A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality

2026-03-11

AI Summary

Estimating the intrinsic dimensionality of high-dimensional data is crucial for machine learning and computer vision, yet existing methods often fail due to reliance on specific geometric or distributional assumptions. This work proposes a nonparametric estimator based on nearest-neighbor distance ratios that requires no prior assumptions about the underlying data manifold or distribution. For the first time, it is theoretically proven that this estimator consistently converges to the true intrinsic dimension under arbitrary data distributions. Extensive experiments demonstrate that the method achieves state-of-the-art performance on both synthetic manifolds and real-world datasets, exhibiting high accuracy, strong robustness, and broad applicability.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Other Foundations of Computer Vision
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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 \emph{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.

Problem

• intrinsic dimensionality
• nearest-neighbor
• dimensionality estimation
• machine learning
• computer vision

Innovation

• intrinsic dimensionality
• nearest-neighbor
• universal estimator
• distance ratios
• distribution-free