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arXiv:1802.03426stat.ML

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Leland McInnes, John Healy, James Melville

Abstract

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.

arXiv comments
Reference implementation available at http://github.com/lmcinnes/umap
Journal reference
DOI
Subjects
stat.MLMachine Learning (Statistics) cs.CGComputational Geometry cs.LGMachine Learning

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Linked by 7 identifiable commenters in 7 comments across 6 threads, from Aug 2018 to Oct 2024. Found in 1 HN submission from Jan 2019 to Jan 2019. Open submission discussions.

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Discussed in comments6 threads

  1. Category Theory Illustrated: Logic (2021) 1 comment

    • The closest I know of is the work on UMAP. I interviewed Leland McInnes who explained to me in detail how category theory was a big part of helping him connect the dots, even though the final result does not strictly need it in the actual code. Given the relative improvement…

      j2kunView on HNParent context

  2. Applied Category Theory 1 comment

    • Check out UMAP [1]. It's an alternative to t-SNE for dimension reduction that's grounded in topological category theory. [1] https://arxiv.org/abs/1802.03426

      wjn0View on HNParent context

  3. Topological methods for unsupervised learning problems [video] 1 comment

    • Uniform Manifold Approximation and Projection https://arxiv.org/abs/1802.03426 https://github.com/lmcinnes/umap

      nabla9View on HNParent context

  4. Structure of recent philosophy (2017) 1 comment

    • UMAP[1] and t-SNE[2] are two very similar and popular ways to map a set of points in a high dimensional space to a low-dimensional (usually 2D or 3D) space by assuming all the points are close to some smooth curved surface (a manifold[3]). These are unsupervised non-linear…

      olooneyView on HNParent context

  5. Let’s Try t-SNE 1 comment

    • To anyone using t sne, consider giving UMAP a try. https://arxiv.org/abs/1802.03426 Equally accessible as tsne in Python.

      b_tterc_pView on HNParent context

  6. A visualization of the prime factors of the first million integers 2 comments

    • structure to the space of prime factors There is topological structure https://math.stackexchange.com/questions/2879/mapping-natura... http://ncatlab.org/nlab/show/arithmetic+topology as well as geometric (arithmetic geometry). Question is how does the picture correspond to any…

      thraway180306View on HNParent context

    • If what you're asking about is the math, the steps are (essentially) as follows: 1. A Riemannian manifold is constructed from the dataset. 2. The manifold is approximately mapped to an n-dimensional topological structure. 3. The reduced embedding is an (n - k)-dimensional…

      throwawaymathView on HNParent context

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