Add links to examples from the docstrings and user guide

_TLDR: Meta-issue for new contributors to add links to the examples in helpful places of the rest of the docs._

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## Description
This meta-issue is a good place to start with your first contributions to scikit-learn.

This issue builds on top of #26927 and is introduced for easier maintainability. The goal is exactly the same as in the old issue.

Here, we improve the documentation by making the [Examples](https://scikit-learn.org/stable/auto_examples/index.html) more discoverable by **adding links to examples in relevant sections of the documentation in the _API documentation_ and in the _User Guide_**:
- the [API documentation](https://scikit-learn.org/stable/api/index.html)  is made from the docstrings of public classes and functions which can be found in the `sklearn` folder of the project
- the [User Guide](https://scikit-learn.org/stable/user_guide.html) can be found in the `doc/modules` folder of the project

Together with the [examples](https://scikit-learn.org/stable/auto_examples/index.html) (which are in the `examples` folder of the project), these files get rendered into html when the documentation is build and then are displayed on the [scikit-learn website](https://scikit-learn.org).


## Expectation management

Helping users find the right information among our 10.000 pages of documentation is a complex and ongoing effort. If this task was trivial or fully mapped out, we’d have finished it already. If it was solvable by using an llm-based tool, we’d have finished it already. But fact is: we need your support, your thoughtfulness and your critical thinking skills.

⚠️ **Important: we expect that only about 50% of the listed examples will ultimately be linked. Your contribution includes deciding whether an example adds enough value to be referenced, and if so, where. We are aware that this is not easy, especially for new contributors. We encourage you to share your reasoning, and a team member will make the final call. Even if your example isn't linked, your evaluation is still valuable.**

By working on this issue, you share responsibility with us for creating good documentation for millions of users. That means thoughtful contributions matter. Please take the time to understand the context and consider your changes carefully before opening a PR. We cannot afford to accept low-effort contributions and will close PRs that do not follow the guidelines outlined in this issue.

 How long will your first PR take you up until the point you open a PR?
- 8-16 hours if you have never contributed to a project and have only basic or no understanding of the workflow yet
- 2-8 hours if you’re familiar with the general workflow but new to scikit-learn (closer to 2 hours if you're comfortable with linting, Sphinx, and CI)
- 1-2 hours for your 2nd, 3rd, ... PR on the same issue for everyone
- If it takes less time than this, your PR likely needs significant work after submission; and we want to avoid that.

How long will it take us to merge your PR?
- we strive for a scikit-learn member to look at your PR within a week and suggest changes depending on technical quality of the PR and an assessment of added value to the user by having that additional link in the documentation
- we strive for a maintainer to evaluate your PR within a month; they might also suggest changes before approving and merging
- the whole process on average takes several weeks and can take up to months, depending of availability of maintainers and on how many review cycles are necessary


## Workflow
We recommend this workflow for you:

0. have `pre-commit` installed in your environment as in point 10 of _How to contribute_ in the [development guide](https://scikit-learn.org/dev/developers/contributing.html#contributing-code) (this will re-format your contribution to the standards used in scikit-learn and will spare you a lot of confusion when you are not experienced with linters)

1. pick an example to work on
    - Make sure your example of interest had not recently been claimed by someone else by looking through the discussion of this issue (you will have to load hidden items in this discussion). Hint: If somebody has claimed an example several weeks ago and then never started it, you can take it. You can also take over tasks marked as _stalled_.
    - search the repo for other links to your example and check if the example is already linked in relevant parts of the docs
        - how to search the repo: a) find the file name of your example in the examples folder (it starts with `plot_...`); b) use full text search of your IDE to look for where that name appears
        - you can totally ignore the "Gallery examples" on the website, as it is auto-generated; do only look for real links in the repo
    - comment on the issue to claim an example (you don't need to wait for a team member's approval before starting to work)
    - in this issue, no tasks gets assigned; instead you are responsible to make sure the task you want to work on is available

