Connectivity-Optimized Representation Learning via Persistent Homology


We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder’s latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.

Proceedings of the 36th International Conference on Machine Learning, ICML 2019, 9-15 June 2019, Long Beach, California, USA
Marc Niethammer
Marc Niethammer
Professor of Computer Science

My research interests include image registration, image segmentation, shape analysis, machine learning, and biomedical applications.