Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

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Preprint
Authors
Cramer, Eike
Rauh, Felix
Mitsos, Alexander
Tempone, Raul cc
Dahmen, Manuel
KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
King Abdullah University of Science and Technology (KAUST), Computer, Electrical, and Mathematical Sciences & Engineering Division (CEMSE), Saudi Arabia
Stochastic Numerics Research Group
KAUST Grant Number
OSR-2019-CRG8- 4033
Date
2022-03-08
Permanent link to this record
http://hdl.handle.net/10754/677947

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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.
Sponsors
This work was performed as part of the Helmholtz School for Data Science in Life, Earth and Energy (HDS-LEE) and received funding from the Helmholtz Association of German Research Centres. This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-2019-CRG8- 4033, and the Alexander von Humboldt Foundation.
Publisher
arXiv
arXiv
2203.03934
Additional Links
https://arxiv.org/pdf/2203.03934.pdf
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Preprints; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division