# Regularization of Persistent Homology Gradient Computation

arXiv: https://arxiv.org/abs/2011.05804 · HTML: https://mlsanity.com/paper/2011.05804/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysis](https://mlsanity.com/paper/2109.00530/) (2021)
- [Optimisation of Spectral Wavelets for Persistence-based Graph Classification](https://mlsanity.com/paper/2101.05201/) (2021)
- [Early Warning Signals of Social Instabilities in Twitter Data](https://mlsanity.com/paper/2303.05401/) (2023)

## Abstract (arXiv)

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.