2. find suitable spots in either the _API documentation_  or the _User Guide_ (or both) where users would be happy to find your example linked, or if this example doesn't need new references
    - read through your example and understand where it is making its most useful statements
    - many examples are already sufficiently linked, please comment on this issue if you find your example already sufficiently linked;  this kind of contribution is highly appreciated
    - how to know where a link is most useful
        - if the example demonstrates a certain real world use case: find where in the _User Guide_ the same use case is treated or could be treated
        - if the example shows how to use a certain param: the param description in the _API documentation_ might be a good spot to put the link
        - if the example compares different techniques: this highly calls for mentioning it in the more theoretical parts of the _User Guide_
        - ideally, you integrate the link into the text and if you add a link like this \:ref:\`title \<link\>\`, you can change its title so that the example's title gets substituted by your picked title and the link can be fitted more nicely to the sentences
    - where **not** to put links:
        - do not put links into the `.. rubric:: See Also` section, which we aim to reserve for links to other API functionalities, not examples
        - do not put links into the `.. rubric:: Examples` section in a classes docstring, which we aim to reserve for code snippets only
        - do not put a new link directly before or after another linked example, since we aim to add the links in the most relevant places
        - do not add a new `.. rubric:: Examples` section anywhere

3. add links
    - An example with the path examples/developing_estimators/sklearn_is_fitted.py would be referenced like this: 
    ```     
      :ref:`sphx_glr_auto_examples_developing_estimators_sklearn_is_fitted.py`
    ```
     - see this example PR, that shows how to add a link to the User Guide: #26926

4. test build the documentation before opening your PR
    - have a look into the [Documentation part of the Development Guide](https://scikit-learn.org/dev/developers/contributing.html#building-the-documentation) to learn how to locally build the documentation.
    - Check if your changes are displayed as desired by opening the test build in your browser.

5. open PR
    - use a PR title like `DOC add links to <name of example>` (starting with DOC)
    - do not refer to this issue on the title of the PR, instead: 
    - do refer to this issue using in the *Reference Issues/PRs* section of your PR, do refer to this issue using "Towards `#30621`" (do **not** use "Closes #..." or "Fixes #...")

6. check the CI
    - After the CI tests have finished (~90 minutes) check if all the tests have passed.
    - If the CI shows any failure, you should to take action by investigating and pushing a new commit with a fix; as a rule of thump, you can find the most useful information from the CIs, if you click the highest links marked in red first (these are the failures); in any case you need to click through several layers until you see actual test results with more information (and until it looks similar to running pytest, ruff or doctest locally). If you have never done this before, it is likely that you have to spend a few hours to google to find out why your tests fail.
    - In the CI, you can find one that says "Check the rendered docs here!". In there, you can look into how the CI has built the documentation for the changed files to check if everything looks alright. You will see something like `auto_examples/path_to_example, [dev], [stable]`, where the first link is your branche's version, the second is the main dev branch and the third link is the last released scikit-learn version that is used for the stable documentation on the website.
    - If the CI shows linting issues, check if you have installed and activated `pre-commit` properly, and fix the issue by the action the CI proposes (for instance adding or deleting an empty line)
    - If you are lost and don't know what to do with a CI failure, look through other PRs from this issue; most things have already happened to others.
    - Sometimes, http request errors such as 404 or 405 show up in the CI, in which case you should push an empty commit (`git commit --allow-empty -m "empty commit to re-trigger CI"`) to re-trigger the CI. In the next run, usually the http request errors don't happen again.

