A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912961159757824 |
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| author | Ong, Eng-Jon Bobrowski, Omer Reinert, Gesine Skraba, Primoz |
| author_facet | Ong, Eng-Jon Bobrowski, Omer Reinert, Gesine Skraba, Primoz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10493 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality Ong, Eng-Jon Bobrowski, Omer Reinert, Gesine Skraba, Primoz Machine Learning 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. |
| title | A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.10493 |