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Is dimensionality reduction considered to be primarily unsupervised learning?

I have always thought of dimensionality reduction as unsupervised learning. It is what you usually see in textbooks. "Now we will present several unsupervised learning types: clustering, dimensionality reduction, etc.". But now I saw that there is also supervised dimensionality reduction. It does make sense though, I can imagine supervised dimensionality reduction scenarios.

But, then I wonder why most of the time people refer to dimensionality reduction as unsupervised learning?

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Even though, I found stuff online using the term "supervised dimensionality reduction", for now I decided to place it in the unsupervised learning part of my book. I am still not sure what they mean by supervised DR, since I didn't have the time to read those articles, but I will treat DR as unsupervised for now. Also, given that I didn't get much response for my question here, I assume most people don't even care about this issue, and they just treat DR as unsupervised learning.

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