# Nonembeddability of Persistence Diagrams with p>2 Wasserstein Metric

arXiv: https://arxiv.org/abs/1910.13935 · HTML: https://mlsanity.com/paper/1910.13935/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [From Geometry to Topology: Inverse Theorems for Distributed Persistence](https://mlsanity.com/paper/2101.12288/) (2021)
- [Estimation and Quantization of Expected Persistence Diagrams](https://mlsanity.com/paper/2105.04852/) (2021)
- [Convolutional Persistence Transforms](https://mlsanity.com/paper/2208.02107/) (2022)

## Abstract (arXiv)

Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the underlying feature map necessarily causes distortion. We prove persistence diagrams with the p-Wasserstein metric do not admit a coarse embedding into a Hilbert space when p > 2.