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In certain UMAP visualization, it appears that the visualizations show the first UMAP "principal component" plotted against the second. For example, like this:

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Apparently, this lets us use the first and second UMAP "principal components" to tell apart the different cell clusterings in a dataset. I'm curious about if we were to use e.g. the second and the third UMAP "principal components" instead - would this let us tell apart different cell clusterings according to the second and third features that explain those clusterings' largest sources of variation? If someone could explain this to me, I would be very grateful, and if you would like to correct whatever misunderstandings I have about UMAP as well, that would be great too - I'd be the first one to tell you that I don't understand it well!

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    $\begingroup$ The clustering is just visualized onto the UMAP, it is based on the principal components of a PCA, don't mix that up. UMAP in many cases is just a 2D compression of the PCA results for visualization. Nice to have and good to get an idea how data look, but that's all about it. $\endgroup$
    – user3051
    Commented Dec 22, 2021 at 9:48

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You can plot UMAP3 too in 3 dimensions, but that's about the limit for viz. You could plot UMAP2 vs. UMAP3, UMAP3 vs. UMAP4 etc. but I'm not sure how informative it is. Instead, you can focus on other analyses like clustering, differential expression, cell type annotation, marker gene analysis, and other machine learning approaches etc. Ultimately, UMAP/t-SNE are nice tools for viz but they can be over interpreted- it is inherently impossible to summarise very highly dimensional data in just a few dimensions without losing information- see here for an (overly) provocative take.

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