"The Currier languages revisited" revisited

[Jorge_Stolfi]

The purpose of PCA is to figure out how to optimally position a hyperdimensional flashlight relative to an N-dimensional point clould so that the shadow the point clould casts on a 2-D plane (or, by analogy, 3-D volume) captures the maximal amount of the covariance in the data.

That s correct; and, lacking better ideas, one may as well run a PCA and use the 2 or 3 components with largest spread.

But one must be aware that those may not be the best axes for the purpose of understanding the data, e.g. to see the shape of the cloud, or to identify clusters and determine criteria to separate clusters.  Even if every cluster is a neat spherical Gaussian cloud with the same radius...

All the best, --stolfi