# Intrinsic Dimensionality Estimation within Tight Localities: A Theoretical and Experimental Analysis

arXiv: https://arxiv.org/abs/2209.14475 · HTML: https://mlsanity.com/paper/2209.14475/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 71 references that are in the map.
- First posted on arXiv 29 Sep 2022.

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

- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [Generative Image Inpainting with Submanifold Alignment](https://mlsanity.com/paper/1908.00211/) (2019)
- [Quality Evaluation of GANs Using Cross Local Intrinsic Dimensionality](https://mlsanity.com/paper/1905.00643/) (2019)

## Built on by (most cited first, 22 of 22)

- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [Bridging Information-Theoretic and Geometric Compression in Language Models](https://mlsanity.com/paper/2310.13620/) (2023)
- [AI-generated text boundary detection with RoFT](https://mlsanity.com/paper/2311.08349/) (2023)
- [The Intrinsic Dimension of Prompts in Internal Representations of Large Language Models](https://mlsanity.com/paper/2501.10573/) (2025)
- [Measuring the Intrinsic Dimension of Earth Representations](https://mlsanity.com/paper/2511.02101/) (2025)
- [Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimation](https://mlsanity.com/paper/2308.01054/) (2023)
- [Unveiling and Mitigating Generalized Biases of DNNs through the Intrinsic Dimensions of Perceptual Manifolds](https://mlsanity.com/paper/2404.13859/) (2024)
- [Scale adaptive and robust intrinsic dimension estimation via optimal neighbourhood identification](https://mlsanity.com/paper/2405.15132/) (2024)
- [Understanding the Structure of QM7b and QM9 Quantum Mechanical Datasets Using Unsupervised Learning](https://mlsanity.com/paper/2309.15130/) (2023)
- [Dimensionality-Aware Outlier Detection: Theoretical and Experimental Analysis](https://mlsanity.com/paper/2401.05453/) (2024)
- [Unveiling Intrinsic Dimension of Texts: from Academic Abstract to Creative Story](https://mlsanity.com/paper/2511.15210/) (2025)
- [Understanding Generalization from Embedding Dimension and Distributional Convergence](https://mlsanity.com/paper/2601.22756/) (2026)
- [Dimensionality of datasets in object detection networks](https://mlsanity.com/paper/2210.07049/) (2022)
- [Geometric Origins of Bias in Deep Neural Networks: A Human Visual System Perspective](https://mlsanity.com/paper/2502.11809/) (2025)
- [A Novel Approach for Intrinsic Dimension Estimation](https://mlsanity.com/paper/2503.09485/) (2025)
- [CoreSPECT: Enhancing Clustering Algorithms via an Interplay of Density and Geometry](https://mlsanity.com/paper/2507.08243/) (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)
- [Intrinsic Dimensionality as a Model-Free Measure of Class Imbalance](https://mlsanity.com/paper/2511.10475/) (2025)
- [On the Use of Bagging for Local Intrinsic Dimensionality Estimation](https://mlsanity.com/paper/2603.24384/) (2026)
- [GLID: Gated Local Intrinsic Dimension Repairs the Blind Spots of Face-Forgery Detectors](https://mlsanity.com/paper/2607.18770/) (2026)
- [FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data](https://mlsanity.com/paper/2608.10857/) (2026)

## Abstract (arXiv)

Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since their convergence generally requires sample sizes (that is, neighborhood sizes) on the order of hundreds of points, existing ID estimation methods may have only limited usefulness for applications in which the data consists of many natural groups of small size. In this paper, we propose a local ID estimation strategy stable even for `tight' localities consisting of as few as 20 sample points. The estimator applies MLE techniques over all available pairwise distances among the members of the sample, based on a recent extreme-value-theoretic model of intrinsic dimensionality, the Local Intrinsic Dimension (LID). Our experimental results show that our proposed estimation technique can achieve notably smaller variance, while maintaining comparable levels of bias, at much smaller sample sizes than state-of-the-art estimators.