# Principal Curvatures Estimation with Applications to Single Cell Data

arXiv: https://arxiv.org/abs/2502.03750 · HTML: https://mlsanity.com/paper/2502.03750/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 18 references that are in the map.
- First posted on arXiv 6 Feb 2025.

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

- [Diffusion Curvature for Estimating Local Curvature in High Dimensional Data](https://mlsanity.com/paper/2206.03977/) (2022)
- [An Intrinsic Approach to Scalar-Curvature Estimation for Point Clouds](https://mlsanity.com/paper/2308.02615/) (2023)

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

- [Assessing local deformation and computing scalar curvature with nonlinear conformal regularization of decoders](https://mlsanity.com/paper/2508.20413/) (2025)

## Abstract (arXiv)

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation.