr,7] <- Sto$`pol_log-likelihood`
Timing[rr,4] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,6] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,6] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,7] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,7] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/20000,Groups,0.6,1-10^-10,20000,
1000,1000,1000)
Results[rr,8] <- Sto$`reg_log-likelihood`
Results[rr,9] <- Sto$`pol_log-likelihood`
Timing[rr,5] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,8] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,8] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,9] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,9] <- adjustedRandIndex(IDs,unlist(Cluster))
# Save and print outputs
# save(Results,file='./Iris1.rdata')
print(c(rr,Results[rr,]))
save(Timing,file='./Iris1timing.rdata')
save(ARI_results,file='./Iris1ARI.rdata')
save(SE_results,file='./Iris1SE.rdata')
print(c(rr,Timing[rr,]))
print(c(rr,ARI_results[rr,]))
print(c(rr,SE_results[rr,]))
# Also sink results to a text file
# sink('./Iris1.txt',append = TRUE)
# cat(ii,Results[ii,],'\n')
# sink()
sink('./Iris1timing.txt',append = TRUE)
cat(rr,Timing[rr,],'\n')
sink()
sink('./Iris1ARI.txt',append = TRUE)
cat(rr,ARI_results[rr,],'\n')
sink()
sink('./Iris1SE.txt',append = TRUE)
cat(rr,SE_results[rr,],'\n')
sink()
}
#################################################################
## Iris2 ##
#################################################################
# Load libraries
library('MixSim')
library('mclust')
# Load source files for minibatch EM algorithms
source('https://raw.githubusercontent.com/hiendn/StoEMMIX/master/Manuscript_files/20190128_main_functions.R')
# Set memory limit
Sys.setenv('R_MAX_VSIZE'=10000000000000)
# Load in Iris data
data("iris", package = "datasets")
## Extract various required variables
# Get dimensions
d <- ncol(iris) - 1
# Get species label
id <- as.integer(iris[, 5])
# Get the number of subpopulations
g <- max(id)
## Estimate mixture model parameters
# Proportions
Pi <- prop.table(tabulate(id))
# Mean vectors
Mu <- t(sapply(1:g, function(k){ colMeans(iris[id == k, -5]) }))
# Covariance matrices
Sigma <- sapply(1:g, function(k){ var(iris[id == k, -5]) })
# Set the dimension of the covariance array
dim(Sigma) <- c(d, d, g)
# True matrix
True_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
True_matrix[ii,] <- c(Pi[ii],Mu[ii,],Sigma[,,ii][upper.tri(Sigma[,,ii],diag = T)])
}
## Setup parameters
# Number of observations to simulation
NN <- 10^7
# Set the number repetitions
Rep <- 100
# Number of components to fit
Groups <- 3
# Set a random seed
set.seed(20190129)
# Construct a matrix to store the results
Results <- matrix(NA,100,9)
Timing <- matrix(NA,100,5)
ARI_results <- matrix(NA,100,9)
SE_results <- matrix(NA,100,9)
# Conduct simulation study
for (rr in 1:Rep) {
# Simulate data
Pre_data <- simdataset(NN,Pi,Mu,Sigma)
IDs <- Pre_data$id
Data <- Pre_data$X
# Randomly generate labels for initialization
Samp <- sample(1:Groups,NN,replace = T)
# Initialize parameters
msEst <- mstep(modelName = "VVV", data = Data, z = unmap(Samp))
# Run batch EM algorithm
Tick <- proc.time()[3]
MC <- em('VVV', data=Data, parameters = msEst$parameters, control = emControl(eps=0,tol=0,itmax=10))
Timing[rr,1] <- proc.time()[3]-Tick
# Get likelihood value for batch EM algorithm
Results[rr,1] <- MC$loglik
# Get parameter estimates
MC_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
MC_matrix[ii,] <- c(MC$parameters$pro[ii],
t(MC$parameters$mean)[ii,],
MC$parameters$variance$sigma[,,ii][upper.tri(MC$parameters$variance$sigma[,,ii],diag = T)])
}
