We have a lot of functions referenced in our API reference.

For our own sanity, I would like to propose to make private any function that either:

• has an obvious estimator equivalent, e.g. k_means or fastica. There should be one obvious way to do things. (Some of them might be subject to debate, like scale which is arguably convenient.)
• isn't immediately useful for users. For example, I don't know much about OPTICS but I feel like cluster_optics_xi should be private (it's not even mentioned in the user guide).

There are plenty of other functions, and even more that aren't in the API ref.

Motivation:
k_means and fastica are making my life difficult right now as I'm working on #13603. KMeans.fit() does nothing but calling k_means which does all the work.

I cannot change anything to the KMeans class now (e.g. add an attribute), because I would I need to change the signature / interface / behaviour of k_means, which is a public function.

(I think that in general the design of having the estimator call a public helper is bad (it should be the other way around), but that's another issue.)