[MRG] Create public kmeans_plusplus including index output - #17937

Thanks for the review

I think we can also rename it to be more explicit, like _kmeans_plusplus.

@jeremiedbb just to be clear you mean renaming _k_init to _kmeans_plusplus?

One question for the docstrings, are you happy for them to be essentially the same text for both _k_init and kmeans_plusplus?

I'll work on the testing and full documentation/examples next.

just to be clear you mean renaming _k_init to _kmeans_plusplus?

yes :)

One question for the docstrings, are you happy for them to be essentially the same text for both _k_init and kmeans_plusplus?

It should yes, the exception being the type of the parameters. For instance, random_state doesn't have to be a RandomState instance but can also be an int.

If you're happy with the test coverage then I'll next start working on adding the documentation and examples

@g-walsh that's nice !

I'm not sure that it requires a example on its own but others might disagree, let's wait for the opinion of other reviewers.
It also needs an example in the docstring. We are trying to put examples in the docstring of each public function/class of sklearn. You could simply adapt this example:

other than that looks good to me, thanks !

I merged master to trigger a rebuild.

Thanks @g-walsh !