# Geometry of Data

arXiv: https://arxiv.org/abs/2203.07208 · HTML: https://mlsanity.com/paper/2203.07208/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 45 references that are in the map.
- First posted on arXiv 14 Mar 2022.

## Builds on (most cited first, 2 of 2)

- [The Vietoris-Rips complexes of a circle](https://mlsanity.com/paper/1503.03669/) (2015)
- [Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius](https://mlsanity.com/paper/2001.07588/) (2020)

## Built on by (most cited first, 1 of 1)

- [Learning from data with structured missingness](https://mlsanity.com/paper/2304.01429/) (2023)

## Abstract (arXiv)

Topological data analysis asks when balls in a metric space (X,d) intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature. This enables us, on one hand, to reconceptualize curvature and link it to the geometric notion of hyperconvexity. On the other hand, we can then also understand methods of topological data analysis from a geometric perspective.