Regularization of Persistent Homology Gradient ComputationDownload PDF

Oct 10, 2020 (edited Dec 02, 2020)NeurIPS 2020 Workshop TDA and Beyond Blind SubmissionReaders: Everyone
  • Keywords: Persistent Homology, Gradient, Regularization
  • 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.
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