系统评估了八种流形维度估计方法的性能与适用场景。
A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesis
- 梳理理论基础并对比八种主流估计器
- 揭示噪声、曲率、样本量对精度的影响
- 提供选型指南与超参数调优方法
流形假设认为高维数据通常位于低维流形上。估计该流形的维度对于利用其结构至关重要，但现有研究分散且缺乏系统评估。本文为研究人员和实践者提供全面综述，回顾常被忽视的理论基础，介绍八种代表性估计器。通过受控实验，分析噪声、曲率、样本量等因子对性能的影响，并在多样化的合成与真实数据集上比较各估计器表现，提出针对数据集的超参数调优原则。结果为估计器选择提供实用指导，并为未来设计提供洞见。
原文摘要 · Abstract (English)
The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is fragmented and lacks systematic evaluation. This article provides a comprehensive survey for both researchers and practitioners. We review often-overlooked theoretical foundations and present eight representative estimators. Through controlled experiments, we analyze how individual factors, such as noise, curvature, and sample size, affect performance. We also compare the estimators on diverse synthetic and real-world datasets, introducing a principled approach to dataset-specific hyperparameter tuning. Our results offer practical guidance for estimator selection and yield insights that will inform future estimator design.
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