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#' @importFrom stats complete.cases
findCorrelation_fast <- function(x, cutoff = .90, verbose = FALSE){
if(any(!complete.cases(x)))
stop("The correlation matrix has some missing values.")
averageCorr <- colMeans(abs(x))
averageCorr <- as.numeric(as.factor(averageCorr))
x[lower.tri(x, diag = TRUE)] <- NA
combsAboveCutoff <- which(abs(x) > cutoff)
colsToCheck <- ceiling(combsAboveCutoff / nrow(x))
rowsToCheck <- combsAboveCutoff %% nrow(x)
colsToDiscard <- averageCorr[colsToCheck] > averageCorr[rowsToCheck]
rowsToDiscard <- !colsToDiscard
if(verbose){
colsFlagged <- pmin(ifelse(colsToDiscard, colsToCheck, NA),
ifelse(rowsToDiscard, rowsToCheck, NA), na.rm = TRUE)
values <- round(x[combsAboveCutoff], 3)
cat('\n',paste('Combination row', rowsToCheck, 'and column', colsToCheck,
'is above the cut-off, value =', values,
'\n \t Flagging column', colsFlagged, '\n'
))
}
deletecol <- c(colsToCheck[colsToDiscard], rowsToCheck[rowsToDiscard])
deletecol <- unique(deletecol)
deletecol
}
findCorrelation_exact <- function(x, cutoff = 0.90, verbose = FALSE)
{
varnum <- dim(x)[1]
if (!isTRUE(all.equal(x, t(x)))) stop("correlation matrix is not symmetric")
if (varnum == 1) stop("only one variable given")
x <- abs(x)
# re-ordered columns based on max absolute correlation
originalOrder <- 1:varnum
averageCorr <- function(x) mean(x, na.rm = TRUE)
tmp <- x
diag(tmp) <- NA
maxAbsCorOrder <- order(apply(tmp, 2, averageCorr), decreasing = TRUE)
x <- x[maxAbsCorOrder, maxAbsCorOrder]
newOrder <- originalOrder[maxAbsCorOrder]
rm(tmp)
deletecol <- rep(FALSE, varnum)
x2 <- x
diag(x2) <- NA
for (i in 1:(varnum - 1)) {
if(!any(x2[!is.na(x2)] > cutoff)){
if (verbose) cat("All correlations <=", cutoff, "\n")
break()
}
if (deletecol[i]) next
for (j in (i + 1):varnum) {
if (!deletecol[i] & !deletecol[j]) {
if (x[i, j] > cutoff) {
mn1 <- mean(x2[i,], na.rm = TRUE)
mn2 <- mean(x2[-j,], na.rm = TRUE)
if(verbose) cat("Compare row", newOrder[i],
" and column ", newOrder[j],
"with corr ", round(x[i,j], 3), "\n")
if (verbose) cat(" Means: ", round(mn1, 3), "vs", round(mn2, 3))
if (mn1 > mn2) {
deletecol[i] <- TRUE
x2[i, ] <- NA
x2[, i] <- NA
if (verbose) cat(" so flagging column", newOrder[i], "\n")
}
else {
deletecol[j] <- TRUE
x2[j, ] <- NA
x2[, j] <- NA
if (verbose) cat(" so flagging column", newOrder[j], "\n")
}
}
}
}
}
newOrder[which(deletecol)]
}
#' Determine highly correlated variables
#'
#' This function searches through a correlation matrix and returns a vector of
#' integers corresponding to columns to remove to reduce pair-wise
#' correlations.
#'
#' The absolute values of pair-wise correlations are considered. If two
#' variables have a high correlation, the function looks at the mean absolute
#' correlation of each variable and removes the variable with the largest mean
#' absolute correlation.
#'
#' Using \code{exact = TRUE} will cause the function to re-evaluate the average
#' correlations at each step while \code{exact = FALSE} uses all the
#' correlations regardless of whether they have been eliminated or not. The
#' exact calculations will remove a smaller number of predictors but can be
#' much slower when the problem dimensions are "big".
#'
#' @param x A correlation matrix
#' @param cutoff A numeric value for the pair-wise absolute correlation cutoff
#' @param verbose A boolean for printing the details
#' @param names a logical; should the column names be returned (\code{TRUE}) or
#' the column index (\code{FALSE})?
#' @param exact a logical; should the average correlations be recomputed at
#' each step? See Details below.
#' @return A vector of indices denoting the columns to remove (when \code{names
#' = TRUE}) otherwise a vector of column names. If no correlations meet the
#' criteria, \code{integer(0)} is returned.
#' @author Original R code by Dong Li, modified by Max Kuhn
#' @seealso \code{\link{findLinearCombos}}
#' @keywords manip
#' @examples
#'
#' R1 <- structure(c(1, 0.86, 0.56, 0.32, 0.85, 0.86, 1, 0.01, 0.74, 0.32,
#' 0.56, 0.01, 1, 0.65, 0.91, 0.32, 0.74, 0.65, 1, 0.36,
#' 0.85, 0.32, 0.91, 0.36, 1),
#' .Dim = c(5L, 5L))
#' colnames(R1) <- rownames(R1) <- paste0("x", 1:ncol(R1))
#' R1
#'
#' findCorrelation(R1, cutoff = .6, exact = FALSE)
#' findCorrelation(R1, cutoff = .6, exact = TRUE)
#' findCorrelation(R1, cutoff = .6, exact = TRUE, names = FALSE)
#'
#'
#' R2 <- diag(rep(1, 5))
#' R2[2, 3] <- R2[3, 2] <- .7
#' R2[5, 3] <- R2[3, 5] <- -.7
#' R2[4, 1] <- R2[1, 4] <- -.67
#'
#' corrDF <- expand.grid(row = 1:5, col = 1:5)
#' corrDF$correlation <- as.vector(R2)
#' levelplot(correlation ~ row + col, corrDF)
#'
#' findCorrelation(R2, cutoff = .65, verbose = TRUE)
#'
#' findCorrelation(R2, cutoff = .99, verbose = TRUE)
#'
#' @export findCorrelation
findCorrelation <- function(x, cutoff = 0.90, verbose = FALSE, names = FALSE, exact = ncol(x) < 100) {
if(names & is.null(colnames(x)))
stop("'x' must have column names when `names = TRUE`")
out <- if(exact)
findCorrelation_exact(x = x, cutoff = cutoff, verbose = verbose) else
findCorrelation_fast(x = x, cutoff = cutoff, verbose = verbose)
out
if(names) out <- colnames(x)[out]
out
}
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