AI

Quantifying Local and Global Fidelity of Nonlinear Embeddings

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Briefings

A new study quantifies fidelity in nonlinear embeddings using a single statistic combining local and global scores. The LG reversal test determines which dimension reduction method is more local or global by comparing two maps. On 156 maps across twelve datasets, the test confirmed that neighbor embeddings are more global than established global scores, with a p-value of 2.6e-5 at the midpoint of the data distribution.

Key points

• The LG reversal test uses a block-jackknife p-value to compare two dimension reduction maps, determining which method is more local or more global.
• On 156 maps of twelve datasets, the test found that neighbor embeddings are more global than established global scores, with a p-value of 2.6e-5 at the midpoint of the data distribution.

Context

This research addresses the common claim that t-SNE and UMAP preserve local structure while PCA preserves global structure. The study provides a unified metric to test these claims across diverse datasets.

Limitations

The study covers 156 maps across twelve datasets with up to 1.38 million points. Results are based on a single curve of scores and a specific test method; uncertainty exists regarding the generalizability of findings to other data types or scales.

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