提出一种无需假设的全新数据内在维度估计方法。
A Universal Nearest-Neighbor Estimator for Intrinsic Dimensionality
- 基于最近邻距离比设计新估计算法，计算简单。
- 理论证明该方法对任意数据分布均收敛到真实维度。
- 适用于高维数据降维与结构分析，适合研究人员参考。
估计数据的内在维度（ID）是机器学习和计算机视觉中的基础问题，有助于理解高维观测背后的真正自由度。现有方法通常依赖几何或分布假设，在假设不成立时表现显著下降。本文提出一种基于最近邻距离比的新ID估计算法，计算简单且达到当前最优性能。更重要的是，我们提供了理论分析，证明该估计器具有‘通用性’——无论数据由何种分布生成，都能收敛到真实内在维度。我们在基准流形和真实数据集上进行了实验，验证了该方法的有效性。
原文摘要 · Abstract (English)
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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