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#'Plot of a Dirichlet process mixture of skew t-distribution partition
#'
#'@param z data matrix \code{d x n} with \code{d} dimensions in rows
#'and \code{n} observations in columns.
#'
#'@param c allocation vector of length \code{n} indicating which observation belongs to which
#'clusters.
#'
#'@param alpha current value of the DP concentration parameter.
#'
#'@param U_SS a list containing \code{"xi"}, \code{"psi"}, \code{"S"}, and \code{"df"}.
#'
#'@param i current MCMC iteration number.
#'
#'@param dims2plot index vector, subset of \code{1:d} indicating which dimensions should be drawn.
#'Default is all of them.
#'
#'@param ellipses a logical flag indicating whether ellipses should be drawn around clusters. Default
#'is \code{TRUE} if only 2 dimensions are plotted, \code{FALSE} otherwise.
#'
#'@param gg.add
#'A list of instructions to add to the \code{ggplot2} instruction (see \code{\link[ggplot2]{gg-add}}).
#'Default is \code{list(theme())}, which adds nothing to the plot.
#'
#'@param nbsim_dens number of simulated points used for computing clusters density contours in 2D
#'plots. Default is \code{1000} points.
#'
#'@param nice logical flag changing the plot looks. Default is \code{FALSE}.
#'
#'@author Boris Hejblum
#'
#'@import ggplot2
#'@import reshape2
#'@importFrom truncnorm rtruncnorm
#'@importFrom stats dnorm pnorm rgamma rnorm
#'
#' @export
plot_DPMst <- function(z, c, i="", alpha="?", U_SS,
dims2plot=1:nrow(z),
ellipses=ifelse(length(dims2plot)<3,TRUE,FALSE),
gg.add=list(theme()), nbsim_dens=1000, nice=FALSE){
mean_sn01 <- (stats::dnorm(0)-stats::dnorm(Inf))/(stats::pnorm(Inf)-stats::pnorm(0))
z <- z[dims2plot,]
n <- ncol(z)
p <- nrow(z)
m <- numeric(n) # number of observations in each cluster
m[unique(c)] <- table(c)[as.character(unique(c))]
fullCl <- which(m!=0)
U_xi2plot=sapply(U_SS, "[[", "xi")
U_psi2plot=sapply(U_SS, "[[", "psi")
U_Sigma2plot=lapply(U_SS, "[[", "S")
U_nu2plot=lapply(U_SS, "[[", "df")
U_SS2plot <- U_SS
U_mu2plot <- U_xi2plot + U_psi2plot*mean_sn01
rownames(U_mu2plot) <- rownames(z)
zClusters <- factor(c, levels=as.character(fullCl), ordered=TRUE)
expK <- ifelse(is.numeric(alpha), round(alpha*(digamma(alpha+n)-digamma(alpha))), NA)
alpha2print <- ifelse(is.numeric(alpha), formatC(alpha, digits=2), alpha)
if(p>2){
zDplot <- melt(cbind.data.frame("ID"=as.character(1:n),
t(z),
"Cluster"=zClusters
),
id.vars=c("ID", "Cluster"),
variable.name = "dimensionX",
value.name="X"
)
zDplotfull <- zDplot
zDplotfull$Y <- zDplot$X
zDplotfull$dimensionY <- zDplot$dimensionX
lev <- as.character(1:length(levels(zDplot$dimensionX)))
for(l in 2:length(lev)){
move <- which(as.numeric(zDplot$dimensionX)<l)
zDplottemp <- rbind.data.frame(zDplot[-move,], zDplot[move,])
zDplottemp$Y <- zDplot$X
zDplottemp$dimensionY <- zDplot$dimensionX
zDplotfull <- rbind.data.frame(
zDplotfull, zDplottemp)
}
UDplot <- melt(cbind.data.frame(t(U_mu2plot),
"Cluster"=factor(as.character(fullCl),
levels=as.character(fullCl),
ordered=TRUE)
),
id.vars=c("Cluster"),
variable.name = "dimensionX",
value.name="X"
)
UDplotfull <- UDplot
UDplotfull$Y <- UDplotfull$X
UDplotfull$dimensionY <- UDplotfull$dimensionX
lev <- levels(UDplotfull$dimensionX)
for(l in 2:length(lev)){
move <- which(as.numeric(UDplotfull$dimensionX)<l)
UDplottemp <- rbind.data.frame(UDplotfull[-move,], UDplotfull[move,])
UDplottemp$Y <- UDplotfull$X
UDplottemp$dimensionY <- UDplotfull$dimensionX
UDplotfull <- rbind.data.frame(
UDplotfull, UDplottemp)
}
p <- (ggplot(zDplotfull) + theme_bw()
+ facet_grid(dimensionY~dimensionX, scales="free")
+ geom_point(aes_string(x="X", y="Y", colour="Cluster"),
data=zDplotfull, alpha=0.15, size=2/(0.4*log(n)))
# + geom_polygon(aes_string(x="X", y="Y", fill="Cluster", colour="Cluster"),
# data=ellipse95, size=0.5, linetype=2, colour="black", alpha=.3)
+ geom_point(aes_string(x="X", y="Y", fill="Cluster"),
data=UDplotfull, alpha = 0.5, shape=22, size=5/(0.3*log(n)))
+ ggtitle(paste(n, " obs.",
"\niteration ", i, " : ",
length(fullCl)," clusters",
"\nexpected number of clusters: ", expK,
" (alpha = ", alpha2print, ")",
sep=""))
+ scale_fill_viridis_d(guide=FALSE) #, option = "magma")
#+ scale_color_viridis_d(option = "magma")
+ guides(colour=guide_legend(override.aes = list(linetype=0, size=6, alpha=1)))#, shape=15)))
+ xlab("") + ylab("")
+ theme(axis.text.x = element_text(angle = 60, hjust = 1))
)
}else{
z2plot <- cbind.data.frame("D1"=z[1,],"D2"=z[2,],"Cluster"=zClusters)
U2plot <- cbind.data.frame("D1"=U_mu2plot[1,],
"D2"=U_mu2plot[2,],
"Cluster"=factor(as.character(fullCl),
levels=as.character(fullCl),
ordered=TRUE)
)
xi2plot <- cbind.data.frame("D1"=U_xi2plot[1,],
"D2"=U_xi2plot[2,],
"Cluster"=factor(as.character(fullCl),
levels=as.character(fullCl),
ordered=TRUE)
)
U2plot$Center="sampled mean"
xi2plot$Center="xi param"
if(!nice){
p <- (ggplot(z2plot) + theme_bw()
+ geom_point(aes_string(x="D1", y="D2", colour="Cluster", fill="Cluster"), alpha=0.7,
data=z2plot, size=2/(0.3*log(n)))
+ scale_alpha_continuous(guide=FALSE)
#+ scale_fill_discrete(guide=FALSE)
+ guides(colour = guide_legend(override.aes = list(size = 6, alpha=1)))
+ ggtitle(paste(n, " obs.",
"\niteration ", i, " : ",
length(fullCl)," clusters",
"\nexpected number of clusters: ", expK,
" (alpha = ", alpha2print, ")",
sep=""))
)
#empirical mean of the clusters
zmean2plot<- cbind.data.frame(D1=tapply(X=z2plot[,1], INDEX=z2plot$Cluster, FUN=mean),
D2=tapply(X=z2plot[,2], INDEX=z2plot$Cluster, FUN=mean)
)
zmean2plot <- cbind.data.frame(zmean2plot, Cluster=rownames(zmean2plot))
zmean2plot$Center="observed mean"
}else{
p <- (ggplot(z2plot) + theme_bw()
+ geom_point(aes_string(x="D1", y="D2", colour="Cluster", shape="Cluster", fill="Cluster"), alpha=min(0.9, max(0.9*6/n^0.3, 0.3)),
data=z2plot, size=2)
+ scale_alpha_continuous(guide=FALSE)
)
}
if(ellipses){
simuDens <- NULL
for(g in 1:length(fullCl)){
glabel <- levels(zClusters)[g]
#gind <- as.numeric(glabel)
w <- stats::rgamma(n=nbsim_dens, shape=U_nu2plot[[g]]/2, rate=U_nu2plot[[g]]/2)
ltnz <- truncnorm::rtruncnorm(n=nbsim_dens, a=0, sd=1/sqrt(w))
eps <- t(sapply(w, function(a){matrix(stats::rnorm(2), ncol=2)%*%chol(U_Sigma2plot[[g]]/a)}))
#eps <- matrix(NA, nrow=nbsim_dens, ncol=2)
#for(i in 1:nbsim_dens){
# eps[i,] <- matrix(rnorm(2), ncol=2)%*%chol(U_Sigma2plot[[g]]/w[i])
#}
simuDenstemp <- data.frame("D1"=U_xi2plot[1,g]+U_psi2plot[1,g]*ltnz+eps[,1],
"D2"=U_xi2plot[2,g]+U_psi2plot[2,g]*ltnz+eps[,2],
"Cluster"=rep(glabel, nbsim_dens))
simuDens <- rbind.data.frame(simuDens, simuDenstemp)
}
simuDens$Type <- "DensContour"
p <- (p
+ stat_density2d(data=simuDens, aes_string(x="D1", y="D2", colour="Cluster", linetype="Type"))
+ scale_linetype_manual(values=c(1),
labels=c("simulations derived\n from sampled parameters"),
name="Density contour")
+ guides(linetype=guide_legend(override.aes = list(color="black")),
colour=guide_legend(override.aes = list(linetype=0, size=6, alpha=1, shape=15)))
)
}
if(nice){
if(length(unique(z2plot$Cluster) < 6)){
p <- (p
+ scale_shape_manual(values=c(21:(20+length(unique(z2plot$Cluster)))))
)
}else{
p <- (p
+ scale_shape_manual(values=rep(21,length(unique(z2plot$Cluster))))
)
}
p <- (p
+ guides(colour=guide_legend(override.aes = list(size = 4, alpha=0.8, linetype=0)))
)
}else{
p <- (p + geom_point(aes_string(x="D1", y="D2", fill="Cluster", shape="Center"),
data=zmean2plot, size=5)
+ geom_point(aes_string(x="D1", y="D2", fill="Cluster", shape="Center"),
data=U2plot, size=5)
+ geom_point(aes_string(x="D1", y="D2", fill="Cluster", shape="Center"),
data=xi2plot, size=5)
+ scale_fill_viridis_d(guide=FALSE)
+ scale_shape_manual(values=c(24,22,23),
breaks=c("observed mean", "sampled mean", "xi param"),
labels=c("observed mean", "sampled mean", "xi param"),
name="Center")
)
}
}
for (a in gg.add) {
p <- p + a
}
print(p)
}
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