Topological Autoencoders

Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt
6/3/2019
cs.LGmath.ATstat.ML

Official code: BorgwardtLab/topological-autoencoders (154 stars, BSD-3-Clause, last commit 2022-01-18).

Abstract

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

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Code Implementations(1)

BorgwardtLab/topological-autoencodersOfficial100%
BSD-3-Clause

Code for the paper "Topological Autoencoders" by Michael Moor, Max Horn, Bastian Rieck, and Karsten Borgwardt.

15434Shell, PythonApr 12, 20194 years agoBSD-3-Clause
autoencoderpersistent-homologytdatopological-data-analysis

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Cite this paper

@article{moor2019topological,
  title  = {Topological Autoencoders},
  author = {Michael Moor and Max Horn and Bastian Rieck and Karsten Borgwardt},
  year   = {2019},
  eprint = {1906.00722},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1906.00722}
}

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