Estimatingtheintrinsicdimensionalityusing NormalizingFlows-Supplementary

Withtheseconditions,adirectconsequenceisthat the singular values inon-manifold directions will not depend onσ2. Hence, if we fix the latent distribution to be standard Gaussian, wehavethat theNFused tolearnqσ2 must be f forall(u,v),i.e. However, these eigenvalues are exactly in direction of large variability, i.e. in on-manifolddirection. Thiswastobeshown. Let us assume thatσ21 = = σ2d in the following. B.1 Lolipop In [11], a manifold consisting of regions of different ID was considered - a 1 dimensional line segment, and atwodimensional disk such that theoverall manfiold resembles alolipop.