Dimensionality Reduction of Curved Structural Data

Question

I have been using PCA dimensionality reduction on datasets that are quite linear and now I am tasked with the same on datasets that are largely curved in space. Imagine a noisy sine wave for simplicity.

Is PCA still useful in this scenario? If not, what is a more appropriate dimensionality reduction method?

Answer 1

This is a tentative answer.

In general PCA may yield good results even if the space is not strictly flat.

However there are variations of PCA, like PGA (ie Principal Geodesic Analysis) which takes account of the underlying Riemannian structure of the space.

One can find references online:

Eg Principal Geodesic Analysis