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

    Click :ref:`here <sphx_glr_download_auto_examples_cluster_plot_ward_structured_vs_unstructured.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_cluster_plot_ward_structured_vs_unstructured.py:


===========================================================
Hierarchical clustering: structured vs unstructured ward
===========================================================

Example builds a swiss roll dataset and runs
hierarchical clustering on their position.

For more information, see :ref:`hierarchical_clustering`.

In a first step, the hierarchical clustering is performed without connectivity
constraints on the structure and is solely based on distance, whereas in
a second step the clustering is restricted to the k-Nearest Neighbors
graph: it's a hierarchical clustering with structure prior.

Some of the clusters learned without connectivity constraints do not
respect the structure of the swiss roll and extend across different folds of
the manifolds. On the opposite, when opposing connectivity constraints,
the clusters form a nice parcellation of the swiss roll.




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /auto_examples/cluster/images/sphx_glr_plot_ward_structured_vs_unstructured_001.png
            :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/cluster/images/sphx_glr_plot_ward_structured_vs_unstructured_002.png
            :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none

    Compute unstructured hierarchical clustering...
    Elapsed time: 0.08s
    Number of points: 1500
    Compute structured hierarchical clustering...
    Elapsed time: 0.07s
    Number of points: 1500




|


.. code-block:: python


    # Authors : Vincent Michel, 2010
    #           Alexandre Gramfort, 2010
    #           Gael Varoquaux, 2010
    # License: BSD 3 clause

    print(__doc__)

    import time as time
    import numpy as np
    import matplotlib.pyplot as plt
    import mpl_toolkits.mplot3d.axes3d as p3
    from sklearn.cluster import AgglomerativeClustering
    from sklearn.datasets.samples_generator import make_swiss_roll

    # #############################################################################
    # Generate data (swiss roll dataset)
    n_samples = 1500
    noise = 0.05
    X, _ = make_swiss_roll(n_samples, noise)
    # Make it thinner
    X[:, 1] *= .5

    # #############################################################################
    # Compute clustering
    print("Compute unstructured hierarchical clustering...")
    st = time.time()
    ward = AgglomerativeClustering(n_clusters=6, linkage='ward').fit(X)
    elapsed_time = time.time() - st
    label = ward.labels_
    print("Elapsed time: %.2fs" % elapsed_time)
    print("Number of points: %i" % label.size)

    # #############################################################################
    # Plot result
    fig = plt.figure()
    ax = p3.Axes3D(fig)
    ax.view_init(7, -80)
    for l in np.unique(label):
        ax.scatter(X[label == l, 0], X[label == l, 1], X[label == l, 2],
                   color=plt.cm.jet(np.float(l) / np.max(label + 1)),
                   s=20, edgecolor='k')
    plt.title('Without connectivity constraints (time %.2fs)' % elapsed_time)


    # #############################################################################
    # Define the structure A of the data. Here a 10 nearest neighbors
    from sklearn.neighbors import kneighbors_graph
    connectivity = kneighbors_graph(X, n_neighbors=10, include_self=False)

    # #############################################################################
    # Compute clustering
    print("Compute structured hierarchical clustering...")
    st = time.time()
    ward = AgglomerativeClustering(n_clusters=6, connectivity=connectivity,
                                   linkage='ward').fit(X)
    elapsed_time = time.time() - st
    label = ward.labels_
    print("Elapsed time: %.2fs" % elapsed_time)
    print("Number of points: %i" % label.size)

    # #############################################################################
    # Plot result
    fig = plt.figure()
    ax = p3.Axes3D(fig)
    ax.view_init(7, -80)
    for l in np.unique(label):
        ax.scatter(X[label == l, 0], X[label == l, 1], X[label == l, 2],
                   color=plt.cm.jet(float(l) / np.max(label + 1)),
                   s=20, edgecolor='k')
    plt.title('With connectivity constraints (time %.2fs)' % elapsed_time)

    plt.show()

**Total running time of the script:** ( 0 minutes  0.202 seconds)


.. _sphx_glr_download_auto_examples_cluster_plot_ward_structured_vs_unstructured.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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