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.
@article{arxiv.1906.00722,
title = {Topological Autoencoders},
author = {Michael Moor and Max Horn and Bastian Rieck and Karsten Borgwardt},
journal= {arXiv preprint arXiv:1906.00722},
year = {2021}
}
Comments
Accepted at the International Conference on Machine Learning (ICML) 2020; camera-ready version