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Understanding UMAP – Topos Institute

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UMAP is a dimension-reduction method that has become very popular, especially in many areas of biology. Recently, a certain figure produced by UMAP has been circulated online to support spurious conclusions about “genetic racial groups”, or, to put it more bluntly, to support scientific racism. In the original paper outlining the method, the section justifying the construction uses a lot of category theory, which many practicing scientists might not be comfortable with. The purpose of this post is simple: much online discussion is stymied by the fact that UMAP is a opaque process for people not comfortable with the language of category theory; can we unpack things in less technical language? As a result, we can more critically evaluate any claims concerning UMAP and “interpretability”. I am a mathematician who works mostly with the tools of category theory and algebraic topology to study geometry, so when I open up a paper and see adjunctions and simplicial sets and geometric realisati

Understanding UMAP – Topos Institute 1 Context I am a mathematician who works mostly with the tools of category theory and algebraic topology to study geometry, so when I open up a paper and see adjunctions and simplicial sets and geometric realisation and Riemannian metrics, I feel pretty happy. One of the infinitely many things I am not is a data scientist, so when I am asked about dimension-reduction methods, I cannot give a meaningful or confident answer. This blog post arises from an odd middle ground, where I hope I can say something useful by being on this side of the fence. UMAP is a d

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