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

.. only:: html

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

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

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

.. _sphx_glr_gyexamples_ml_basic_plot_clustering.py:


Clustering
==========

Le `clustering <https://fr.wikipedia.org/wiki/Partitionnement_de_donn%C3%A9es>`_
est une méthode non supervisée qui vise à répartir les données selon
leur similarité dans des clusters. L'inconnu de ce type de problèmes
est le nombre de clusters.

.. contents::
    :local:

.. GENERATED FROM PYTHON SOURCE LINES 17-21

Principe
--------

On commence par générer un nuage de points artificiel.

.. GENERATED FROM PYTHON SOURCE LINES 22-30

.. code-block:: default


    import numpy
    from sklearn.metrics import silhouette_samples, silhouette_score
    from sklearn.cluster import KMeans
    import matplotlib.pyplot as plt
    from sklearn.datasets import make_blobs
    X, Y = make_blobs(n_samples=500, n_features=2, centers=4)








.. GENERATED FROM PYTHON SOURCE LINES 31-32

On représente ces données.

.. GENERATED FROM PYTHON SOURCE LINES 32-36

.. code-block:: default


    fig, ax = plt.subplots(1, 1, figsize=(5, 5))
    ax.plot(X[:, 0], X[:, 1], '.')




.. image-sg:: /gyexamples/ml_basic/images/sphx_glr_plot_clustering_001.png
   :alt: plot clustering
   :srcset: /gyexamples/ml_basic/images/sphx_glr_plot_clustering_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    [<matplotlib.lines.Line2D object at 0x7f5f36dedc70>]



.. GENERATED FROM PYTHON SOURCE LINES 37-40

On utilise un algorithme très utilisé :
`KMeans <http://scikit-learn.org/stable/modules/generated/
sklearn.cluster.KMeans.html>`_.

.. GENERATED FROM PYTHON SOURCE LINES 40-44

.. code-block:: default


    km = KMeans()
    km.fit(X)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /usr/local/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
      warnings.warn(


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>#sk-container-id-5 {color: black;background-color: white;}#sk-container-id-5 pre{padding: 0;}#sk-container-id-5 div.sk-toggleable {background-color: white;}#sk-container-id-5 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-5 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-5 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-5 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-5 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-5 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-5 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-5 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-5 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-5 div.sk-item {position: relative;z-index: 1;}#sk-container-id-5 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-5 div.sk-item::before, #sk-container-id-5 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-5 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-5 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-5 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-5 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-5 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-5 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-5 div.sk-label-container {text-align: center;}#sk-container-id-5 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-5 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-5" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>KMeans()</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 sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-7" type="checkbox" checked><label for="sk-estimator-id-7" class="sk-toggleable__label sk-toggleable__label-arrow">KMeans</label><div class="sk-toggleable__content"><pre>KMeans()</pre></div></div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 45-47

L'optimisation du modèle produit autant de points
que de clusters.

.. GENERATED FROM PYTHON SOURCE LINES 47-49

.. code-block:: default

    print(km.cluster_centers_)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    [[ 2.81219206 -8.66796052]
     [-5.39610266  1.66554465]
     [-7.93921872 -6.77276865]
     [ 6.77222059 -2.35684426]
     [ 1.13637447 -9.37453472]
     [-4.45946923  2.99653347]
     [-6.93449447 -5.51329065]
     [ 8.44625973 -2.46233653]]




.. GENERATED FROM PYTHON SOURCE LINES 50-52

On dessine le résultat en choisissant une couleur
différente pour chaque cluster.