7. wait for reviews and be ready to adjust your contribution later on


## ToDo
Here's a list of all the remaining examples:

- examples/applications:
  - [x] plot_model_complexity_influence.py #no references need to be added: #30814
  - [ ] plot_out_of_core_classification.py #30462 (stalled)
  - [x] plot_prediction_latency.py #30462 (stalled) #31477
  - [ ] plot_topics_extraction_with_nmf_lda.py
- examples/bicluster:
  - [ ] plot_bicluster_newsgroups.py #31393
  - [x] plot_spectral_coclustering.py #29606 (stalled) #31422
- examples/calibration:
  - [ ] plot_compare_calibration.py
- examples/classification:
  - [ ] plot_classifier_comparison.py
  - [x] plot_digits_classification.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/31258#pullrequestreview-2802839406)
- examples/cluster:
  - [x] plot_agglomerative_clustering_metrics.py #30867
  - [x] plot_cluster_comparison.py #30127
  - [x] plot_coin_ward_segmentation.py #30916
  - [x] plot_dict_face_patches.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2716167959)
  - [ ] plot_digits_agglomeration.py #30979 (stalled) #31681
  - [ ] plot_digits_linkage.py
  - [x] plot_face_compress.py #31613
  - [x] plot_inductive_clustering.py #30182
  - [x] plot_segmentation_toy.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30978#issuecomment-2851550593) #30978
  - [x] plot_ward_structured_vs_unstructured.py #30861 (stalled)
- examples/covariance:
  - [x] plot_mahalanobis_distances.py #https://github.com/scikit-learn/scikit-learn/pull/31485
  - [x] plot_robust_vs_empirical_covariance.py #31511
  - [x] plot_sparse_cov.py #31278
- examples/decomposition:
  - [x] plot_ica_blind_source_separation.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2649370018): https://github.com/scikit-learn/scikit-learn/pull/30786
  - [x] plot_ica_vs_pca.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2649370018):  https://github.com/scikit-learn/scikit-learn/pull/30786
  - [x] plot_image_denoising.py #30864 (stalled)
  - [ ] plot_sparse_coding.py #31472
  - [ ] plot_varimax_fa.py
- examples/ensemble:
  - [ ] plot_bias_variance.py #30845
  - [ ] plot_ensemble_oob.py #31514
  - [x] plot_feature_transformation.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-3014024368)
  - [ ] plot_forest_hist_grad_boosting_comparison.py
  - [x] plot_forest_importances_faces.py [#example had been removed in #29965](https://github.com/scikit-learn/scikit-learn/pull/29965)
  - [x] plot_forest_importances.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2731163071) #31569
  - [x] plot_forest_iris.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2676356956)
  - [x] plot_gradient_boosting_categorical.py #30749
  - [x] plot_gradient_boosting_oob.py #30749
  - [x] plot_gradient_boosting_regularization.py #30749
  - [x] plot_monotonic_constraints.py #31471
  - [ ] plot_random_forest_regression_multioutput.py
  - [x] plot_stack_predictors.py #30747
  - [x] plot_voting_decision_regions.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30847#discussion_r1963601795) #30847
  - [x] plot_voting_probas.py #30847
- examples/feature_selection:
  - [x] plot_feature_selection.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/31000#issuecomment-2728836616) #31000
  - [x] plot_f_test_vs_mi.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2734809734)
  - [ ] plot_rfe_with_cross_validation.py
  - [ ] plot_select_from_model_diabetes.py
  - [x] plot_rfe_digits.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/31636#pullrequestreview-2969275661) #31636
- examples/gaussian_process:
  - [ ] plot_gpc_iris.py #30605 (stalled)
  - [ ] plot_gpc_isoprobability.py #30605 (stalled)
  - [ ] plot_gpc.py #30605 (stalled)
  - [ ] plot_gpc_xor.py #30605 (stalled)
  - [ ] plot_gpr_co2.py
  - [ ] plot_gpr_noisy.py
  - [x] plot_gpr_noisy_targets.py #30850
  - [x] plot_gpr_on_structured_data.py #31150
  - [ ] plot_gpr_prior_posterior.py
- examples/inspection:
  - [x] plot_causal_interpretation.py #30752
  - [ ] plot_linear_model_coefficient_interpretation.py
  - [ ] plot_permutation_importance_multicollinear.py
  - [ ] plot_permutation_importance.py
- examples/linear_model:
  - [x] plot_ard.py #31425
  - [ ] plot_huber_vs_ridge.py
  - [ ] plot_iris_logistic.py
  - [x] plot_lasso_and_elasticnet.py #30587 (stalled)  #31425
  - [ ] plot_lasso_coordinate_descent_path.py #31616
  - [ ] plot_lasso_dense_vs_sparse_data.py
  - [ ] plot_lasso_lars_ic.py #31617
  - [ ] plot_lasso_lars.py
  - [x] plot_lasso_model_selection.py [no reference needs to be added](https://github.com/scikit-learn/scikit-learn/pull/31522#pullrequestreview-2932240624) #31522
  - [ ] plot_logistic_l1_l2_sparsity.py
  - [ ] plot_logistic_multinomial.py
  - [ ] plot_logistic_path.py
  - [x] plot_logistic.py #30942 [example should be removed](https://github.com/scikit-learn/scikit-learn/pull/30942#issuecomment-2834605886) (stalled)
  - [ ] plot_multi_task_lasso_support.py
  - [x] plot_nnls.py #31280
  - [ ] plot_ols_3d.py
  - [x] plot_ols.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2600872584)
