gooblywooblygoobly t1_iydf4z2 wrote on November 30, 2022 at 4:05 PM Reply to comment by vikigenius in [D] What method is state of the art dimensionality reduction by olmec-akeru A super trivial example is that a (hyper)plane is a Riemannian manifold. Since we know that PCA is lossy, and PCA projects to a (hyper)plane, it can't be that projecting to manifolds are enough to perfectly preserve information. Permalink Parent 1
gooblywooblygoobly t1_iydf4z2 wrote
Reply to comment by vikigenius in [D] What method is state of the art dimensionality reduction by olmec-akeru
A super trivial example is that a (hyper)plane is a Riemannian manifold. Since we know that PCA is lossy, and PCA projects to a (hyper)plane, it can't be that projecting to manifolds are enough to perfectly preserve information.