.. GENERATED FROM PYTHON SOURCE LINES 52-58

.. code-block:: default


    cmap = plt.cm.get_cmap("hsv", km.cluster_centers_.shape[0])
    fig, ax = plt.subplots(1, 1, figsize=(5, 5))
    colors = [cmap(i) for i in km.fit_predict(X)]
    ax.scatter(X[:, 0], X[:, 1], c=colors)




.. image-sg:: /gyexamples/ml_basic/images/sphx_glr_plot_clustering_002.png
   :alt: plot clustering
   :srcset: /gyexamples/ml_basic/images/sphx_glr_plot_clustering_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    somewhere/workspace/papierstat/papierstat_UT_39_std/_doc/examples/ml_basic/plot_clustering.py:53: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.
      cmap = plt.cm.get_cmap("hsv", km.cluster_centers_.shape[0])
    /usr/local/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
      warnings.warn(

    <matplotlib.collections.PathCollection object at 0x7f5f36c2f610>



.. GENERATED FROM PYTHON SOURCE LINES 59-71

Autre graphe et métrique silhouette
-----------------------------------

Inspiré de `Selecting the number of clusters with silhouette
analysis on KMeans clustering <http://scikit-learn.org/stable/
auto_examples/cluster/plot_kmeans_silhouette_analysis.html>`_.
Il s'agit de représenter la dispersion au sein de chaque cluster.
Sont-ils concentrés autour d'un point ou plutôt regroupés
parce que loin de tout ?
On commence par calculer le score silhouette
puis à prendre un échantillon aléatoire sous
peine d'avoir un graphique surchargé.

.. GENERATED FROM PYTHON SOURCE LINES 72-79

.. code-block:: default


    cluster_labels = km.fit_predict(X)
    silhouette_avg = silhouette_score(X, cluster_labels)
    sample_silhouette_values = silhouette_samples(X, cluster_labels)
    centers = km.cluster_centers_
    n_clusters = centers.shape[0]





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    /usr/local/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning
      warnings.warn(




.. GENERATED FROM PYTHON SOURCE LINES 80-81

On dessine.

.. GENERATED FROM PYTHON SOURCE LINES 81-131

.. code-block:: default


    try:
        from matplotlib.cm import spectral as color_map
    except ImportError:
        from matplotlib.cm import summer as color_map

    fig, (ax1, ax2) = plt.subplots(1, 2)
    fig.set_size_inches(9, 5)

    ax1.set_xlim([-0.1, 1])
    ax1.set_ylim([0, len(X) + (km.n_clusters + 1) * 10])

    y_lower = 10
    for i in range(n_clusters):
        ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i]
        ith_cluster_silhouette_values.sort()

        size_cluster_i = ith_cluster_silhouette_values.shape[0]
        y_upper = y_lower + size_cluster_i

        color = color_map(float(i) / n_clusters)
        ax1.fill_betweenx(numpy.arange(y_lower, y_upper),
                          0, ith_cluster_silhouette_values,
                          facecolor=color, edgecolor=color, alpha=0.7)

        ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
        y_lower = y_upper + 10

    ax1.set_title("Score silhouette / clusters.")
    ax1.set_xlabel("silhouette")
    ax1.set_ylabel("Cluster")

    ax1.axvline(x=silhouette_avg, color="red", linestyle="--")

    ax1.set_yticks([])
    ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])

    colors = color_map(cluster_labels.astype(float) / n_clusters)
    ax2.scatter(X[:, 0], X[:, 1], marker='.', s=30,
                lw=0, alpha=0.7, c=colors, edgecolor='k')
    ax2.scatter(centers[:, 0], centers[:, 1], marker='o',
                c="white", alpha=1, s=200, edgecolor='k')

    for i, c in enumerate(centers):
        ax2.scatter(c[0], c[1], marker='$%d$' % i, alpha=1,
                    s=50, edgecolor='k')

    plt.suptitle(("Analyse silhouette pour un échantillon"
                  "n_clusters = %d" % n_clusters),
                 fontsize=14, fontweight='bold')



.. image-sg:: /gyexamples/ml_basic/images/sphx_glr_plot_clustering_003.png
   :alt: Analyse silhouette pour un échantillonn_clusters = 8, Score silhouette / clusters.
   :srcset: /gyexamples/ml_basic/images/sphx_glr_plot_clustering_003.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    findfont: Font family ['STIXGeneral'] not found. Falling back to DejaVu Sans.
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    Text(0.5, 0.98, 'Analyse silhouette pour un échantillonn_clusters = 8')




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

   **Total running time of the script:** ( 0 minutes  3.387 seconds)


.. _sphx_glr_download_gyexamples_ml_basic_plot_clustering.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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