
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/semi_supervised/plot_label_propagation_structure.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_semi_supervised_plot_label_propagation_structure.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_semi_supervised_plot_label_propagation_structure.py:


=======================================================
Label Propagation circles: Learning a complex structure
=======================================================

Example of LabelPropagation learning a complex internal structure
to demonstrate "manifold learning". The outer circle should be
labeled "red" and the inner circle "blue". Because both label groups
lie inside their own distinct shape, we can see that the labels
propagate correctly around the circle.

.. GENERATED FROM PYTHON SOURCE LINES 13-17

.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause








.. GENERATED FROM PYTHON SOURCE LINES 18-22

We generate a dataset with two concentric circles. In addition, a label
is associated with each sample of the dataset that is: 0 (belonging to
the outer circle), 1 (belonging to the inner circle), and -1 (unknown).
Here, all labels but two are tagged as unknown.

.. GENERATED FROM PYTHON SOURCE LINES 22-34

.. code-block:: Python


    import numpy as np

    from sklearn.datasets import make_circles

    n_samples = 200
    X, y = make_circles(n_samples=n_samples, shuffle=False)
    outer, inner = 0, 1
    labels = np.full(n_samples, -1.0)
    labels[0] = outer
    labels[-1] = inner








.. GENERATED FROM PYTHON SOURCE LINES 35-36

Plot raw data

.. GENERATED FROM PYTHON SOURCE LINES 36-67

.. code-block:: Python

    import matplotlib.pyplot as plt

    plt.figure(figsize=(4, 4))
    plt.scatter(
        X[labels == outer, 0],
        X[labels == outer, 1],
        color="navy",
        marker="s",
        lw=0,
        label="outer labeled",
        s=10,
    )
    plt.scatter(
        X[labels == inner, 0],
        X[labels == inner, 1],
        color="c",
        marker="s",
        lw=0,
        label="inner labeled",
        s=10,
    )
    plt.scatter(
        X[labels == -1, 0],
        X[labels == -1, 1],
        color="darkorange",
        marker=".",
        label="unlabeled",
    )
    plt.legend(scatterpoints=1, shadow=False, loc="center")
    _ = plt.title("Raw data (2 classes=outer and inner)")




.. image-sg:: /auto_examples/semi_supervised/images/sphx_glr_plot_label_propagation_structure_001.png
   :alt: Raw data (2 classes=outer and inner)
   :srcset: /auto_examples/semi_supervised/images/sphx_glr_plot_label_propagation_structure_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 68-70

The aim of :class:`~sklearn.semi_supervised.LabelSpreading` is to associate
a label to sample where the label is initially unknown.

.. GENERATED FROM PYTHON SOURCE LINES 71-76

.. code-block:: Python

    from sklearn.semi_supervised import LabelSpreading

    label_spread = LabelSpreading(kernel="knn", alpha=0.8)
    label_spread.fit(X, labels)






.. raw:: html

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      --sklearn-color-unfitted-level-0: #fff5e6;
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      --sklearn-color-unfitted-level-2: #ffe0b3;
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      /* Definition of color scheme for fitted estimators */
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    .sk-estimator-doc-link.fitted,
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    }

    .features.fitted {
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    }

    .features summary {
      cursor: pointer;
      display: flex;
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    .features details[open] > summary {
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    .features details > summary .arrow::before {
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    .features details:hover > summary {
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      max-height: 10em;
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    </style><body><div id="sk-container-id-45" tabindex="0" class="sk-top-container sk-global"><div class="sk-text-repr-fallback"><pre>LabelSpreading(alpha=0.8, kernel=&#x27;knn&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually sk-global" id="sk-estimator-id-152" type="checkbox" checked><label for="sk-estimator-id-152" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>LabelSpreading</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html">?<span>Documentation for LabelSpreading</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted" data-param-prefix="">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('kernel',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-kernel;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=kernel,-%7B%27knn%27%2C%20%27rbf%27%7D%20or%20callable%2C%20default%3D%27rbf%27">
                kernel
                <span class="param-doc-description"
                style="position-anchor: --doc-link-kernel;">
                kernel: {&#x27;knn&#x27;, &#x27;rbf&#x27;} or callable, default=&#x27;rbf&#x27;<br><br>String identifier for kernel function to use or the kernel function<br>itself. Only &#x27;rbf&#x27; and &#x27;knn&#x27; strings are valid inputs. The function<br>passed should take two inputs, each of shape (n_samples, n_features),<br>and return a (n_samples, n_samples) shaped weight matrix.</span>
            </a>
        </td>
                <td class="value">&#x27;knn&#x27;</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('alpha',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-alpha;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=alpha,-float%2C%20default%3D0.2">
                alpha
                <span class="param-doc-description"
                style="position-anchor: --doc-link-alpha;">
                alpha: float, default=0.2<br><br>Clamping factor. A value in (0, 1) that specifies the relative amount<br>that an instance should adopt the information from its neighbors as<br>opposed to its initial label.<br>alpha=0 means keeping the initial label information; alpha=1 means<br>replacing all initial information.</span>
            </a>
        </td>
                <td class="value">0.8</td>
            </tr>
    

