Topological Autoencoders
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Publication:6319840
arXiv1906.00722MaRDI QIDQ6319840
Bastian Rieck, Karsten Borgwardt, Max Horn, Michael Moor
Publication date: 3 June 2019
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.
Has companion code repository: https://github.com/BorgwardtLab/topo-ae-distances
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