I project a great number of Siberian, Central Asian, and South Asian populations on the first two principal components created by Han, West Asians, and Northern Europeans.
PC1 captures east-west variation across Eurasia, although the Han are also related to Ancestral South Asians, a major component in the ancestry of South Asians. PC2 captures West Asian-North European variation, so it is quite useful to extract the relative northern vs. southern Caucasoid elements in the populations examined.
Here are the first two PCs with the populations used to create them. Northeastern European (N=49) includes Lithuanians, Belorussians, Russians, Poles, and various non-Balkan Slavs. Northwestern European (N=46) includes Germans, Irish, Norwegians, and various continental Germanics. West Asian (N=93) includes Armenians, Iranians, Adygei, Lezgins, and Georgians.
Population labels are always placed on population averages. Notice that the Han form a tight cluster, halfway (along PC2) between West Asians and Northeast Europeans; this is expected as they are an outgroup that has not been significantly affected by Caucasoids.
We will now project various populations onto the previous 2-D map: their horizontal position (along PC1) depends on the extent of Caucasoid admixture, while their vertical position (along PC2) depends on whether this admixture is more northern or southern Caucasoid.
UPDATE (May 9):
I have also carried out supervised ADMIXTURE analysis, using the dataset of this post, adding Onge from the Indian Ocean as a fourth ancestral group together with Han, Northern Europeans, and West Asians.
The results seem consistent with the PCA projection, while the distinctiveness of the East Asian (dark blue) and Ancestral South Indian (light blue) components emerges.