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simulation_S2.R
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# devtools::install_github('CrossD/RFPCA')
# devtools::install_url("https://cran.r-project.org/src/contrib/Archive/Funclustering/Funclustering_1.0.2.tar.gz")
library(RFPCA) # RFPCA and MFPCA
library(mclust) # clustering measure
library(Funclustering) # funclust (Currently, it is not supported by cran.)
library(funHDDC) # funHDDC
library(gmfd) # gmfd
library(tidyverse)
source("functions.R")
n <- 100 # number of curves
m <- 20 # number of different time points
K <- 20 # number of components
k <- 2 # number of clusters
n_k <- c(rep(round(n/k), k-1),
n - (round(n/k) * (k-1))) # number of curves for each cluster
num.sim <- 100 # number of simulations
### Option for the number of PCs
num.pc.method <- "FVE" # using FVE thresholds
# num.pc.method <- 2 # fixed number
if (num.pc.method == "FVE") {
FVEthresholdSW <- 0.90
FVEthresholdCS <- 0.70
maxK <- Inf
} else if (as.integer(num.pc.method)) {
FVEthresholdSW <- 1
FVEthresholdCS <- 1
maxK <- num.pc.method
}
### Simulation for 3 types of data
clust_list <- list() # clustering objects
for (sim.type in 1:3) {
# sim.type <- 3 # type of generated data
method_list <- c("kCFC(R)","kCFC(M)","K-means(R)","K-means(M)",
"funclust","funHDDC","gmfd")
CCR <- matrix(0, num.sim, length(method_list))
aRand <- matrix(0, num.sim, length(method_list))
colnames(CCR) <- method_list
colnames(aRand) <- method_list
clust_obj_list <- list() # clustering objects per seed
for (seed in 1:num.sim) {
print(paste0("Seed: ", seed))
set.seed(seed)
### Generate curves for each cluster
Lt <- list()
Ly <- list()
mu_list <- list() # meanfunction for each cluster
xi_list <- list() # true FPC scores
phi_list <- list() # true eigenfunctions
cluster <- rep(1:k, n_k) # cluster index
for (i in 1:k) { # generate for each cluster
lambda <- 0.07^(seq_len(K) / 2)
basisType <- 'legendre01'
xiFun <- rnorm
sigma2 <- 0.01
muList <- list(
function(x) x * 2,
function(x) sin(x * 1 * pi) * pi / 2 * 0.6,
function(x) rep(0, length(x))
)
if (i == 2) {
# basisType <- "fourier"
if (sim.type == 1) {
lambda <- (i*0.07)^(seq_len(K) / 2)
muList[[2]] <- function(x) (-sin(x * 1 * pi)) * pi / 2 * 0.6
} else if (sim.type == 2) {
lambda <- (i*0.07)^(seq_len(K) / 2)
muList[[2]] <- function(x) (cos(x * 4 * pi)) * pi / 2 * 0.6
} else if (sim.type == 3) {
# lambda <- (i*0.07)^(seq_len(K) / 2)
# muList[[2]] <- function(x) (sin(x * 3 * pi)) * pi / 2 * 0.6
lambda <- ((i+1)*0.07)^(seq_len(K) / 2)
muList[[2]] <- function(x) (-sin(x * 2 * pi)) * pi / 2 * 0.6
}
}
pts <- seq(0, 1, length.out = m)
mfd <- structure(1, class = 'Sphere')
mu <- Makemu(mfd, muList, c(0, 0, 1), pts)
# Generate samples
samp <- MakeMfdProcess(mfd = mfd,
n = n_k[i],
mu = mu,
pts = pts,
K = K,
xiFun = xiFun,
lambda = lambda,
basisType = basisType,
sigma2 = sigma2)
spSamp <- array2list(samp$X, samp$T)
Ly <- c(Ly, spSamp$Ly)
Lt <- c(Lt, spSamp$Lt)
mu_list <- c(mu_list, list(mu))
xi_list <- c(xi_list, list(samp$xi))
phi_list <- c(phi_list, list(samp$phi))
}
### kCFC with Riemannian metric
fit.kCFC.Riemann <- kCRFC(y = Ly,
t = Lt,
k = k,
kSeed = seed,
maxIter = 125,
optnsSW = list(mfdName = "Sphere",
FVEthreshold = FVEthresholdSW,
maxK = maxK,
# error = T,
userBwMu = "GCV",
userBwCov = "GCV"),
optnsCS = list(mfdName = "Sphere",
FVEthreshold = FVEthresholdCS,
maxK = maxK,
# error = T,
userBwMu = 'GCV',
userBwCov = 'GCV'))
# fit.kCFC.Riemann$cluster # clustering index
# fit.kCFC.Riemann$clustConf0 # initial clustering index from k-means
### kCFC with Euclidean metric (multivariate FPCA)
fit.kCFC.L2 <- kCRFC(y = Ly,
t = Lt,
k = k,
kSeed = seed,
maxIter = 125,
optnsSW = list(mfdName = "Euclidean",
FVEthreshold = FVEthresholdSW,
maxK = maxK,
# error = T,
userBwMu = "GCV",
userBwCov = "GCV"),
optnsCS = list(mfdName = "Euclidean",
FVEthreshold = FVEthresholdCS,
maxK = maxK,
# error = T,
userBwMu = 'GCV',
userBwCov = 'GCV'))
