← 研踪 PaperTrailarXiv:2611.00290 · v2
Quantifying Local and Global Fidelity of Nonlinear Embeddings
首次提交 2026-10-31 03:16
版本更新 2026-11-04 06:23
雷达观测 2026-11-05 10:08
摘要
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).
作者备注：29 pages, 17 figures, 12 tables
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v2 · 2026-11-04 06:23 · 最新观测版本
Quantifying Local and Global Fidelity of Nonlinear Embeddings
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).
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