Topological representation learning

Topological features as computed via persistent homology offer a non-parametric approach to robustly capture multi-scale connectivity information of complex datasets. This has started to gain attention in various machine learning applications. Conventionally, in topological data analysis, this method has been employed as an immutable feature descriptor in order to characterize topological properties of datasets. In this talk, however, I will explore how topological features can be directly integrated into deep learning architectures. This allows us to impose differentiable topological constraints for preserving the global structure of the data space when learning low-dimensional representations.