mlcc.bic.R

#' Multiple Latent Components Clustering - Subspace clustering with automatic
#' estimation of number of clusters and their dimension
#'
#' This function is an implementation of Multiple Latent Components Clustering
#' (MLCC) algorithm which clusteres quantitative variables into a number, chosen
#' using mBIC, of groups. For each considered number of clusters in
#' \emph{numb.clusters} \code{\link{mlcc.reps}} function is called. It invokes
#' K-means based algorithm (\code{\link{mlcc.kmeans}}) finding local minimum of
#' mBIC, which is run a given number of times (\emph{numb.runs}) with different
#' initializations. The best partition is choosen with mBIC (see
#' \code{\link{mlcc.reps}} function).
#'
#' @param X A data frame or a matrix with only continuous variables.
#' @param numb.clusters A vector, numbers of clusters to be checked.
#' @param numb.runs An integer, number of runs (initializations) of
#'   \code{\link{mlcc.kmeans}}.
#' @param stop.criterion An integer, if an iteration of
#'   \code{\link{mlcc.kmeans}} algorithm makes less changes in partitions than
#'   \code{stop.criterion}, \code{\link{mlcc.kmeans}} stops.
#' @param max.iter An integer, maximum number of iterations of the loop in
#'   \code{\link{mlcc.kmeans}} algorithm.
#' @param max.dim An integer, if estimate.dimensions is FALSE then max.dim is
#'   dimension of each subspace. If estimate.dimensions is TRUE then subspaces
#'   dimensions are estimated from the range [1, max.dim].
#' @param scale A boolean, if TRUE (value set by default) then variables in
#'   dataset are scaled to zero mean and unit variance.
#' @param numb.cores An integer, number of cores to be used, by default all
#'   cores are used.
#' @param greedy A boolean, if TRUE (value set by default) the clusters are
#'   estimated in a greedy way - first local minimum of mBIC is chosen.
#' @param estimate.dimensions A boolean, if TRUE (value set by default)
#'   subspaces dimensions are estimated.
#' @param verbose A boolean, if TRUE plot with mBIC values for different numbers
#'   of clusters is produced and values of mBIC, computed for every number of
#'   clusters and subspaces dimensions, are printed (value set by default is
#'   FALSE).
#' @param flat.prior A boolean, if TRUE then, instead of an informative prior
#'   that takes into account number of models for a given number of clusters,
#'   flat prior is used.
#' @param show.warnings A boolean, if set to TRUE all warnings are displayed,
#'   default value is FALSE.
#' @export
#' @return An object of class mlcc.fit consisting of \item{segmentation}{a
#'   vector containing the partition of the variables} \item{BIC}{numeric, value
#'   of mBIC} \item{subspacesDimensions}{a list containing dimensions of the
#'   subspaces} \item{nClusters}{an integer, estimated number of clusters}
#'   \item{factors}{a list of matrices, basis for each subspace}
#'   \item{all.fit}{a list of segmentation, mBIC, subspaces dimension for all
#'   numbers of clusters considered for an estimated subspace dimensions}
#'   \item{all.fit.dims}{a list of lists of segmentation, mBIC, subspaces
#'   dimension for all numbers of clusters and subspaces dimensions considered}
#' @examples
#' \donttest{
#' sim.data <- data.simulation(n = 50, SNR = 1, K = 3, numb.vars = 50, max.dim = 3)
#' mlcc.res <- mlcc.bic(sim.data$X, numb.clusters = 1:5, numb.runs = 20,
#' numb.cores = 1, verbose = TRUE)
#' show.clusters(sim.data$X, mlcc.res$segmentation)
#' }
mlcc.bic <- function(X, numb.clusters = 1:10, numb.runs = 30, stop.criterion = 1,
                     max.iter = 30, max.dim = 4, scale = TRUE, numb.cores = NULL,
                     greedy = TRUE, estimate.dimensions = TRUE,
                     verbose = FALSE, flat.prior = FALSE, show.warnings = FALSE) {
  if (is.data.frame(X)) {
    warning("X is not a matrix. Casting to matrix.")
    X <- as.matrix(X)
  }
  if (any(is.na(X))) {
    warning("Missing values are imputed by the mean of the variable")
    X[is.na(X)] <- matrix(apply(X, 2, mean, na.rm = TRUE),
      ncol = ncol(X), nrow = nrow(X),
      byrow = TRUE
    )[is.na(X)]
  }
  if (any(!sapply(X, is.numeric))) {
    auxi <- NULL
    for (j in 1:ncol(X)) {
      if (!is.numeric(X[, j])) {
        auxi <- c(auxi, j)
      }
    }
    stop(paste("\nThe following variables are not quantitative: ", auxi))
  }
  if (scale) {
    X <- scale(X)
  }
  n <- nrow(X)
  p <- ncol(X)
  greedy.stop <- max(numb.clusters)
  results <- list()
  if (verbose) {
    cat("Number of clusters \t BIC \n")
  }

  for (i in 1:length(numb.clusters)) {
    number.clusters <- numb.clusters[i]
    MLCC.fit <- mlcc.reps(
      X = X, numb.clusters = number.clusters, numb.runs = numb.runs,
      max.dim = max.dim, scale = FALSE, numb.cores = numb.cores, estimate.dimensions = estimate.dimensions,
      flat.prior = flat.prior, show.warnings = show.warnings
    )

    results[[i]] <- list(
      segmentation = MLCC.fit$segmentation, BIC = MLCC.fit$BIC,
      subspacesDimensions = lapply(MLCC.fit$basis, ncol), nClusters = number.clusters,
      factors = MLCC.fit$basis
    )
    if (greedy & (i > 2)) {
      if ((results[[i]]$BIC < results[[i - 1]]$BIC) & (results[[i - 2]]$BIC <
        results[[i - 1]]$BIC)) {
        greedy.stop <- i
        if (verbose) {
          cat(paste("       ", number.clusters, "        ", formatC(results[[i]]$BIC,
            digits = ceiling(log(abs(results[[i]]$BIC), 10))
          ), "\n"))
        }
        break
      }
    }
    if (verbose) {
      cat(paste("       ", number.clusters, "        ", formatC(results[[i]]$BIC,
        digits = ceiling(log(abs(results[[i]]$BIC), 10))
      ), "\n"))
    }
  }
  BICs <- lapply(results, function(res) res$BIC)
  if (verbose) {
    plot(numb.clusters[1:greedy.stop], BICs,
      type = "b", xaxt = "n", ylab = "BIC",
      xlab = "Number of clusters"
    )
    axis(side = 1, labels = numb.clusters[1:greedy.stop], at = numb.clusters[1:greedy.stop])
  }
  result <- results[[which.max(BICs)]]
  result$factors <- lapply(1:result$nClusters, function(i) {
    d <- ncol(result$factors[[i]])
    colnames(result$factors[[i]]) <- paste(i, 1:d)
    result$factors[[i]]
  })
  result$all.fit <- results
  class(result) <- "mlcc.fit"
  return(result)
}