量化非线性嵌入的局部与全局保真度
Quantifying Local and Global Fidelity of Nonlinear Embeddings
AI 导读
arXiv 论文提出 DLP 曲线方法，量化 t-SNE、UMAP、PCA 等降维映射的局部与全局保真度，并给出 LG reversal 检验来判断两个映射哪个更保局部、哪个更保全局。在最多 138 万点的 12 个数据集上，其全局保真度 G 与既有全局分数相关性达 0.84 和 0.93。在 100 万条 agent 记忆实验中，t-SNE 与 PCA 在 15 万条处交叉（p=2.6e-5）。
正文 · 原文
Abstract:Dimension reduction rests on a claim: t-SNE and UMAP preserve local structure, PCA global structure. Our DLP curve is the share of each point's k nearest neighbors a map keeps. Corrected for chance, it gives L at k=10 and G over 30 to 50% of the data, local and global fidelity. At the midpoint the curve is provably a rank correlation of distances. The LG reversal test decides, with a stated error rate, which of two maps is local and which global. On twelve datasets of up to 1.38 million points, G agrees with established global scores at 0.84 and 0.93, and the area under R_NX at 0.22 and 0.30. The entity fidelity E, read at each point's entity size, predicts which entities a map loses beyond L and G where entity sizes differ. In an agent memory of one million passages, t-SNE and PCA cross at 150,000 passages (p=2.6e-5).
| Comments: | 29 pages, 17 figures, 12 tables |
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2611.00290 [cs.AI] |
| (or arXiv:2611.00290v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2611.00290 arXiv-issued DOI via DataCite |
Submission history
From: Henry Han [view email]
[v1]
Fri, 30 Oct 2026 19:16:23 UTC (6,671 KB)
[v2]
Tue, 3 Nov 2026 22:23:19 UTC (7,303 KB)
来源：arXiv cs.AI · arxiv.org