提出eDCF方法，精准估算数据内在维度，抗噪能力强。
eDCF: Estimating Intrinsic Dimension using Local Connectivity
- 基于局部连通性构造新指标，可跨尺度稳定估计
- 在含噪数据上误差更小，精确匹配率最高达25.0%
- 适用于大样本和复杂结构数据，如决策边界分形分析
现代数据集常包含高维特征并呈现复杂依赖关系。为有效分析此类数据，降维方法需估计数据的内在维度（ID）以衡量其潜在复杂度。然而，由于对尺度敏感——极细尺度下噪声会夸大ID估计值，粗尺度则趋于稳定且与尺度无关——导致估计困难。本文提出一种新型、可扩展且可并行化的估计方法eDCF，基于局部连通性指标（CF），能稳健地跨尺度估计内在维度。该方法在合成基准测试中表现优于现有主流方法，均方误差（MAE）相当；同时在精确匹配真实维度方面，准确率达25.0%，显著高于MLE的16.7%和TWO-NN的12.5%，尤其在中高噪声水平及大规模数据下优势明显。此外，我们验证了该方法可准确识别决策边界中的分形几何结构，证明其在真实、有结构数据中的分析价值。
原文摘要 · Abstract (English)
Modern datasets often contain high-dimensional features exhibiting complex dependencies. To effectively analyze such data, dimensionality reduction methods rely on estimating the dataset's intrinsic dimension (id) as a measure of its underlying complexity. However, estimating id is challenging due to its dependence on scale: at very fine scales, noise inflates id estimates, while at coarser scales, estimates stabilize to lower, scale-invariant values. This paper introduces a novel, scalable, and parallelizable method called eDCF, which is based on Connectivity Factor (CF), a local connectivity-based metric, to robustly estimate intrinsic dimension across varying scales. Our method consistently matches leading estimators, achieving comparable values of mean absolute error (MAE) on synthetic benchmarks with noisy samples. Moreover, our approach also attains higher exact intrinsic dimension match rates, reaching up to 25.0% compared to 16.7% for MLE and 12.5% for TWO-NN, particularly excelling under medium to high noise levels and large datasets. Further, we showcase our method's ability to accurately detect fractal geometries in decision boundaries, confirming its utility for analyzing realistic, structured data.
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