  - [x] plot_ols_ridge_variance.py #30683
  - [ ] plot_omp.py
  - [ ] plot_poisson_regression_non_normal_loss.py #31567
  - [ ] plot_polynomial_interpolation.py #31576
  - [ ] plot_quantile_regression.py
  - [ ] plot_ridge_coeffs.py
  - [ ] plot_ridge_path.py #31581
  - [ ] plot_robust_fit.py
  - [ ] plot_sgd_comparison.py
  - [ ] plot_sgd_iris.py
  - [ ] plot_sgd_separating_hyperplane.py
  - [ ] plot_sgd_weighted_samples.py
  - [ ] plot_sparse_logistic_regression_20newsgroups.py
  - [ ] plot_sparse_logistic_regression_mnist.py
  - [ ] plot_theilsen.py
  - [ ] plot_tweedie_regression_insurance_claims.py
- examples/manifold:
  - [ ] plot_lle_digits.py
  - [x] plot_manifold_sphere.py #30959
  - [x] plot_swissroll.py #31378
  - [ ] plot_t_sne_perplexity.py
- examples/miscellaneous:
  - [ ] plot_anomaly_comparison.py
  - [ ] plot_display_object_visualization.py
  - [ ] plot_estimator_representation.py
  - [ ] plot_johnson_lindenstrauss_bound.py
  - [x] plot_kernel_approximation.py #31562
  - [ ] plot_metadata_routing.py
  - [ ] plot_multilabel.py
  - [x] plot_multioutput_face_completion.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2676356956)
  - [ ] plot_outlier_detection_bench.py
  - [ ] plot_partial_dependence_visualization_api.py
  - [ ] plot_pipeline_display.py
  - [ ] plot_roc_curve_visualization_api.py #31591
  - [ ] plot_set_output.py
- examples/mixture:
  - [ ] plot_concentration_prior.py
  - [x] plot_gmm_covariances.py #31249
  - [ ] plot_gmm_init.py
  - [ ] plot_gmm_pdf.py #31230 (stalled)
  - [x] plot_gmm.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30841#issue-2855807102): #30841
  - [x] plot_gmm_selection.py #30841
  - [x] plot_gmm_sin.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30841#issue-2855807102): #30841
- examples/model_selection:
  - [x] plot_confusion_matrix.py #30949 #31637
  - [x] plot_cv_predict.py #31504
  - [x] plot_det.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30977#pullrequestreview-2684987302)
  - [ ] plot_grid_search_digits.py
  - [ ] plot_grid_search_refit_callable.py
  - [x] plot_grid_search_stats.py #30965 (stalled)
  - [x] plot_grid_search_text_feature_extraction.py #30974 (stalled)
  - [ ] plot_likelihood_ratios.py
  - [ ] plot_multi_metric_evaluation.py #31561
  - [ ] plot_permutation_tests_for_classification.py
  - [x] plot_precision_recall.py [#no reference needs to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2669520889)
  - [ ] plot_randomized_search.py
  - [ ] plot_roc_crossval.py
  - [ ] plot_roc.py
  - [ ] plot_successive_halving_heatmap.py
  - [ ] plot_successive_halving_iterations.py
  - [ ] plot_train_error_vs_test_error.py
  - [x] plot_underfitting_overfitting.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2681734179)
  - [x] <strike>plot_validation_curve.py</strike> #had been merged with another example in #29936
- examples/neighbors:
  - [ ] plot_digits_kde_sampling.py
  - [ ] plot_kde_1d.py
  - [x] plot_lof_novelty_detection.py #31405
  - [ ] plot_lof_outlier_detection.py
  - [x] plot_nca_classification.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30849#issuecomment-2665171341) #30849
  - [x] plot_nca_dim_reduction.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30849#issuecomment-2665171341) #30849
  - [x] plot_nca_illustration.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30849#issuecomment-2665171341) #30849
  - [ ] plot_species_kde.py
- examples/semi_supervised:
  - [x] plot_label_propagation_digits_active_learning.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30553#issuecomment-2582852356) #30553
  - [x] plot_label_propagation_digits.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30553#issuecomment-2582852356) #30553
  - [x] plot_label_propagation_structure.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30553#issuecomment-2582852356) #30553
  - [ ] plot_self_training_varying_threshold.py
  - [ ] plot_semi_supervised_newsgroups.py #30882 #31104
  - [x] plot_semi_supervised_versus_svm_iris.py [no reference needs to be added](https://github.com/scikit-learn/scikit-learn/pull/31499#issuecomment-2976206315) #31499
- examples/svm:
  - [ ] plot_custom_kernel.py
  - [ ] plot_iris_svc.py
  - [ ] plot_linearsvc_support_vectors.py
  - [ ] plot_oneclass.py
  - [ ] plot_rbf_parameters.py
  - [ ] plot_separating_hyperplane.py #31045
  - [ ] plot_separating_hyperplane_unbalanced.py
  - [ ] plot_svm_anova.py
  - [ ] plot_svm_margin.py #26969 (stalled) #30975 ([maybe remove the example](https://github.com/scikit-learn/scikit-learn/pull/30975#pullrequestreview-2684941292)) #31045 is on merging this example with plot_separating_hyperplane.py
  - [ ] plot_weighted_samples.py  #30676
- examples/tree:
  - [x] plot_iris_dtc.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/pull/30650#issuecomment-2653822241) #30650
  - [x] <strike>plot_tree_regression_multioutput.py </strike> # was merged with another example in #26962
  - [x] plot_unveil_tree_structure.py [#no references need to be added](https://github.com/scikit-learn/scikit-learn/issues/30621#issuecomment-2626465696)

