Wasserstein stability for persistence diagrams
[Moved Online] Hot Topics: Topological Insights in Neuroscience May 04, 2021 - May 11, 2021
Location: SLMath: Online/Virtual
Persistence diagram
Wasserstein distance
stability
image analysis
Rips complex
Wasserstein Stability for Persistence Diagrams
The stability of persistence diagrams is among the most important results in applied and computational topology but most results are with respect to the bottleneck distance between diagrams. This has two main implications: it makes the space of persistence diagrams rather pathological and it is often provides very pessimistic bounds with respect to outliers. In this talk I will discuss new stability results with respect to the p-Wasserstein distance between persistence diagrams. The main result is stability of persistence diagrams between different functions on the same finite simplicial complex in terms of the p-norm of the functions. This has applications to image analysis, persistence homology transforms and Vietoris-Rips complexes. This is joint work with Primoz Skraba.
Wasserstein Stability for Persistence Diagrams
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