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Regularization of persistent homology gradient computation

Corcoran, Padraig ORCID: and Deng, Bailin ORCID: 2020. Regularization of persistent homology gradient computation. Presented at: Topological Data Analysis and Beyond Workshop, Virtual, 11 December 2020.

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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: Computer Science & Informatics
Date of First Compliant Deposit: 11 February 2021
Date of Acceptance: 1 November 2020
Last Modified: 27 Nov 2022 13:25

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