            <tr class="default">
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                     onclick="copyToClipboard('gamma',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
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                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=gamma,-float%2C%20default%3D20">
                gamma
                <span class="param-doc-description"
                style="position-anchor: --doc-link-gamma;">
                gamma: float, default=20<br><br>Parameter for rbf kernel.</span>
            </a>
        </td>
                <td class="value">20</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_neighbors',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_neighbors;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=n_neighbors,-int%2C%20default%3D7">
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                <td class="value">7</td>
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                style="position-anchor: --doc-link-max_iter;">
                max_iter: int, default=30<br><br>Maximum number of iterations allowed.</span>
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                <td class="value">30</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('tol',
                              this.parentElement.nextElementSibling)"
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                tol
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                tol: float, default=1e-3<br><br>Convergence tolerance: threshold to consider the system at steady<br>state.</span>
            </a>
        </td>
                <td class="value">0.001</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_jobs',
                              this.parentElement.nextElementSibling)"
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                n_jobs
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                <td class="value">None</td>
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                      </tbody>
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                </details>
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            <div class="estimator-table">
                <details>
                    <summary>Fitted attributes</summary>
                    <table class="parameters-table">
                        <tbody>
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                            <th>Name</th>
                            <th>Type</th>
                            <th>Value</th>
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           <tr class="default">
               <td class="param">
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                X_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-X_;">
                X_: ndarray of shape (n_samples, n_features)<br><br>Input array.</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](200, 2)</td>
               <td>[[ 1.  , 0.  ],
     [ 1.  , 0.06],
     [ 0.99, 0.13],
     ...,
     [ 0.79,-0.15],
     [ 0.79,-0.1 ],
     [ 0.8 ,-0.05]]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-classes_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=classes_,-ndarray%20of%20shape%20%28n_classes%2C%29">
                classes_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-classes_;">
                classes_: ndarray of shape (n_classes,)<br><br>The distinct labels used in classifying instances.</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](2,)</td>
               <td>[0.,1.]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-label_distributions_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=label_distributions_,-ndarray%20of%20shape%20%28n_samples%2C%20n_classes%29">
                label_distributions_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-label_distributions_;">
                label_distributions_: ndarray of shape (n_samples, n_classes)<br><br>Categorical distribution for each item.</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](200, 2)</td>
               <td>[[1.,0.],
     [1.,0.],
     [1.,0.],
     ...,
     [0.,1.],
     [0.,1.],
     [0.,1.]]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_features_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=n_features_in_,-int">
                n_features_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_features_in_;">
                n_features_in_: int<br><br>Number of features seen during :term:`fit`.<br><br>.. versionadded:: 0.24</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>2</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_iter_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=n_iter_,-int">
                n_iter_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_iter_;">
                n_iter_: int<br><br>Number of iterations run.</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>18</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-transduction_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.semi_supervised.LabelSpreading.html#:~:text=transduction_,-ndarray%20of%20shape%20%28n_samples%2C%29">
                transduction_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-transduction_;">
                transduction_: ndarray of shape (n_samples,)<br><br>Label assigned to each item during :term:`fit`.</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](200,)</td>
               <td>[0.,0.,0.,...,1.,1.,1.]</td>


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.. GENERATED FROM PYTHON SOURCE LINES 77-79

Now, we can check which labels have been associated with each sample
when the label was unknown.

.. GENERATED FROM PYTHON SOURCE LINES 79-106

.. code-block:: Python

    output_labels = label_spread.transduction_
    output_label_array = np.asarray(output_labels)
    outer_numbers = (output_label_array == outer).nonzero()[0]
    inner_numbers = (output_label_array == inner).nonzero()[0]

    plt.figure(figsize=(4, 4))
    plt.scatter(
        X[outer_numbers, 0],
        X[outer_numbers, 1],
        color="navy",
        marker="s",
        lw=0,
        s=10,
        label="outer learned",
    )
    plt.scatter(
        X[inner_numbers, 0],
        X[inner_numbers, 1],
        color="c",
        marker="s",
        lw=0,
        s=10,
        label="inner learned",
    )
    plt.legend(scatterpoints=1, shadow=False, loc="center")
    plt.title("Labels learned with Label Spreading (KNN)")
    plt.show()



.. image-sg:: /auto_examples/semi_supervised/images/sphx_glr_plot_label_propagation_structure_002.png
   :alt: Labels learned with Label Spreading (KNN)
   :srcset: /auto_examples/semi_supervised/images/sphx_glr_plot_label_propagation_structure_002.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.219 seconds)


.. _sphx_glr_download_auto_examples_semi_supervised_plot_label_propagation_structure.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_label_propagation_structure.ipynb <plot_label_propagation_structure.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_label_propagation_structure.py <plot_label_propagation_structure.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_label_propagation_structure.zip <plot_label_propagation_structure.zip>`


.. include:: plot_label_propagation_structure.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
