# A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality

arXiv: https://arxiv.org/abs/2603.10493 · HTML: https://mlsanity.com/paper/2603.10493/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks](https://mlsanity.com/paper/2111.13171/) (2021)
- [Multiple Instance Captioning: Learning Representations from Histopathology Textbooks and Articles](https://mlsanity.com/paper/2103.05121/) (2021)
- [On the Intrinsic Dimensionality of Image Representations](https://mlsanity.com/paper/1803.09672/) (2018)
- [Detecting Images Generated by Deep Diffusion Models using their Local Intrinsic Dimensionality](https://mlsanity.com/paper/2307.02347/) (2023)
- [LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood](https://mlsanity.com/paper/2206.14882/) (2022)
- [Statistical exploration of the Manifold Hypothesis](https://mlsanity.com/paper/2208.11665/) (2022)
- [Estimating the effective dimension of large biological datasets using Fisher separability analysis](https://mlsanity.com/paper/1901.06328/) (2019)
- [Metric Space Magnitude and Generalisation in Neural Networks](https://mlsanity.com/paper/2305.05611/) (2023)
- [A Survey of Dimension Estimation Methods](https://mlsanity.com/paper/2507.13887/) (2025)

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

- [Interpretable intrinsic dimension estimation through componentwise calibration of distance and angle](https://mlsanity.com/paper/2609.37114/) (2026)

## Abstract (arXiv)

Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely on geometric or distributional assumptions and can significantly fail when these assumptions are violated. In this paper, we introduce a novel ID estimator based on nearest-neighbor distance ratios that involves simple calculations and achieves state-of-the-art results. Most importantly, we provide a theoretical analysis proving that our estimator is universal, namely, it converges to the true ID independently of the distribution generating the data. We present experimental results on benchmark manifolds and real-world datasets to demonstrate the performance of our estimator.