18 citations · 22 across the 4 of their papers we have counts for
5 papers
On the Convergence of Optimizing Persistent-Homology-Based Losses
Yikai Zhang, Jiachen Yao, Yusu Wang +1
Topological loss based on persistent homology has shown promise in various applications. A topological loss enforces the model to achieve certain desired topological property. Desp…
Annotating Simplices with a Homology Basis and Its Applications
Oleksiy Busaryev, Sergio Cabello, Chao Chen +2
Let be a simplicial complex and the rank of its -th homology group defined with coefficients. We show that we can compute a basis of and anno…
Quantifying Homology Classes
Chao Chen, Daniel Freedman
We develop a method for measuring homology classes. This involves three problems. First, we define the size of a homology class, using ideas from relative homology. Second, we defi…
Quantifying Homology Classes II: Localization and Stability
Chao Chen, Daniel Freedman
In the companion paper, we measured homology classes and computed the optimal homology basis. This paper addresses two related problems, namely, localization and stability. We loca…
Measuring and Localing Homology Classes
Daniel Freedman, Chao Chen
We develop a method for measuring and localizing homology classes. This involves two problems. First, we define relevant notions of size for both a homology class and a homology gr…