Sierpi'nski--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation

arXiv:2609.01528 · cs.CG, cs.LG · Submitted 2026-09-01 · Read on arXiv

cs.CG, cs.LG

Submitted: 2026-09-01

Updated: 2026-09-01

Code: https://github.com/sebastien-tchitchek/SK-WassersteinReproducibility

Project page: https://topology-tool-kit.github.io

Terminology

• Clustering — 39× in this paper · explained in 2 episodes
• Wasserstein Distance — 38× in this paper · explained in 4 episodes
• Benchmark — 20× in this paper · explained in 2 episodes
• Spectral clustering — 13× in this paper · explained in 2 episodes
• 2-Wasserstein Distance — 12× in this paper · explained in 1 episode
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Adjusted Rand Index — 4× in this paper
• Optimal Transport — 4× in this paper · explained in 5 episodes
• Vector Representations — 3× in this paper · explained in 2 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Pairwise Comparisons — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Approximation Bound — 1× in this paper · explained in 1 episode
• Hamming Distance — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Persistent Homology — 1× in this paper · explained in 3 episodes
• Point Clouds — 1× in this paper · explained in 2 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Topological Data Analysis (TDA) — 1× in this paper · explained in 2 episodes

Sources

• A User's Guide to Sampling Strategies for Sliced Optimal Transport
• Robust Barycenters of Persistence Diagrams
• Fr'echet Means for Distributions of Persistence diagrams

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