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arXiv · 2603.10493

A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality

Eng-Jon Ong·Omer Bobrowski·Gesine Reinert·Primoz Skraba
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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.

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Eng-Jon Ong, Omer Bobrowski, Gesine Reinert, Primoz Skraba. 2026-03-11. A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality. https://arxiv.org/abs/2603.10493

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