# How to interpret data spread across diagonal lines in a PCA plot?

On occasion, I'll construct a PCA plot and find that instead of data spreading across PC1 or PC2, it appears to spread across some diagonal line(s) in the plot.

For example, in this article on human population diversity by Mallick et al. (2016), Figure 4a from the extended data shows this phenomenon:

I haven't looked at the data used to generate this figure, and the variance explained by PC1 and PC2 is quite small, but I'm mainly just using it as an example to illustrate the phenomenon.

In the PCA plot, there appear to be two subgroups, separate by PC1, but then within PC1, the samples are spread roughly across the $PC2 = PC1$ axis. On the other side, the right subgroup of PC1 appears to be spread more subtly from bottom-right to top-left.

Any ideas what is going on here?

• I'd say the first two PCs separate Africa from the other continents well enough. However, two PCs is clearly not enough to separate the other continents from each other. How many dimensions is the original dataset? Unfortunately we are limited to visualizing only 2 (maybe 3) dimensions at once. Perhaps this data is not be linearly separable in only 2 dimensions (or at all...) – ilanman Sep 23 '16 at 11:47
• "In the PCA plot, there appear to be two subgroups, separate by PC1, but then within PC1," - did you want to say "within left subgroup"? – amoeba Sep 23 '16 at 12:05
• +1. Possibly related: stats.stackexchange.com/questions/158552. – amoeba Sep 23 '16 at 12:25