Topological Autoencoders
This addresses the challenge of maintaining multi-scale connectivity information in latent spaces for machine learning applications, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackles the problem of preserving topological structures in autoencoder latent representations by introducing a topological loss term based on persistent homology, showing favorable results on synthetic and real-world image datasets while maintaining low reconstruction errors.
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.