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#' Non-Parametric Jackstraw for K-means Clustering using RcppArmadillo
#'
#' Test the cluster membership for K-means clustering, using K-means++ initialization
#'
#' K-means clustering assign \code{m} rows into \code{K} clusters. This function enable statistical
#' evaluation if the cluster membership is correctly assigned. Each of \code{m} p-values refers to
#' the statistical test of that row with regard to its assigned cluster.
#' Its resampling strategy accounts for the over-fitting characteristics due to direct computation of clusters from the observed data
#' and protects against an anti-conservative bias.
#'
#' Generally, it functions identical to \code{jackstraw_kmeans}, but this uses \code{ClusterR::KMeans_rcpp} instead of \code{stats::kmeans}.
#' A speed improvement is gained by K-means++ initialization and \code{RcppArmadillo}. If the input data is still too large,
#' consider using \code{jackstraw_MiniBatchKmeans}.
#'
#' The input data (\code{dat}) must be of a class `matrix`.
#'
#' @param dat a matrix with \code{m} rows as variables and \code{n} columns as observations.
#' @param kmeans.dat an output from applying \code{ClusterR::KMeans_rcpp} onto \code{dat}.
#' @param s a number of ``synthetic'' null variables. Out of \code{m} variables, \code{s} variables are independently permuted.
#' @param B a number of resampling iterations.
#' @param center a logical specifying to center the rows. By default, \code{TRUE}.
#' @param covariate a model matrix of covariates with \code{n} observations. Must include an intercept in the first column.
#' @param verbose a logical specifying to print the computational progress. By default, \code{FALSE}.
#' @param pool a logical specifying to pool the null statistics across all clusters. By default, \code{TRUE}.
#' @param ... optional arguments to control the k-means clustering algorithm (refers to \code{ClusterR::KMeans_rcpp}).
#'
#' @return \code{jackstraw_kmeanspp} returns a list consisting of
#' \item{F.obs}{\code{m} observed F statistics between variables and cluster centers.}
#' \item{F.null}{F null statistics between null variables and cluster centers, from the jackstraw method.}
#' \item{p.F}{\code{m} p-values of membership.}
#'
#' @author Neo Christopher Chung \email{nchchung@@gmail.com}
#' @references Chung (2020) Statistical significance of cluster membership for unsupervised evaluation of cell identities. Bioinformatics, 36(10): 3107–3114 \doi{10.1093/bioinformatics/btaa087}
#' @examples
#' \dontrun{
#' library(ClusterR)
#' dat = t(scale(t(Jurkat293T), center=TRUE, scale=FALSE))
#' kmeans.dat <- KMeans_rcpp(dat, clusters = 10, num_init = 1,
#' max_iters = 100, initializer = 'kmeans++')
#' jackstraw.out <- jackstraw_kmeanspp(dat, kmeans.dat)
#' }
#'
#' @export
jackstraw_kmeanspp <- function(
dat,
kmeans.dat,
s = NULL,
B = NULL,
center = TRUE,
covariate = NULL,
verbose = FALSE,
pool = TRUE,
...
) {
# check mandatory data
if ( missing( dat ) )
stop( '`dat` is required!' )
if ( missing( kmeans.dat ) )
stop( '`kmeans.dat` is required!' )
if ( !is.matrix( dat ) )
stop( '`dat` must be a matrix!' )
if ( !methods::is( kmeans.dat, "k-means clustering" ) )
stop( "`kmeans.dat` must be an object of class `k-means clustering`. See ?ClusterR::KMeans_rcpp." )
m <- nrow(dat)
n <- ncol(dat)
# if there are covariates, the dimensions must agree
# covariate can be either a vector or a matrix, test both cases
if ( !is.null( covariate ) ) {
if ( is.matrix( covariate ) ) {
if ( nrow( covariate ) != n )
stop( 'Matrix `covariate` must have `n` rows, has: ', nrow( covariate ), ', expected: ', n )
} else {
if ( length( covariate ) != n )
stop( 'Vector `covariate` must have `n` elements, has: ', length( covariate ), ', expected: ', n )
}
}
if (is.null(s)) {
s <- round(m/10)
if (verbose)
message( "A number of null variables (s) to be permuted is not specified: s=round(0.10*m)=", s, "." )
}
if (is.null(B)) {
B <- round(m * 10/s)
if (verbose)
message( "A number of resampling iterations (B) is not specified: B=round(m*10/s)=", B, "." )
}
k <- nrow(kmeans.dat$centroids)
if (verbose)
cat(paste0("\nComputating null statistics (", B, " total iterations): "))
# compute the observed
# statistics between rows and
# cluster centers
F.obs <- vector("numeric", m)
for (i in 1:k) {
F.obs[kmeans.dat$clusters == i] <- FSTAT(
dat[kmeans.dat$clusters == i, , drop = FALSE],
LV = t(kmeans.dat$centroids[i, , drop = FALSE]),
covariate = covariate
)$fstat
}
# set-up empty matrices for
# null statistics
F.null <- vector("list", length = k)
for (j in 1:B) {
if (verbose)
cat(paste(j, " "))
jackstraw.dat <- dat
# randomly choose s variables
# to permute
ind <- sample.int( m, s )
jackstraw.dat[ind, ] <- apply(
dat[ind, , drop = FALSE],
1,
function(x) sample(x, replace = TRUE)
)
if (center)
jackstraw.dat[ind, ] <- t(scale(
t( jackstraw.dat[ ind, , drop = FALSE ] ),
center = TRUE,
scale = FALSE
))
# re-cluster the jackstraw data
kmeans.null <- ClusterR::KMeans_rcpp(jackstraw.dat,clusters=k,
CENTROIDS = kmeans.dat$centroids,
...)
for (i in 1:k) {
ind.i <- intersect(ind,
which(kmeans.null$clusters ==
i))
if (length(ind.i) >
0) {
F.null[[i]] <- c(F.null[[i]],
as.vector(FSTAT(dat = jackstraw.dat[ind.i,
, drop = FALSE],
LV = t(kmeans.null$centroids[i,
, drop = FALSE]),
covariate = covariate)$fstat))
}
}
}
# compute p-values
p.F <- vector("numeric", m)
if(pool) {
p.F <- empPvals( F.obs, unlist( F.null ) )
} else {
for (i in 1:k) {
# warn about a relatively low
# number of null statistics
if (length(F.null[[i]]) < (B * s/k * 0.1)) {
warning( "The number of empirical null statistics for the cluster [", i, "] is [", length(F.null[[i]]), "].")
}
p.F[ kmeans.dat$cluster == i] <- empPvals( F.obs[kmeans.dat$clusters == i], F.null[[i]] )
}
}
return(
list(
call = match.call(),
F.obs = F.obs,
F.null = F.null,
p.F = p.F
)
)
}
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