Regularization of persistent homology gradient computation

Corcoran, Padraig ORCID: https://orcid.org/0000-0001-9731-3385 and Deng, Bailin ORCID: https://orcid.org/0000-0002-0158-7670 2020. Regularization of persistent homology gradient computation. Presented at: Topological Data Analysis and Beyond Workshop, Virtual, 11 December 2020.

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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.

Item Type:	Conference or Workshop Item (Poster)
Date Type:	Published Online
Status:	Published
Schools:	Schools > Computer Science & Informatics
Date of First Compliant Deposit:	11 February 2021
Date of Acceptance:	1 November 2020
Last Modified:	27 Nov 2022 13:25
URI:	https://orca.cardiff.ac.uk/id/eprint/138450

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