Reduce a Matrix X via PCA and Reconstruct All or Part to Give Xhat

This function allows one to do "round trip" PCA by reducing a matrix X using PCA and then reconstruct an approximation (Xhat) using some or all of the principal components. Inspired by https://stats.stackexchange.com/q/229092/26909. We are grateful for this post by StackOverflow contributor Amoeba.

XtoPCAtoXhat(X, ncomp = 3, scale.fun = NULL)

Arguments

X

A matrix of data, or a structure which can be coerced to a matrix. Samples should be in rows, and variables in columns.

ncomp

Integer. The number of principal components to use in reconstructing the data set. Must be no larger than the number of variables.

scale.fun

A function to use to scale the data. If NULL no scaling will be done.

Value

A matrix with the same dimensions as X.

Examples

# Example data from ?prcomp (see discussion at Stats.StackExchange.com/q/397793)
C <- chol(S <- toeplitz(.9 ^ (0:31)))
set.seed(17)
X <- matrix(rnorm(32000), 1000, 32)
Z <- X %*% C

tst <- XtoPCAtoXhat(Z)
mean(tst - Z)
#> [1] -1.05009e-18

# Plot to show the effect of increasing ncomp

ntests <- ncol(Z)
rmsd <- rep(NA_real_, ntests)
for (i in 1:ntests) {
  ans <- XtoPCAtoXhat(X, i, sd)
  del<- ans - X
  rmsd[i] <- sqrt(sum(del^2)/length(del)) # RMSD
}
plot(rmsd, type = "b",
  main = "Root Mean Squared Deviation\nReconstructed - Original Data",
  xlab = "No. of Components Retained", ylab = "RMSD")
abline(h = 0.0, col = "pink")