PCA : Can I reverse the axis of the first principal component in R?

Question

Here is a reproducible example :

set.seed(10)
pick <- sample(nrow(iris),nrow(iris)/2)
iris.training <- iris[pick,] 
iris.testing <- iris[-pick,]
pca.training <- prcomp(iris.training[-5])
pca.testing <- prcomp(iris.testing[-5])
autoplot(pca.training,loadings.label=T,loadings=T)
autoplot(pca.testing,loadings.label=T,loadings=T)

Which produces the following output :

As one can see, pca on data.training and on data.testing produces very similar biplots but the first principal components has reversed its sign, they are mirrored. Is it possible to force a 180 degree rotation on the two components ?

Answer 1

You are not returning the rotated variables. Changed code is as below. Notice retx=TRUE

set.seed(10)
pick <- sample(nrow(iris),nrow(iris)/2)
iris.training <- iris[pick,] 
iris.testing <- iris[-pick,]
pca.training <- prcomp(iris.training[-5], retx=TRUE)
pca.testing <- prcomp(iris.testing[-5], retx=TRUE)
autoplot(pca.training,loadings.label=TRUE,loadings=TRUE)
autoplot(pca.testing,loadings.label=TRUE,loadings=TRUE)

It produced the following outputs for training and testing.

Answer 2

I'm assuming autoplot is the function from the ggfortify package. There are probably two ways to do this. The easiest is to just ask to reverse the x axis, by writing

autoplot(pca.testing,loadings.label=TRUE,loadings=TRUE) + scale_x_reverse()

Notice that this didn't change any values: the X axis now runs from positive to negative instead of the usual direction.

The second is to modify the pca.testing object to swap the signs on the x axis. This is statistically valid: PCA doesn't determine the signs of any components, but it's a bit tricky, because the signs show up in two places: component x for the data points, and component rotation for the arrows:

pca.testing$x[,1] <- - pca.testing$x[,1]
pca.testing$rotation[,1] <- -pca.testing$rotation[,1]
autoplot(pca.testing,loadings.label=TRUE,loadings=TRUE)

Not related to your question, but some advice: don't use T, use TRUE, otherwise the next time you have temperature data, you may inadvertantly change the value, and cause havoc with your analysis.