Researchers propose LG reversal test to compare local and global fidelity in embeddings
A new paper on arXiv introduces a method to measure and compare how well dimension reduction techniques like t-SNE, UMAP, and PCA preserve local versus global structure in data. The authors define local fidelity (L) as the chance-corrected share of a point’s 10 nearest neighbors retained, and global fidelity (G) as the mean agreement over 30–50% of the dataset. Their LG reversal test uses a…
Key points
- LG reversal test compares local/global fidelity of embeddings using a single statistic and p-value
- Validated on 156 embeddings across 12 datasets, including one with 1.38M points
- Finds neighbor embeddings outperform traditional methods globally on retail and manifold data
The study validates the test on 156 embeddings across 12 datasets, including one with up to 1.38 million points. It confirms traditional claims on seven datasets but finds neighbor embeddings perform better globally on retail and manifold data. In an AI agent memory of one million passages, the test shows a crossover point at 150,000 passages (p = 2.6e-5). Applications span pathology, single-cell analysis, supply chains, and agent memory optimization.
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