A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams

1 code implementation • 22 Feb 2024 • Rolando Kindelan Nuñez, Mircea Petrache, Mauricio Cerda, Nancy Hitschfeld

In this work we introduce a class of pseudodistances called Extended Topological Pseudodistances (ETD)s, which have tunable complexity, and can approximate Sliced and classical Wasserstein distances at the high-complexity extreme, while being computationally lighter and close to Persistence Statistics at the lower complexity extreme, and thus allow users to interpolate between the two metrics.

Topological Data Analysis