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Topological Autoencoders

Michael Moor · Max Horn · Bastian Rieck · Karsten Borgwardt

Keywords: [ Dimensionality Reduction ] [ Representation Learning ] [ Unsupervised Learning ] [ Autoencoders ] [ Unsupervised and Semi-supervised Learning ]


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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