Papers › On the Expectation of a Persistence Diagram by the Persistence Weighted Kernel
On the Expectation of a Persistence Diagram by the Persistence Weighted Kernel
Genki Kusano
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively developed, and the persistence weighted kernel shows several advantages over other statistical methods for persistence diagrams. If data is drawn from some probability distribution, the corresponding persistence diagram have randomness. Then, the expectation of the persistence diagram by the persistence weighted kernel is well-defined. In this paper, we study relationships between a probability distribution and the persistence weighted kernel in the viewpoint of (1) the strong law of large numbers and the central limit theorem, (2) a confidence interval to estimate the expectation of the persistence weighted kernel numerically, and (3) the stability theorem to ensure the continuity of the map from a probability distribution to the expectation. In numerical experiments, we demonstrate our method gives an interesting counterexample to a common view in topological data analysis.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections