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#' Run hierarchical clustering following by a group-lasso on all the different partition.
#'
#' @author Quentin Grimonprez
#' @param X matrix of size n*p
#' @param y vector of size n
#' @param hc output of \code{\link{hclust}} function. If not provided, \code{\link{hclust}} is run with ward.D2 method
#' @param lambda lambda values for group lasso. If not provided, the function generates its own values of lambda
#' @param weightLevel a vector of size p for each level of the hierarchy. A zero indicates that the level will be ignored. If not provided, use 1/(height between 2 successive levels)
#' @param weightSizeGroup a vector of size 2*p-1 containing the weight for each group. Default is the square root of the size of each group
#' @param intercept should an intercept be included in the model ?
#' @param verbose print some information
#' @param ... Others parameters for \code{\link{gglasso}} function
#'
#' @return a HCgglasso object containing :
#' \describe{
#' \item{lambda}{lambda values}
#' \item{b0}{intercept values for \code{lambda}}
#' \item{beta}{A list containing the values of estimated coefficients for each values of \code{lambda}}
#' \item{var}{A list containing the index of selected variables for each values of \code{lambda}}
#' \item{group}{A list containing the values index of selected groups for each values of \code{lambda}}
#' \item{nVar}{A vector containing the number of non zero coefficients for each values of \code{lambda}}
#' \item{nGroup}{A vector containing the number of non zero groups for each values of \code{lambda}}
#' \item{structure}{A list containing 3 vectors. var : all variables used. group : associated groups.
#' weight : weight associated with the different groups.
#' level : for each group, the corresponding level of the hierarchy where it appears and disappears. 3 indicates the level with a partition of 3 groups.}
#' \item{time}{computation time}
#' \item{dim}{dimension of \code{X}}
#' \item{hc}{Output of hierarchical clustering}
#' \item{call}{Code executed by user}
#' }
#'
#'
#' @examples
#' set.seed(42)
#' X = simuBlockGaussian(50,12,5,0.7)
#' y = drop(X[,c(2,7,12)]%*%c(2,2,-2)+rnorm(50,0,0.5))
#' res = HCgglasso(X,y)
#'
#' @seealso \link{cv.HCgglasso}, \link{stability.HCgglasso}, \link{listToMatrix}, \link{predict.HCgglasso}, \link{coef.HCgglasso}, \link{plot.cv.HCgglasso}
#'
#' @export
HCgglasso <- function(X, y, hc = NULL, lambda = NULL, weightLevel = NULL, weightSizeGroup = NULL, intercept = TRUE, verbose = FALSE,...)
{
#check parameters
.checkParameters(X, y, hc, lambda, weightLevel, weightSizeGroup, intercept, verbose)
# define some usefull variables
n = nrow(X)
p = ncol(X)
tcah = rep(NA,3)
######## hierarchical clustering
#if no hc output provided, we make one
if(is.null(hc))
{
if(verbose)
cat("Computing hierarchical clustering...")
t1 = proc.time()
d = dist(t(X))
hc = fastcluster::hclust(d, method = "ward.D2")
t2 = proc.time()
tcah = t2-t1
if(verbose)
cat("DONE in ",tcah[3],"s\n")
}
######## compute weight, active variables and groups
if(verbose)
cat("Preliminary step...")
t1 = proc.time()
prelim = preliminaryStep(hc, weightLevel, weightSizeGroup)
#duplicate data
Xb = X[,prelim$var]
t2 = proc.time()
if(verbose)
cat("DONE in ",(t2-t1)[3],"s\n")
######## group lasso
if(verbose)
cat("Computing group-lasso...")
t1 = proc.time()
res = gglasso(Xb,y,prelim$group,pf=prelim$weight,lambda=lambda,intercept=intercept,...)
t2 = proc.time()
tgglasso = t2-t1
if(verbose)
cat("DONE in ",tgglasso[3],"s\n")
######## create output object
res2 = list()
res2$lambda = res$lambda
non0 = apply(res$beta,2,FUN=function(x){which(x!=0)})
res2$var = lapply(non0,FUN=function(x){prelim$var[x]})
res2$nVar = sapply(res2$var,FUN=function(x){length(unique(x))})
res2$group = lapply(non0,FUN=function(x){prelim$group[x]})
res2$nGroup = sapply(res2$group,FUN=function(x){length(unique(x))})
res2$beta = lapply(1:length(res$lambda),FUN=function(x){res$beta[non0[[x]],x]})
res2$b0 = res$b0
res2$structure = prelim
res2$dim = dim(X)
res2$hc = hc
res2$time = c(tcah[3],tgglasso[3])
res2$call = match.call()
names(res2$time) = c("hclust","glasso")
class(res2) = "HCgglasso"
return(res2)
}
#
# compute the mnimimum weight of each group
#
# @param hc outup of hclust function
#
levelMinWeight <- function(hc, weightLevel = NULL)
{
p=length(hc$order)
# highest level at which cluster are seen for the last time
# the p first are the single variables and the p-2 next are the cluster in the order of apparition
lvSingle = sapply((-1):(-p),FUN=function(i){which(hc$merge==i)%%(p-1)})
lvCluster = sapply(1:(p-2),FUN=function(i){which(hc$merge==i)%%(p-1)})
lvCluster[lvCluster==0] = p-1
lvCluster = c(lvCluster,p)
# branch length. The first one is associated with the partition in 2 clusters
if(is.null(weightLevel))
weightLevel = c(0,sqrt(1/diff(hc$height)),0)
# minimum weight of levels of each cluster
minLevelWeight = rep(0, 2*p-1)
