# The meaning of units on the axes of a PCA plot

I've used the R packages DESeq2 and ggplot2 and the following code

vsd <- varianceStabilizingTransformation(dds)
data <- plotPCA(vsd, intgroup=c("condition"), returnData=TRUE)
percentVar <- round(100 * attr(data, "percentVar"))
plotPCA <- ggplot(data, aes(PC1, PC2, color=condition)) +
geom_point(size=3) +
xlab(paste0("PC1: ",percentVar[1],"% variance")) +
ylab(paste0("PC2: ",percentVar[2],"% variance")) +
geom_text(aes(label=names),hjust=0.25, vjust=-0.5, show_guide = F)
ggsave("PCA.pdf", plot = plotPCA)


to produce the following PCA plot:

I know the axes are the principal components but I am confused by the units displayed. I thought the axes of a PCA plot are unit-less. But then I did image search on Google for "PCA plot" and saw tons of plots displaying units on their axes. Does anyone know what is the meaning of these units?

• FYI you need to have + coord_fixed() at the end (well anywhere within) the building of the plot; a 1 unit change in the x axis should be the same shift in the y axis. The axis are unitless in that a point is not -40 "something", it is just -40, for example. The axis is not numberless of course. The values are derived from the formation of the principal components as orthogonal linear combinations of the variables in the data set. – Reinstate Monica - G. Simpson Feb 15 '15 at 19:46

It seems the question has been answered here - the units are, apparently, the raw component scores. Which makes sense, actually.

The principal components are linear combinations of the original variables. If the original variables have different units, then it will not give meaning to give units to the PCA axes. But in the very special case that all the original variables have the same unit, then the principal component will have that same unit.

Can you reference some specific example you have seen with units on the principal components?