Witness Autoencoder: Shaping the Latent Space with Witness Complexes
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).
Cite
Text
Schönenberger et al. "Witness Autoencoder: Shaping the Latent Space with Witness Complexes ." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.Markdown
[Schönenberger et al. "Witness Autoencoder: Shaping the Latent Space with Witness Complexes ." NeurIPS 2020 Workshops: TDA_and_Beyond, 2020.](https://mlanthology.org/neuripsw/2020/schonenberger2020neuripsw-witness/)BibTeX
@inproceedings{schonenberger2020neuripsw-witness,
title = {{Witness Autoencoder: Shaping the Latent Space with Witness Complexes }},
author = {Schönenberger, Simon Till and Varava, Anastasiia and Polianskii, Vladislav and Chung, Jen Jen and Kragic, Danica and Siegwart, Roland},
booktitle = {NeurIPS 2020 Workshops: TDA_and_Beyond},
year = {2020},
url = {https://mlanthology.org/neuripsw/2020/schonenberger2020neuripsw-witness/}
}