ICML 2020poster236 citations
Topological Autoencoders
Michael Moor, Max Horn, Bastian Rieck, Karsten Borgwardt
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.
BibTeX
@InProceedings{pmlr-v119-moor20a,
title = {Topological Autoencoders},
author = {Moor, Michael and Horn, Max and Rieck, Bastian and Borgwardt, Karsten},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {7045--7054},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/moor20a/moor20a.pdf},
url = {https://proceedings.mlr.press/v119/moor20a.html},
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.}
}