#' Jackstraw for the User-Defined Clustering Algorithm
#'
#' Test the cluster membership using a user-defined clustering algorithm
#'
#' The clustering algorithms 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.
#'
#' The user is expected to explore the data with a given clustering algorithm and
#' determine the number of clusters \code{k}.
#' Furthermore, provide \code{cluster} and \code{centers} as given by applying \code{algorithm} onto \code{dat}.
#' The rows of \code{centers} correspond to \code{k} clusters, as well as available levels in \code{cluster}.
#' This function allows you to specify a parametric distribution of a noise term. It is an experimental feature.
#'
#' @param dat a data matrix with \code{m} rows as variables and \code{n} columns as observations.
#' @param k a number of clusters.
#' @param cluster a vector of cluster assignments.
#' @param centers a matrix of all cluster centers.
#' @param algorithm a clustering algorithm to use, where an output must include `cluster` and `centers`. For exact specification, see \code{\link[stats]{kmeans}}.
#' @param noise specify a parametric distribution to generate a noise term. If \code{NULL}, a non-parametric jackstraw test is performed.
#' @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 pool a logical specifying to pool the null statistics across all clusters. By default, \code{TRUE}.
#' @param verbose a logical specifying to print the computational progress. By default, \code{FALSE}.
#' @param ... additional, optional arguments to `algorithm`.
#'
#' @return \code{jackstraw_cluster} 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}
#'
#' @export
jackstraw_cluster <- function(
dat,
k,
cluster,
centers,
algorithm = function(x, centers, ...) stats::kmeans(x, centers, ...),
s = 1,
B = 1000,
center = TRUE,
noise = NULL,
covariate = NULL,
pool = TRUE,
verbose = FALSE,
...
) {
# check mandatory data
if ( missing( dat ) )
stop( '`dat` is required!' )
if ( missing( k ) )
stop( '`k` is required!' )
if ( missing( cluster ) )
stop( '`cluster` is required!' )
if ( missing( centers ) )
stop( '`centers` is required!' )
if ( !is.matrix( dat ) )
stop( '`dat` must be a matrix!' )
m <- nrow(dat)
n <- ncol(dat)
# check additional dimensions
if ( length(cluster) != m )
stop( 'Length of `cluster` (', length(cluster), ') does not equal numbber of rows of data (', m , ').')
if ( length(unique(cluster)) != k )
stop( 'Number of clusters in `cluster` (', length(unique(cluster)), ') does not equal `k` (, k, )' )
if ( nrow(centers) != k )
stop( 'Number of rows in `centers` (', nrow(centers), ') does not equal `k` (', k, ')' )
if ( ncol(centers) != n )
stop( 'Number of columns in `centers` (', ncol(centers), ') does not equal number of columns in `dat` (', n, ')' )
# 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 )
}
}
algorithm <- match.fun(algorithm)
# compute the observed
# statistics between observed
# variables and cluster centers
F.obs <- vector("numeric", m)
for (i in 1:k) {
F.obs[cluster == i] <- FSTAT(
dat[cluster == i, , drop = FALSE],
LV = t( centers[i, , drop = FALSE] ),
covariate = covariate
)$fstat
}
if (!is.null(noise)) {
noise <- match.fun(noise)
if (verbose)
message("The distribution for the noise term is specified; performing the parametric jackstraw test.")
}
if (verbose)
cat(paste0("\nComputating null statistics (", B, " total iterations): "))
# set-up empty matrices for
# null statistics
F.null <- vector("list", length = k)
for (j in 1:B) {
if ( verbose )
cat(paste(j, " "))
jackstraw.dat <- dat
# randomly choose s variables
# to permute
ind <- sample.int( m, s )
if (!is.null(noise)) {
jackstraw.dat[ind, ] <- matrix(noise(n * s), nrow = s, ncol = n)
} else {
jackstraw.dat[ind, ] <- apply(
dat[ind, , drop = FALSE],
1,
function(x) sample(x, replace = TRUE)
)
}
if (center) {
jackstraw.dat[ind, ] <- t(scale(
t( jackstraw.dat[ ind, , drop = FALSE ] ),
center = TRUE,
scale = FALSE
))
}
# re-cluster the jackstraw data
recluster <- algorithm(
jackstraw.dat,
centers = centers,
...
)
for (i in 1:k) {
ind.i <- intersect( ind, which(recluster$cluster == 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(recluster$centers[i, , drop = FALSE]),
covariate = covariate
)$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]]) == 0)
stop( "There are no null statistics for the cluster ", i, ". Check if B is large enough, clusters stable, and k selected appropriately. Also consider running the algorithm with the pool option." )
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[cluster == i] <- empPvals( F.obs[ cluster == 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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