RipsNet: fast and robust estimation of persistent homology for point clouds

“I will talk about the data-driven approach to estimating persistence diagrams (PDs) of point clouds. In the practical use of persistent homology, there are two major limitations: the computational complexity of computing PDs exactly and their sensitivity to even low-level proportions of outliers. To overcome these difficulties, we propose a neural network architecture, RipsNet, to estimate the vectorization of PDs of point clouds. Once trained on a given set, RipsNet can efficiently estimate topological descriptors. Moreover, we prove that RipsNet is robust to input perturbations in terms of 1-Wasserstein distance, allowing RipsNet to substantially outperform exactly-computed PDs in noisy settings.”