.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_cluster_plot_linkage_comparison.py>`     to download the full example code or to run this example in your browser via Binder
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_examples_cluster_plot_linkage_comparison.py:


================================================================
Comparing different hierarchical linkage methods on toy datasets
================================================================

This example shows characteristics of different linkage
methods for hierarchical clustering on datasets that are
"interesting" but still in 2D.

The main observations to make are:

- single linkage is fast, and can perform well on
  non-globular data, but it performs poorly in the
  presence of noise.
- average and complete linkage perform well on
  cleanly separated globular clusters, but have mixed
  results otherwise.
- Ward is the most effective method for noisy data.

While these examples give some intuition about the
algorithms, this intuition might not apply to very high
dimensional data.


.. code-block:: default

    print(__doc__)

    import time
    import warnings

    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn import cluster, datasets
    from sklearn.preprocessing import StandardScaler
    from itertools import cycle, islice

    np.random.seed(0)








Generate datasets. We choose the size big enough to see the scalability
of the algorithms, but not too big to avoid too long running times


.. code-block:: default


    n_samples = 1500
    noisy_circles = datasets.make_circles(n_samples=n_samples, factor=.5,
                                          noise=.05)
    noisy_moons = datasets.make_moons(n_samples=n_samples, noise=.05)
    blobs = datasets.make_blobs(n_samples=n_samples, random_state=8)
    no_structure = np.random.rand(n_samples, 2), None

    # Anisotropicly distributed data
    random_state = 170
    X, y = datasets.make_blobs(n_samples=n_samples, random_state=random_state)
    transformation = [[0.6, -0.6], [-0.4, 0.8]]
    X_aniso = np.dot(X, transformation)
    aniso = (X_aniso, y)

    # blobs with varied variances
    varied = datasets.make_blobs(n_samples=n_samples,
                                 cluster_std=[1.0, 2.5, 0.5],
                                 random_state=random_state)








Run the clustering and plot


.. code-block:: default


    # Set up cluster parameters
    plt.figure(figsize=(9 * 1.3 + 2, 14.5))
    plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
                        hspace=.01)

    plot_num = 1

    default_base = {'n_neighbors': 10,
                    'n_clusters': 3}

    datasets = [
        (noisy_circles, {'n_clusters': 2}),
        (noisy_moons, {'n_clusters': 2}),
        (varied, {'n_neighbors': 2}),
        (aniso, {'n_neighbors': 2}),
        (blobs, {}),
        (no_structure, {})]

    for i_dataset, (dataset, algo_params) in enumerate(datasets):
        # update parameters with dataset-specific values
        params = default_base.copy()
        params.update(algo_params)

        X, y = dataset

        # normalize dataset for easier parameter selection
        X = StandardScaler().fit_transform(X)

        # ============
        # Create cluster objects
        # ============
        ward = cluster.AgglomerativeClustering(
            n_clusters=params['n_clusters'], linkage='ward')
        complete = cluster.AgglomerativeClustering(
            n_clusters=params['n_clusters'], linkage='complete')
        average = cluster.AgglomerativeClustering(
            n_clusters=params['n_clusters'], linkage='average')
        single = cluster.AgglomerativeClustering(
            n_clusters=params['n_clusters'], linkage='single')

        clustering_algorithms = (
            ('Single Linkage', single),
            ('Average Linkage', average),
            ('Complete Linkage', complete),
            ('Ward Linkage', ward),
        )

        for name, algorithm in clustering_algorithms:
            t0 = time.time()

            # catch warnings related to kneighbors_graph
            with warnings.catch_warnings():
                warnings.filterwarnings(
                    "ignore",
                    message="the number of connected components of the " +
                    "connectivity matrix is [0-9]{1,2}" +
                    " > 1. Completing it to avoid stopping the tree early.",
                    category=UserWarning)
                algorithm.fit(X)

            t1 = time.time()
            if hasattr(algorithm, 'labels_'):
                y_pred = algorithm.labels_.astype(np.int)
            else:
                y_pred = algorithm.predict(X)

            plt.subplot(len(datasets), len(clustering_algorithms), plot_num)
            if i_dataset == 0:
                plt.title(name, size=18)

            colors = np.array(list(islice(cycle(['#377eb8', '#ff7f00', '#4daf4a',
                                                 '#f781bf', '#a65628', '#984ea3',
                                                 '#999999', '#e41a1c', '#dede00']),
                                          int(max(y_pred) + 1))))
            plt.scatter(X[:, 0], X[:, 1], s=10, color=colors[y_pred])

            plt.xlim(-2.5, 2.5)
            plt.ylim(-2.5, 2.5)
            plt.xticks(())
            plt.yticks(())
            plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'),
                     transform=plt.gca().transAxes, size=15,
                     horizontalalignment='right')
            plot_num += 1

    plt.show()



.. image:: /auto_examples/cluster/images/sphx_glr_plot_linkage_comparison_001.png
    :alt: Single Linkage, Average Linkage, Complete Linkage, Ward Linkage
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  2.179 seconds)


.. _sphx_glr_download_auto_examples_cluster_plot_linkage_comparison.py:


.. only :: html

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


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      :width: 150 px


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

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



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

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.. only:: html

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