.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/cluster/plot_linkage_comparison.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_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.

.. GENERATED FROM PYTHON SOURCE LINES 25-39

.. code-block:: Python


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

    import time
    import warnings
    from itertools import cycle, islice

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn import cluster, datasets
    from sklearn.preprocessing import StandardScaler








.. GENERATED FROM PYTHON SOURCE LINES 40-42

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

.. GENERATED FROM PYTHON SOURCE LINES 42-63

.. code-block:: Python


    n_samples = 1500
    noisy_circles = datasets.make_circles(
        n_samples=n_samples, factor=0.5, noise=0.05, random_state=170
    )
    noisy_moons = datasets.make_moons(n_samples=n_samples, noise=0.05, random_state=170)
    blobs = datasets.make_blobs(n_samples=n_samples, random_state=170)
    rng = np.random.RandomState(170)
    no_structure = rng.rand(n_samples, 2), None

    # Anisotropicly distributed data
    X, y = datasets.make_blobs(n_samples=n_samples, random_state=170)
    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=170
    )








.. GENERATED FROM PYTHON SOURCE LINES 64-65

Run the clustering and plot

.. GENERATED FROM PYTHON SOURCE LINES 65-179

.. code-block:: Python


    # Set up cluster parameters
    plt.figure(figsize=(9 * 1.3 + 2, 14.5))
    plt.subplots_adjust(
        left=0.02, right=0.98, bottom=0.001, top=0.96, wspace=0.05, hspace=0.01
    )

    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(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(
                0.99,
                0.01,
                ("%.2fs" % (t1 - t0)).lstrip("0"),
                transform=plt.gca().transAxes,
                size=15,
                horizontalalignment="right",
            )
            plot_num += 1

    plt.show()



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






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

   **Total running time of the script:** (0 minutes 1.428 seconds)


.. _sphx_glr_download_auto_examples_cluster_plot_linkage_comparison.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/cluster/plot_linkage_comparison.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

    .. 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-zip

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


.. include:: plot_linkage_comparison.recommendations


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

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