# A Survey of Dimension Estimation Methods

arXiv: https://arxiv.org/abs/2507.13887 · HTML: https://mlsanity.com/paper/2507.13887/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2025.

## Built on by (most cited first, 12 of 12)

- [Abstraction Induces the Brain Alignment of Language and Speech Models](https://mlsanity.com/paper/2602.04081/) (2026)
- [IdEst: Assessing Self-Supervised Learning Representations via Intrinsic Dimension](https://mlsanity.com/paper/2606.03338/) (2026)
- [Intrinsic Dimension Estimating Autoencoder (IDEA) Using CancelOut Layer and a Projected Loss](https://mlsanity.com/paper/2509.10011/) (2025)
- [A general framework for adaptive nonparametric dimensionality reduction](https://mlsanity.com/paper/2511.09486/) (2025)
- [A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality](https://mlsanity.com/paper/2603.10493/) (2026)
- [A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesis](https://mlsanity.com/paper/2509.15517/) (2025)
- [Concentration bounds for intrinsic dimension estimation using Gaussian kernels](https://mlsanity.com/paper/2512.04861/) (2025)
- [Rethinking Intrinsic Dimension Estimation in Neural Representations](https://mlsanity.com/paper/2604.20276/) (2026)
- [Critical Percolation as a Synthetic Data Model for Interpretability](https://mlsanity.com/paper/2606.20347/) (2026)
- [HyperShadow: A Benchmark for Detecting 3D Projections of Higher-Dimensional Spatial Objects](https://mlsanity.com/paper/2607.14419/) (2026)
- [FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data](https://mlsanity.com/paper/2608.10857/) (2026)
- [Interpretable intrinsic dimension estimation through componentwise calibration of distance and angle](https://mlsanity.com/paper/2609.37114/) (2026)

## Abstract (arXiv)

It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence the complexity of the dataset at hand. A great variety of dimension estimators have been developed to find the intrinsic dimension of the data but there is little guidance on how to reliably use these estimators. This survey reviews a wide range of dimension estimation methods, categorising them by the geometric information they exploit: tangential estimators which detect a local affine structure; parametric estimators which rely on dimension-dependent probability distributions; and estimators which use topological or metric invariants. The paper evaluates the performance of these methods, as well as investigating varying responses to curvature and noise. Key issues addressed include robustness to hyperparameter selection, sample size requirements, accuracy in high dimensions, precision, and performance on non-linear geometries. In identifying the best hyperparameters for benchmark datasets, overfitting is frequent, indicating that many estimators may not generalise well beyond the datasets on which they have been tested.