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Hi in PCA one can interpret the level of variance with x vs y, with x often times explaining much of the variance. As one plot higher dimensions the variance percent would go down. My question is, are the axis in UMAP plots similar. What does it mean when the axis is -5 to 2 vs something that is -10 to 15?

thanks!

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There is no such clean interpretation for UMAP. It's non-linear, which is nice because unlike PCA it will reveal structure beyond linear relationships. Unfortunately by doing this you lose the connections to linear algebra which is the basis for inferential statistics. These non-linear methods are just nice visualization techniques to justify further exploration with other tests, but you should not spend too much time reading into them (though it can be fun, it is ultimately a waste of time).

There probably are nice interpretations of UMAP, but it is not within linear algebra and requires a lot more advanced math as UMAP is based on Reimannian geometry. https://arxiv.org/abs/1802.03426

UMAP may have predictive value in some circumstances in ML, but building a predictive model is not the same as making inferences. What is the difference between prediction and inference?

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  • $\begingroup$ thanks. At the very least can we get any other information from comparing ranges. For example if one axis is range from -10 to 15+ while the other is is from -2 to 3+, are there any between these ranges? $\endgroup$
    – Ahdee
    Jun 3, 2021 at 22:52
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    $\begingroup$ No. Please read the publication on it. This is not an inference technique, you would say these points look like they group together using umap these ones don't. No inferences may be drawn. In a predictive model you may apply a clustering technique to the embedding (which is the space UMAP plots the data points onto). So UMAP may find a machine readable mapping. But again this is not inference it is prediction. $\endgroup$
    – Angus Campbell
    Jun 3, 2021 at 23:43
  • $\begingroup$ ok thank for clarification. I will read the link you posted. $\endgroup$
    – Ahdee
    Jun 4, 2021 at 2:13
  • $\begingroup$ @Ahdee If you want a non-linear dimensionality reduction method that still has that nice relation to eigenvectors look at spectral clustering, also called heat map diffusion. Its a bit more complicated than PCA but it may be what you're looking for. Again though none of these embeddings should be used for inference. $\endgroup$
    – Angus Campbell
    Jun 4, 2021 at 18:54

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