# ### K-means with RFPCA
# fit.rfpca <- RFPCA(Ly = Ly,
# Lt = Lt,
# optns = list(mfdName = "Sphere",
# userBwMu = "GCV",
# userBwCov = "GCV",
# # kernel = kern,
# FVEthreshold = FVEthresholdSW,
# maxK = maxK,
# error = FALSE))
# set.seed(seed)
# fit.kmeans.Riemann <- kmeans(fit.rfpca$xi, centers = k,
# iter.max = 30, nstart = 50)
#
# ### K-means with MFPCA
# fit.mfpca <- RFPCA(Ly = Ly,
# Lt = Lt,
# optns = list(mfdName = "Euclidean",
# userBwMu = "GCV",
# userBwCov = "GCV",
# # kernel = kern,
# FVEthreshold = FVEthresholdSW,
# maxK = maxK,
# error = FALSE))
# set.seed(seed)
# fit.kmeans.L2 <- kmeans(fit.mfpca$xi, centers = k,
# iter.max = 30, nstart = 50)
### funclust - set.seed does not working!!
set.seed(seed)
CWtime <- Lt[[1]]
CWfd <- lapply(1:3, function(mdim){
data <- sapply(Ly, function(y){ y[mdim, ] })
fda::smooth.basisPar(CWtime, data, lambda = 1e-2)$fd # B-spline basis
})
# set.seed(seed)
fit.funclust <- funclust(CWfd, K = k, increaseDimension = T)
# 1 - classError(cluster, fit.funclust$cls)$errorRate
# fit.funclust$cls
### funHDDC
set.seed(seed)
fit.funHDDC <- funHDDC(CWfd,
K = k,
model = "AkjBQkDk",
init = "kmeans",
threshold = 0.2)
# fit.funHDDC$class
### gmfd
# A k-means procedure based on a Mahalanobis type distance for clustering multivariate functional data
# https://link.springer.com/content/pdf/10.1007/s10260-018-00446-6.pdf
set.seed(seed)
FD <- funData(Lt[[1]], list(
t( sapply(Ly, function(y){ y[1, ] }) ),
t( sapply(Ly, function(y){ y[2, ] }) ),
t( sapply(Ly, function(y){ y[3, ] }) )
))
fit.gmfd <- gmfd_kmeans(FD, n.cl = k, metric = "mahalanobis", p = 10^5)
graphics.off() # remove plot panel
# fit.gmfd$cluster
# CCR (correct classification rate) and aRand (adjusted Rand index)
CCR[seed, ] <- c(
1 - classError(cluster, fit.kCFC.Riemann$cluster)$errorRate,
1 - classError(cluster, fit.kCFC.L2$cluster)$errorRate,
## initial clustering (k-means)
1 - classError(cluster, fit.kCFC.Riemann$clustConf0)$errorRate,
1 - classError(cluster, fit.kCFC.L2$clustConf0)$errorRate,
1 - classError(cluster, fit.funclust$cls)$errorRate,
1 - classError(cluster, fit.funHDDC$class)$errorRate,
1 - classError(cluster, fit.gmfd$cluster)$errorRate
)
aRand[seed, ] <- c(
adjustedRandIndex(cluster, fit.kCFC.Riemann$cluster),
adjustedRandIndex(cluster, fit.kCFC.L2$cluster),
## initial clustering (k-means)
adjustedRandIndex(cluster, fit.kCFC.Riemann$clustConf0),
adjustedRandIndex(cluster, fit.kCFC.L2$clustConf0),
adjustedRandIndex(cluster, fit.funclust$cls),
adjustedRandIndex(cluster, fit.funHDDC$class),
adjustedRandIndex(cluster, fit.gmfd$cluster)
)
print(CCR[seed, ])
### Save clustering objects per seed
clust_obj_list[[seed]] <- list(
fit.kCFC.Riemann = fit.kCFC.Riemann,
fit.kCFC.L2 = fit.kCFC.L2,
fit.funclust = fit.funclust,
fit.funHDDC = fit.funHDDC,
fit.gmfd = fit.gmfd
)
}
### Save clustering objects per sim.type
clust_list[[sim.type]] <- clust_obj_list
# colMeans(CCR)
# colMeans(aRand)
# apply(CCR, 2, sd)
# apply(aRand, 2, sd)
### Combine results
if (sim.type == 1) {
res <- data.frame(Method = method_list) %>%
# CCR
left_join(data.frame(
Method = colnames(CCR),
"CCR" = paste0(
format(round(colMeans(CCR), 3), 3),
" (",
format(round(apply(CCR, 2, sd), 3), 3),
")"
)
), by = "Method") %>%
# aRand
left_join(data.frame(
Method = colnames(aRand),
"aRand" = paste0(
format(round(colMeans(aRand), 3), 3),
" (",
format(round(apply(aRand, 2, sd), 3), 3),
")"
)
), by = "Method")
} else if (sim.type > 1) {
res2 <- data.frame(Method = method_list) %>%
# CCR
left_join(data.frame(
Method = colnames(CCR),
"CCR" = paste0(
format(round(colMeans(CCR), 3), 3),
" (",
format(round(apply(CCR, 2, sd), 3), 3),
")"
)
), by = "Method") %>%
# aRand
left_join(data.frame(
Method = colnames(aRand),
"aRand" = paste0(
format(round(colMeans(aRand), 3), 3),
" (",
format(round(apply(aRand, 2, sd), 3), 3),
")"
)
), by = "Method")
res <- cbind(res, res2[, -1])
}
}
res
# save(res, file = "RData/2022_0127.RData")
save(clust_list, res, file = "RData/2022_0926.RData")
length(clust_list)
length(clust_list[[1]])
length(clust_list[[1]][[1]])