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arXiv AI By Henry Han

Quantifying Local and Global Fidelity of Nonlinear Embeddings

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The paper introduces the DLP curve, a metric that quantifies how well nonlinear embeddings like t‑SNE and UMAP preserve local and global structure by measuring the share of each point’s k‑nearest neighbors retained in the map. Corrected for chance, the curve yields local fidelity (L) at k=10 and global fidelity (G) over 30–50% of the data, with the midpoint provably equivalent to a rank correlation of distances. The authors also present the LG reversal test to compare two maps and the entity fidelity (E) to predict which entities a map loses, demonstrating strong agreement with established global scores on twelve large datasets.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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