Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

Cramer, Eike; Rauh, Felix; Tempone, Raúl; Mitsos, Alexander; Dahmen, Manuel

doi:10.48550/ARXIV.2203.03934

Preprint

FZJ-2023-00760

Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

Cramer, E.FZJ*RWTH* ; Rauh, F.FZJ*RWTH* ; Mitsos, A.FZJ*RWTH* ; Tempone, R.RWTH* ; Dahmen, M. (Corresponding author)FZJ*

2022
arXiv

arXiv (2022) [10.48550/ARXIV.2203.03934]

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Please use a persistent id in citations: http://hdl.handle.net/2128/33644 doi:10.48550/ARXIV.2203.03934

Abstract: To model manifold data using normalizing flows, we propose to employ the isometric autoencoder to design nonlinear encodings with explicit inverses. The isometry allows us to separate manifold learning and density estimation and train both parts to high accuracy. Applied to the MNIST data set, the combined approach generates high-quality images.

Keyword(s): Machine Learning (cs.LG) ; FOS: Computer and information sciences

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