UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction · HackerPapers discussions

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by j2kun

Fri, 25 Oct 2024 17:26:39 GMT

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 over the previous state of the art (t-SNE), it's the only example that really makes me reconsider my poo-pooing the way category theory is discussed in software. https://arxiv.org/abs/1802.03426

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UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by wjn0

Fri, 19 Apr 2019 23:39:11 GMT

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

Paper and discussion history. A mention is not an endorsement.

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by nabla9

Thu, 28 Feb 2019 19:50:48 GMT

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

Paper and discussion history. A mention is not an endorsement.

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — HN submission

Tue, 22 Jan 2019 20:43:39 GMT

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

3 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by olooney

Tue, 22 Jan 2019 15:31:08 GMT

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 dimensional reduction techniques; if you're familar with linear dimensional reduction techniques like PCA[4] you can think of UMAP and t-SNE as curved generalizations of that. t-SNE is widely known to be hard to interpret and unstable with respect to arbitrary hyper-parameters[5] and I would assume UMAP suffers similar…

Paper and discussion history. A mention is not an endorsement.

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by b_tterc_p

Sun, 23 Dec 2018 05:07:48 GMT

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

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UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by throwawaymath

Wed, 22 Aug 2018 15:11:44 GMT

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 projection equivalent to the initial topological structure, where k is the number of dimensions you'd like to reduce by. I don't know how well that answers your question because it's difficult to simplify the math beyond that. But you can also check out the paper on arXiv. [1] The underlying idea is to transform the data…

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UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction — mentioned by thraway180306

Wed, 22 Aug 2018 14:13:42 GMT

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 of it. Glancing at the UMAP paper https://arxiv.org/abs/1802.03426 it looks like a proper invariant preserving embedding, so maybe loops in the image are real. Even if not, it does hint artistically at sorts of stuff that exist.

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