Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation

Paper recorded by Signals 4 on 2026-09-01 in cs.LG. Abstract reproduced from arXiv; link to the original below.

Published 2026-09-01 on arXiv · recorded by Signals 4 on 2026-09-02

Category: cs.LG · 机器学习 · first seen 2026-09-02

Abstract

This paper introduces the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. The SK-Wasserstein distance, denoted $d_{\mathrm{SK}}$, maps diagram points and their diagonal projections to the unit interval via the Sierpiński-Knopp space-filling curve on the upper diagonal triangle. The encoded point sets are then efficiently matched via one-dimensional optimal a

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