# minimal weight of single variable
minLevelWeight[1:p] = sapply(lvSingle,FUN=function(i){ind=(weightLevel[1:i]!=0);ifelse(sum(ind),min(weightLevel[1:i][ind]),0)})#If there is only 0, we return 0, else we return the min > 0
# mininmal weight for groups of 2 and more variables
minLevelWeight[(p+1):(2*p-1)] = sapply(1:length(lvCluster),FUN=function(i){ind=(weightLevel[(i+1):lvCluster[i]]!=0);ifelse(sum(ind),min(weightLevel[(i+1):lvCluster[i]][ind]),0)})
return(minLevelWeight)
}
#
# @param hc output of hierarchical clustering
#
# @return A matrix with 2 rows, the first row contains the level at which appears each group during the hierarchical clustering
# the second row contains the last level where the group is present. The p first columns represent single variable, the other the cluster in the order
# they appear in the hierarchical clustering
#
levelGroupHC <- function(hc)
{
# Number of variables in the HC
p <- nrow(hc$merge) + 1
# Output matrix
startend <- matrix(nrow = 2, ncol = 2*p-1)
# Level where first appeared each group (j = level containg j groups)
startend[1,] = c(rep(p,p),(p-1):1)
# Find the level where each group diassapear
for(i in 1:nrow(hc$merge))
{
for(j in 1:2)
{
# a negative number indicates a single variable
if(hc$merge[i,j] < 0)
{
startend[2,abs(hc$merge[i,j])] = p - i + 1
}
else # a positive number indicates a cluster of 2 or more variables
{
startend[2,p + hc$merge[i,j]] = p - i + 1
}
}# end for col os hs$merge
}# end for row of hc$merge
# Last group containing all variables
startend[2,ncol(startend)] = 1
rownames(startend) <- c("start", "end")
return(startend)
}
#
# preliminary step for HCgglasso. Compute weight, active variables and groups
#
preliminaryStep <- function(hc, weightLevel = NULL, weightSizeGroup = NULL)
{
#find unique groups of the hclust output
uni = uniqueGroupHclust(hc)
######## Compute weights
#compute the minimal weight of partition
weightLevelGroup = levelMinWeight(hc, weightLevel)
# CORRECTION : If weight is infinite, we change in 0 and it will be ignored
weightLevelGroup[which(is.infinite(weightLevelGroup))] = 0
#weight for group size
if(is.null(weightSizeGroup))
weightSizeGroup = as.vector(sqrt(table(uni$indexGroup)))
#weight for each group
weight = weightSizeGroup*weightLevelGroup
# new weight without ignored groups
weightb = weight
ignoredGroup = which(weight==0)#groups with 0 weights
weightb = weightb[-ignoredGroup]#we delete zeros weight
#level of hc associated to groups
p = length(hc$order)
lv = levelGroupHC(hc)
lv = lv[,-ignoredGroup]
######## Create data for gglasso
varToDelete = uni$indexGroup%in%ignoredGroup
var = uni$varGroup[!varToDelete]
group = uni$indexGroup[!varToDelete]
#group must be consecutively numbered 1,2,3,...
#need a correction when some groups have to be ignored
if(length(ignoredGroup)>0)
{
difNumber = rep(0,length(group))
for(i in 1:length(ignoredGroup))
{
ind = which(group>ignoredGroup[i])
difNumber[ind] = difNumber[ind]-1
}
group = group + difNumber
}
return(list(group=group,var=var,weight=weightb,level=lv))
}
# check parameters of HCgglasso function
.checkParameters <- function(X, y, hc, lambda, weightLevel, weightSizeGroup, intercept, verbose)
{
#check X
if(!is.matrix(X))
stop("X has to be a matrix.")
if(any(is.na(X)))
stop("Missing values in X not allowed.")
if(!is.numeric(X))
stop("X has to be a matrix of real.")
#check y
if(!is.numeric(y))
stop("y has to be a vector of real.")
if(any(is.na(y)))
stop("Missing values in y not allowed.")
#check if X and y are compatible
if(nrow(X)!=length(drop(y)))
stop("The length of y and the number of rows of X don't match.")
#check hc
if(!is.null(hc))
{
#check if hc is a hclust object
if(class(hc)!="hclust")
stop("hc must be an hclust object.")
#check if hc and X are compatible
if(length(hc$order)!=ncol(X))
stop("hc is not a clustering of the p covariates of X.")
}
#check if lambda is a vector of positive real
if(!is.null(lambda))
{
if(!is.numeric(lambda))
stop("lambda must be a vector of positive real.")
if(any(lambda < 0))
stop("lambda must be a vector of positive real.")
}
#check if weightLevel is a vector of positive real
if(!is.null(weightLevel))
{
if(!is.numeric(weightLevel))
stop("weightLevel must be a vector of positive real.")
if(length(weightLevel)!=ncol(X))
stop("weightLevel must have the same length as the number of columns of matrix X.")
if(any(weightLevel < 0))
stop("weightLevel must be a vector of positive real.")
}
#check if weightSizeGroup is a vector of positive real
if(!is.null(weightSizeGroup))
{
if(!is.numeric(weightSizeGroup))
stop("weightSizeGroup must be a vector of real.")
if(any(weightSizeGroup < 0))
stop("weightSizeGroup must be a vector of positive real.")
}
#check if intercept is a boolean
if(length(intercept)!=1)
stop("intercept must be a boolean.")
if(!is.logical(intercept))
stop("intercept must be a boolean.")
#check if verbose is a boolean
if(length(verbose)!=1)
stop("verbose must be a boolean.")
if(!is.logical(verbose))
stop("verbose must be a boolean.")
invisible(return(NULL))
}
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