Quantifying Local and Global Fidelity of Nonlinear Embeddings

arXiv cs.AINovember 3, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2611.00290v1 Announce Type: new Abstract: Dimension reduction methods are chosen by a common claim: t-SNE and UMAP preserve local structure, and PCA preserves global structure. Checking it on given data takes local and global scores on one scale and a test that compares two maps. Both scores come from one curve. The locality profile is the chance-corrected share of each point's k nearest neighbors that a map keeps, over all neighborhood sizes. Its value at k = 10 is the local fidelity L, and its mean over 30 to 50 percent of the data is the global fidelity G. We prove that at the midpoint the profile is the agreement on which half of the data is near each point, a rank correlation of t

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