R: prcomp, Order of columns in data table matter? - r

Question

I ran the prcomp function on a data table containing 91 columns and 2030 rows and obtained a PCA plot. However, when I re-ordered the same data table to make it easier to color-code the data points, I got an entirely different looking PCA plot.
Does the order of the columns matter in prcomp()?
Just a note, the code included was provided for me by someone previously in my lab, who is no longer here to ask. I have a moderate understanding of what it is doing.
Thanks for the help!
pcaPlotter3d <- function(fileName, startColumn, endColumn){
x<- read.table(fileName, sep = '\t', header =TRUE, stringsAsFactors = FALSE)
pcaData <- prcomp(~., x[,startColumn:endColumn], na.action=na.exclude, scale = TRUE)
library(scatterplot3d)
colorList <- c(rep("magenta", 2), rep("blue", 12), rep("red",33), rep("purple", 2), rep("green", 6), rep("black",36))
shapeList <- c(rep(19, 91))#, rep(15, 24))
with (pcaData, {
pointsForPlot <- scatterplot3d(pcaData$rotation[,1:3], color=colorList,
pch = shapeList, main = "TAP Proteins PCA", mar = c(3,3,3,5), xlab = "PC1 (16.5%)", ylab = "PC2 (3.67%)", zlab = "PC3 (2.79%)",
col.grid = NULL)
pointsForPlot.coords <- pointsForPlot$xyz.convert(pcaData$rotation[,1:3])
legend(8,5, bty = "n", xpd = TRUE, cex = 0.75, inset = .1,
title = "Groups", c("Bio", "EF", "IF", "RF", "Rib", "Unk"),
col = c("magenta", "blue", "red", "purple", "green", "black") , pch = c(19,19,19,19,19,19));
})
print(summary(pcaData))
}

Answer 1

It's hard to see in the perspective plots, but it seems that all that has happened is that the signs of PC2 and PC3 have been flipped. (Eigenvectors/PCA directions are only defined up to a change in sign, and a trivial change like changing the order of the columns can indeed cause them to flip.) Given that the inertias/proportions of variance are the same and the ranges of the axes are inverted (e.g. PC2 goes from -0.1 to 0.5 in plot 1 and -0.5 to 0.1 in plot 2), this is the most likely explanation. You can simply multiply the PC2 and PC3 coordinates by -1 in the appropriate places if you want to recover the original plot ...