TFARM: Transcription Factors Association Rules Miner

#' Principal Components Analysis for distributions of variations of support and 
#' confidence obtained removing a transcription factor
#' from a set of rules.
#'
#' The function is used for validation of the defined Importance Index.
#' It is defined as the linear combination of variations of
#' support and confidence measures.
#' The Principal Component Analysis lets the user evaluate
#' if in the 1D reference system defined by such linear combination,
#' it is possible to describe the variability of the data.
#'
#' @param delta_list list of variations of distributions
#' of support and confidence measures, obtained using the \code{IComp}.
#' @param IMP the importance matrix with the mean Importance Index
#' of every candidate co-regulator transcription factor and the number of rules
#' in which each of them appears.
#' @return Variance explained by every principal component (\code{summary}),
#' scores (i.e., the coordinates) of data in delta_list in the reference system
#' defined by the principal components (\code{scores}) and loadings
#' (i.e., the coefficinets) of the linear combination that defines
#' each principal component (\code{loadings}).
#' The plots of the variability, the cumulate percentage of variance explained
#' by each principal component and loadings of every principal component are
#' also returned.
#'
#' @export
#' @importFrom stats princomp
#' @importFrom graphics layout barplot plot title abline box
#'
#' @examples
#' # Load IMP, DELTA and TF_Imp from the data_man collection of datasets:
#' data('data_man')
#'
#' colnames(IMP)
#' TF_Imp <- data.frame(IMP$TF, IMP$imp, IMP$nrules)
#' i.pc <- IPCA(DELTA, TF_Imp)
#' names(i.pc)


IPCA <- function (delta_list, IMP) 
{
  D_2 <- unlist(delta_list)[which(!is.na(unlist(delta_list)))]
  Delta_0 <- data.frame(TF = rep(IMP[, 1], IMP[, 3]), matrix(D_2, 
                                                             ncol = 2, byrow = TRUE))
  colnames(Delta_0)[2:3] <- c("delta s", "delta c")
  Delta <- Delta_0[, 2:3]
  pc <- princomp(Delta, cor = FALSE, scores = TRUE)
  layout(matrix(c(1, 2, 3, 4), 2, 2, byrow = TRUE), 
         heights = c(1, 0.9))
  barplot(pc$sdev^2/sum(pc$sde^2), las = 1, main = "Variances of the principal components", 
          ylab = "Variances", ylim = c(0, 1), cex.lab = 1.3, cex.main = 1.3, cex.names = 1.3, cex.axis = 1.2)
  plot(cumsum(pc$sdev^2)/sum(pc$sde^2), type = "b", axes = TRUE, 
       xlab = "Number of components", ylab = "Cum. variances", cex.lab = 1.3, cex.axis=1.2)
  box()
  title(main = "Cumulate variances of the principal components", 
        cex.main = 1.3)
  scores <- pc$scores
  load <- pc$loadings
  for (i in 1:2) {
    barplot(load[, i], ylim = c(-1, 1), yaxt='none', ylab = paste("Comp.", i, sep = ""), cex.lab = 1.6, cex.names = 1.6)
    axis(2, seq(-1,1,1), cex.axis = 1.2)
    abline(h = 0)
    title(main = "Loadings of the principal components", cex.main = 1.4)
  }
  return(list(summary = summary(pc), scores = scores, loadings = load))
}