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TriMap: Large-scale Dimensionality Reduction Using Triplets

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arxiv 1910.00204 v2 pith:UTD4NQJL submitted 2019-10-01 cs.LG stat.ML

TriMap: Large-scale Dimensionality Reduction Using Triplets

Ehsan Amid , Manfred K. Warmuth This is my paper
classification cs.LG stat.ML
keywords trimapdimensionalityembeddingglobalintroducelargevisperformancepoints
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Neighbor Embedding for High-Dimensional Sparse Poisson Data

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    p-SNE embeds sparse Poisson count data into low dimensions by using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the layout.

  2. The General Theory of Localization Methods

    cs.LG 2026-05 unverdicted novelty 6.0

    The localization method unifies kernel methods, local learning algorithms, MeanShift, Hopfield networks, and Transformers through local models, localization tricks, and hierarchical extensions.

  3. FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling

    cs.LG 2026-05 unverdicted novelty 6.0

    FastUMAP speeds up UMAP by 15x on 70k-point datasets via bipartite landmark sampling and Nystrom initialization while retaining 96% of the kNN accuracy of stronger baselines.

  4. Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph

    cs.LG 2026-07 conditional novelty 5.0

    Running PageRank, k-core, and clustering coefficient on UMAP's pre-projection kNN graph yields competitive exemplar selection, density hierarchies, and local-cohesion signals on MNIST and Fashion MNIST.

  5. Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph

    cs.LG 2026-07 conditional novelty 5.0

    Running PageRank, k-core decomposition, and clustering coefficient on UMAP's internal kNN graph finds representative points, dense cores, and tight micro-clusters at sub-second cost, rivaling purpose-built methods.

  6. Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph

    cs.LG 2026-07 accept novelty 5.0

    Applying PageRank, k-core decomposition, and clustering coefficient to UMAP's internal kNN graph yields sensemaking capabilities complementary to the 2D scatter plot.

  7. mlx-vis: GPU-Native Dimensionality Reduction on Apple Silicon

    cs.LG 2026-03 conditional novelty 5.0

    mlx-vis is a pure-MLX library that runs eight dimensionality-reduction methods and k-NN construction on Apple Silicon GPUs, claiming 3–13x speedups over CPU packages.

  8. The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction

    cs.LG 2025-03 unverdicted novelty 5.0

    Analysis of UMAP embedding forces shows repulsion controls cluster boundaries while attraction has dual effects, motivating a modification that improves consistency under random initialization.

  9. Hyperboloid GPLVM for Discovering Continuous Hierarchies via Nonparametric Estimation

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    Introduces three variants of hyperboloid GP-LVMs for continuous hierarchical embedding via nonparametric estimation and Riemannian optimization.

  10. Cluster Exploration using Informative Manifold Projections

    cs.LG 2023-09 unverdicted novelty 5.0

    A manifold optimization method combining contrastive PCA and kurtosis projection pursuit generates embeddings that discount prior knowledge structures while revealing underlying cluster separation in high-dimensional data.

  11. On Out-of-sample Embedding in UMAP

    cs.LG 2026-06 unverdicted novelty 4.0

    Optimizing pairwise interactions within the kNN graph and using parameterized UMAP mitigates repulsion in out-of-sample embedding and improves performance on complex data.

  12. FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling

    cs.LG 2026-05 unverdicted novelty 4.0

    FastUMAP approximates UMAP via sparse bipartite point-landmark graphs and Nystrom initialization to deliver lower runtimes than Barnes-Hut t-SNE on most tested datasets while retaining competitive kNN accuracy.

  13. The General Theory of Localization Methods

    cs.LG 2026-05 unverdicted novelty 3.0

    The localization method is presented as a unifying framework connecting kernel methods, MeanShift, Hopfield networks, LLE, fuzzy inference, denoising autoencoders, and Transformers via local models and the localization trick.