How UMAP Works | Hacker News Reader

How UMAP Works

umap-learn.readthedocs.io

53 pointstmalsburg210 comments

Shameless self plug here, but I saw this today and figured I should link to an interactive overview article "Understanding UMAP" my colleagues and I put together:

https://pair-code.github.io/understanding-umap/

UMAP is a really useful piece in the modern data science toolkit, and despite its power it's surprisingly simple and elegant. But as with all dimensionality reduction techniques, there's a lot of ways to misread the results. High dimensional data behaves very counterintuitively, and any reduction in dimensionality fundamentally distorts the original data in some way. Understanding the fundamental concepts behind UMAP and exploring how it works is the best way to develop an intuition of what the technique can and can't tell you about your data.

generally I abhor videos, but to get a "simple" version of "how UMAP works", I found this presentation by Leland mcInnes, one of the creators of UMAP.

https://www.youtube.com/watch?v=nq6iPZVUxZU

There's a beautiful visualization of prime factorization using UMAP: https://johnhw.github.io/umap_primes/index.md.html. I recommend watching the video!

So the reduced features can be used for inference/prediction?

Also, is there some rule for choosing a) the number of dimensions the unreduced dataset should be mapped on to, b) the number of neighbors?

I assume the default parameters would work for most tasks.

UMAP is typically used for embeddings that get displayed to a human, so 2 or 3 dimensions is typical.

It doesn’t really suit inference/prediction because you can’t really add new data without influencing the embedding values of the other data. It’s not like PCA where you can learn a projection once and then map new data points to the same embedding space.

Yes you can. https://umap-learn.readthedocs.io/en/latest/transform.html

You can but it is both costly and a hack (the resulting embedding will not be as good as the one you would have gotten restarting from scratch). So I would not recommend using it in an inference pipeline.

If this is a thing you want to be able to do efficiently then ParametricUMAP (see [docs](https://umap-learn.readthedocs.io/en/latest/parametric_umap....) and [the paper](https://arxiv.org/abs/2009.12981)) will be very effective. It uses a neural network to learn a mapping directly from data to embedding space using a UMAP loss. Pushing new data through is only slightly more expensive than PCA, so being part of an inference pipeline is fine.

But then you have to train a neural network and lose on the speed advantage of UMAP (offline yes but still much slower and finicky).

It is really not that much slower for training (see the paper), and if you are interested in pipelines the difference is not so great considering you are looking at a one off training time vs. lots of inference.

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