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2019

TriMap: Large-scale Dimensionality Reduction Using Triplets

Amid, Ehsan, Warmuth, Manfred K.

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We introduce "TriMap"; a dimensionality reduction technique based on triplet constraints, which preserves the global structure of the data better than the other commonly used methods such as t-SNE, LargeVis, and UMAP.

To quantify the global accuracy of the embedding, we introduce a score that roughly reflects the relative placement of the clusters rather than the individual points.
We empirically show the excellent performance of TriMap on a large variety of datasets in terms of the quality of the embedding as well as the runtime.
On our performance benchmarks, TriMap easily scales to millions of points without depleting the memory and clearly outperforms t-SNE, LargeVis, and UMAP in terms of runtime.

TriMap: Large-scale Dimensionality Reduction Using Triplets · Around

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Liii. on lines and planes of closest fit to systems of points in space
Karl Pearson · 1901
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Deformed exponentials and logarithms in generalized thermostatistics
Jan Naudts · 2002
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Global versus local methods in nonlinear dimensionality reduction
Vin D Silva and Joshua B Tenenbaum · 2003
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Local multidimensional scaling with controlled tradeoff between trustworthiness and continuity
Jarkko Venna and Samuel Kaski · 2005
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