Excuse me for all these commits, I got confused because I had made commits on the main directly for another issue. I only changed the path of the image for this issue.

@thomasjpfan

Thank you very much for your first feedback. I didn't understand what the problem was and now I've made the connection.
To fix this, I made now a mix between the new version of plot_lle_digits.py and the old version present in #20543.
I kept all the function grouping as it was done in the new version but I took the old code for plot_embedding and tried to bring some aspects of the new code like the axis.

Does it look right to you?

The images are well generated again :)

Also, I have this error:

WARNING: Since version 2.0, Sphinx uses "index" as default root_doc. Please add "root_doc = 'contents'" to your conf.py.

Should we add this to the Sphinx config?

Thanks in advance for your feedback

Should we add this to the Sphinx config?

No it is unrelated to the PR. If we want to update sphinx config, it should be done in another PR.

There are a few things that needs to be done with this PR:

1. The Azure CI is failing because of linting issues having to do with black. You can find instructions on how to run black in the Pull Request checklist on step 5. (Install black==21.6b0 and run black .) Once the linting issues are fixed circleci will render this PR's docs, so we can see if the HTML are rendered correctly.
2. We have to make sure that both https://scikit-learn.org/stable/auto_examples/manifold/plot_lle_digits.html and mainfold.rst are generated nicely in HTML
3. The best workflow to do part 2 is described in Building the documentation where you can use EXAMPLES_PATTERN to build one example locally.
4. To rework plot_lle_digits.py one needs to be aware of the narrative style docs we are moving toward. For example: https://github.com/scikit-learn/scikit-learn/blob/main/examples/compose/plot_column_transformer_mixed_types.py there is a mixture of using # %% to construct cells so the rendered HTML has separate headings.

With all the points above, I do not think this is a great first issue. I recommend looking at #21350 for a good first issue to start getting use to scikit-learn's workflow.

@cathelineparisot Would you be okay if another contributor continues this work?

@cathelineparisot Would you be okay if another contributor continues this work?

Hello, yes of course. I am no longer working on this issue so someone can take over. Thanks for asking !