# CA-PCA: Manifold Dimension Estimation, Adapted for Curvature

arXiv: https://arxiv.org/abs/2309.13478 · HTML: https://mlsanity.com/paper/2309.13478/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 23 Sep 2023.

## Builds on (most cited first, 7 of 7)

- [Intrinsic Dimension Estimation Using Wasserstein Distances](https://mlsanity.com/paper/2106.04018/) (2021)
- [Spectral Clustering Based on Local PCA](https://mlsanity.com/paper/1301.2007/) (2013)
- [Non-Parametric Estimation of Manifolds from Noisy Data](https://mlsanity.com/paper/2105.04754/) (2021)
- [Efficient Manifold and Subspace Approximations with Spherelets](https://mlsanity.com/paper/1706.08263/) (2017)
- [Tangent Space and Dimension Estimation with the Wasserstein Distance](https://mlsanity.com/paper/2110.06357/) (2021)
- [Distributional Results for Model-Based Intrinsic Dimension Estimators](https://mlsanity.com/paper/2104.13832/) (2021)
- [Effective Estimation of the Dimensions of a Manifold from Random Samples](https://mlsanity.com/paper/2209.01839/) (2022)

## Built on by (most cited first, 4 of 4)

- [Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry](https://mlsanity.com/paper/2505.08087/) (2025)
- [A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesis](https://mlsanity.com/paper/2509.15517/) (2025)
- [Manifold Dimension Estimation via Local Graph Structure](https://mlsanity.com/paper/2510.15141/) (2025)
- [Missing Data Imputation under Manifold Hypothesis](https://mlsanity.com/paper/2607.03641/) (2026)

## Abstract (arXiv)

The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension. It is often useful to determine or estimate the dimension of this manifold before performing dimension reduction, for instance. Existing methods for dimension estimation are calibrated using a flat unit ball. In this paper, we develop CA-PCA, a version of local PCA based instead on a calibration of a quadratic embedding, acknowledging the curvature of the underlying manifold. Numerous careful experiments show that this adaptation improves the estimator in a wide range of settings.