Regularization of Persistent Homology Gradient Computation
Abstract
Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In order for a given computation to be integrated in such a way, the computation in question must be differentiable. Computing the gradients of persistent homology is an ill-posed inverse problem with infinitely many solutions. Consequently, it is important to perform regularization so that the solution obtained agrees with known priors. In this work we propose a novel method for regularizing persistent homology gradient computation through the addition of a grouping term. This has the effect of helping to ensure gradients are defined with respect to larger entities and not individual points.
Cite
@article{arxiv.2011.05804,
title = {Regularization of Persistent Homology Gradient Computation},
author = {Padraig Corcoran and Bailin Deng},
journal= {arXiv preprint arXiv:2011.05804},
year = {2020}
}