Category: math.CT
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The Theory behind UMAP?
The Theory behind UMAP? arXiv:2603.03375v1 Announce Type: new Abstract: In 2018, McInnes et al. introduced a dimensionality reduction algorithm called UMAP, which enjoys wide popularity among data scientists. Their work introduces a finite variant of a functor called the metric realization, based on an unpublished draft by Spivak. This draft contains many errors, most of…
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Categorical and geometric methods in statistical, manifold, and machine learning
Categorical and geometric methods in statistical, manifold, and machine learning arXiv:2505.03862v1 Announce Type: new Abstract: We present and discuss applications of the category of probabilistic morphisms, initially developed in cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics,…