Witness Autoencoder: Shaping the Latent Space with Witness Complexes

Simon Till Schönenberger, Anastasiia Varava, Vladislav Polianskii, Jen Jen Chung, Danica Kragic, Roland Siegwart

Keywords: Autoencoder, Witness Complex, Manifold Learning, Isometry

TL;DR: We present a Witness Autoencoder (W-AE) – an autoencoder that captures geodesic distances of the data in the latent space.

Abstract: We present a Witness Autoencoder (W-AE) – an autoencoder that captures geodesic distances of the data in the latent space. Our algorithm uses witness complexes to compute geodesic distance approximations on a mini-batch level, and leverages topological information from the entire dataset while performing batch-wise approximations. This way, our method allows to capture the global structure of the data even with a small batch size, which is beneficial for large-scale real-world data. We show that our method captures the structure of the manifold more accurately than the recently introduced topological autoencoder (TopoAE).

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