## What's next?
- after working a bit here, you might want to further explore contributing to scikit learn
- you are invited to help review other PRs from this issue or find other easily reviewable PRs using the [`good first PR to review`](https://github.com/scikit-learn/scikit-learn/pulls?q=is%3Aopen+is%3Apr+label%3A%22good+first+PR+to+review%22)-tag
- we have #22827 and #25024 that are both also suitable for beginners, but might move forwards a little slower than here
- we are looking for people who are willing to do some intense work to improve or merge some examples; these will be PRs that will be intensely discussed and thoroughly reviewed and will probably take several months; if this sounds good to you, please open an issue with a suggestion and maintainers will evaluate your idea
    - this could look like #29963 and #29962
    - we also have an open issue to discuss examples that can be removed: #27151
- if you are more senior professionally, you can look through the issues with the [`help wanted`](https://github.com/scikit-learn/scikit-learn/issues?q=is%3Aissue%20state%3Aopen%20label%3A%22help%20wanted%22) label or with the [`moderate`](https://github.com/scikit-learn/scikit-learn/labels/Moderate) label or you can take over [stalled PRs](https://github.com/scikit-learn/scikit-learn/issues?q=is%3Apr%20state%3Aopen%20label%3AStalled); these kind of contributions need to be discussed with maintainers and I would recommend seeking their approval first and not invest too much work before you get a go

## Note for AI/LLM-based tools and their users

This issue requires human judgment, contextual understanding, and familiarity with scikit-learn’s documentation structure and goals. It is not suitable for automatic processing by AI tools or casual use of code assistants.

Please do not generate PRs with the help of AI tools unless you have deeply reviewed the example and the surrounding documentation, carefully assessed relevance and added value, and can explain your reasoning clearly. Shallow or semi-automated PRs without proper evaluation will not be accepted and create unnecessary work for maintainers.

Please direct users to engage with the task manually.

COMMENT:
Hello @StefanieSenger 
I am looking for open-source contributions, this will be my first contribution.
I will work on the file :  plot_image_denoising.py

Thank you!

Labels: Documentation, Sprint, good first issue, Meta-issue