SE_results[rr,1] <- sum(apply((as.matrix(dist(rbind(MC_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI
ARI_results[rr,1] <- adjustedRandIndex(IDs,apply(MC$z,1,which.max))
# Run minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/100000,Groups,0.6,1-10^-10,100000)
Results[rr,2] <- Sto$`reg_log-likelihood`
Results[rr,3] <- Sto$`pol_log-likelihood`
Timing[rr,2] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,2] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,2] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,3] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,3] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_pol(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/200000,Groups,0.6,1-10^-10,200000)
Results[rr,4] <- Sto$`reg_log-likelihood`
Results[rr,5] <- Sto$`pol_log-likelihood`
Timing[rr,3] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,4] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,4] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,5] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,5] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 10000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/100000,Groups,0.6,1-10^-10,100000,
1000,1000,1000)
Results[rr,6] <- Sto$`reg_log-likelihood`
Results[rr,7] <- Sto$`pol_log-likelihood`
Timing[rr,4] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,6] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,6] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,7] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,7] <- adjustedRandIndex(IDs,unlist(Cluster))
# Run truncated minibatch algorithm with batch size 20000
Tick <- proc.time()[3]
Sto <- stoEMMIX_poltrunc(t(Data), msEst$parameters$pro, msEst$parameters$mean,
msEst$parameters$variance$sigma,
10*NN/200000,Groups,0.6,1-10^-10,200000,
1000,1000,1000)
Results[rr,8] <- Sto$`reg_log-likelihood`
Results[rr,9] <- Sto$`pol_log-likelihood`
Timing[rr,5] <- proc.time()[3]-Tick
# Get parameter estimates (regular)
Reg_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Reg_matrix[ii,] <- c(Sto$reg_proportions[ii],
t(Sto$reg_means)[ii,],
Sto$reg_covariances[,,ii][upper.tri(Sto$reg_covariances[,,ii],diag = T)])
}
SE_results[rr,8] <- sum(apply((as.matrix(dist(rbind(Reg_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (reg)
Cluster <- GMM_arma_cluster(t(Data),Sto$reg_proportions,Sto$reg_means,Sto$reg_covariances)
ARI_results[rr,8] <- adjustedRandIndex(IDs,unlist(Cluster))
# Get parameter estimates (polyak)
Pol_matrix <- matrix(NA,g,1+d+d+choose(d,2))
for (ii in 1:g) {
Pol_matrix[ii,] <- c(Sto$pol_proportions[ii],
t(Sto$pol_means)[ii,],
Sto$pol_covariances[,,ii][upper.tri(Sto$pol_covariances[,,ii],diag = T)])
}
SE_results[rr,9] <- sum(apply((as.matrix(dist(rbind(Pol_matrix,True_matrix),diag=T,upper=T))[1:g,(g+1):(2*g)])^2,1,min))
# Get ARI (pol)
Cluster <- GMM_arma_cluster(t(Data),Sto$pol_proportions,Sto$pol_means,Sto$pol_covariances)
ARI_results[rr,9] <- adjustedRandIndex(IDs,unlist(Cluster))
# Save and print outputs
# save(Results,file='./Iris2.rdata')
print(c(rr,Results[rr,]))
save(Timing,file='./Iris2timing.rdata')
save(ARI_results,file='./Iris2ARI.rdata')
save(SE_results,file='./Iris2SE.rdata')
print(c(rr,Timing[rr,]))
print(c(rr,ARI_results[rr,]))
print(c(rr,SE_results[rr,]))
# Also sink results to a text file
# sink('./Iris2.txt',append = TRUE)
# cat(ii,Results[ii,],'\n')
# sink()
sink('./Iris2timing.txt',append = TRUE)
cat(rr,Timing[rr,],'\n')
sink()
sink('./Iris2ARI.txt',append = TRUE)
cat(rr,ARI_results[rr,],'\n')
sink()
sink('./Iris2SE.txt',append = TRUE)
cat(rr,SE_results[rr,],'\n')
sink()
}
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