Contributed Talk 2: Witness Autoencoder: Shaping the Latent Space with Witness Complexes

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).