论文标题
持续同源梯度计算的正规化
Regularization of Persistent Homology Gradient Computation
论文作者
论文摘要
持续的同源性是一种计算给定数据中存在的拓扑特征的方法。最近，人们对将持续同源性作为神经网络或深度学习的计算步骤的整合引起了很多兴趣。为了以这种方式集成给定的计算，所讨论的计算必须是可区分的。计算持续同源性的梯度是无限多种解决方案的一个不当反对问题。因此，执行正规化很重要，以便获得的解决方案与已知的先验一致。在这项工作中，我们提出了一种通过添加分组术语正规化持续同源梯度计算的新方法。这具有帮助确保梯度在较大的实体而不是个别观点方面定义的效果。
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.
