# Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension

arXiv: https://arxiv.org/abs/2509.13385 · HTML: https://mlsanity.com/paper/2509.13385/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Topological implications of negative curvature for biological and social networks](https://mlsanity.com/paper/1403.1228/) (2014)
- [IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations](https://mlsanity.com/paper/2407.17835/) (2024)

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

- [Understanding Differentiable Embeddings Through Differential and Integral Geometry](https://mlsanity.com/paper/2608.06809/) (2026)

## Abstract (arXiv)

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations between triples of points and other points. More significantly, based on this curvature profile, we introduce a quantitative measure to evaluate the effectiveness of data representations, such as those produced by dimensionality reduction techniques. Furthermore, Our experiments demonstrate that this curvature-based analysis can be employed to estimate the intrinsic dimensionality of datasets. We use this to explore the large-scale geometry of empirical networks and to evaluate the effectiveness of dimensionality reduction techniques.