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

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

.. _sphx_glr_auto_examples_cluster_plot_optics.py:


===================================
Demo of OPTICS clustering algorithm
===================================
Finds core samples of high density and expands clusters from them.
This example uses data that is generated so that the clusters have
different densities.
The :class:`sklearn.cluster.OPTICS` is first used with its Xi cluster detection
method, and then setting specific thresholds on the reachability, which
corresponds to :class:`sklearn.cluster.DBSCAN`. We can see that the different
clusters of OPTICS's Xi method can be recovered with different choices of
thresholds in DBSCAN.




.. image:: /auto_examples/cluster/images/sphx_glr_plot_optics_001.png
    :class: sphx-glr-single-img





.. code-block:: python


    # Authors: Shane Grigsby <refuge@rocktalus.com>
    #          Adrin Jalali <adrin.jalali@gmail.com>
    # License: BSD 3 clause


    from sklearn.cluster import OPTICS, cluster_optics_dbscan
    import matplotlib.gridspec as gridspec
    import matplotlib.pyplot as plt
    import numpy as np

    # Generate sample data

    np.random.seed(0)
    n_points_per_cluster = 250

    C1 = [-5, -2] + .8 * np.random.randn(n_points_per_cluster, 2)
    C2 = [4, -1] + .1 * np.random.randn(n_points_per_cluster, 2)
    C3 = [1, -2] + .2 * np.random.randn(n_points_per_cluster, 2)
    C4 = [-2, 3] + .3 * np.random.randn(n_points_per_cluster, 2)
    C5 = [3, -2] + 1.6 * np.random.randn(n_points_per_cluster, 2)
    C6 = [5, 6] + 2 * np.random.randn(n_points_per_cluster, 2)
    X = np.vstack((C1, C2, C3, C4, C5, C6))

    clust = OPTICS(min_samples=50, xi=.05, min_cluster_size=.05)

    # Run the fit
    clust.fit(X)

    labels_050 = cluster_optics_dbscan(reachability=clust.reachability_,
                                       core_distances=clust.core_distances_,
                                       ordering=clust.ordering_, eps=0.5)
    labels_200 = cluster_optics_dbscan(reachability=clust.reachability_,
                                       core_distances=clust.core_distances_,
                                       ordering=clust.ordering_, eps=2)

    space = np.arange(len(X))
    reachability = clust.reachability_[clust.ordering_]
    labels = clust.labels_[clust.ordering_]

    plt.figure(figsize=(10, 7))
    G = gridspec.GridSpec(2, 3)
    ax1 = plt.subplot(G[0, :])
    ax2 = plt.subplot(G[1, 0])
    ax3 = plt.subplot(G[1, 1])
    ax4 = plt.subplot(G[1, 2])

    # Reachability plot
    colors = ['g.', 'r.', 'b.', 'y.', 'c.']
    for klass, color in zip(range(0, 5), colors):
        Xk = space[labels == klass]
        Rk = reachability[labels == klass]
        ax1.plot(Xk, Rk, color, alpha=0.3)
    ax1.plot(space[labels == -1], reachability[labels == -1], 'k.', alpha=0.3)
    ax1.plot(space, np.full_like(space, 2., dtype=float), 'k-', alpha=0.5)
    ax1.plot(space, np.full_like(space, 0.5, dtype=float), 'k-.', alpha=0.5)
    ax1.set_ylabel('Reachability (epsilon distance)')
    ax1.set_title('Reachability Plot')

    # OPTICS
    colors = ['g.', 'r.', 'b.', 'y.', 'c.']
    for klass, color in zip(range(0, 5), colors):
        Xk = X[clust.labels_ == klass]
        ax2.plot(Xk[:, 0], Xk[:, 1], color, alpha=0.3)
    ax2.plot(X[clust.labels_ == -1, 0], X[clust.labels_ == -1, 1], 'k+', alpha=0.1)
    ax2.set_title('Automatic Clustering\nOPTICS')

    # DBSCAN at 0.5
    colors = ['g', 'greenyellow', 'olive', 'r', 'b', 'c']
    for klass, color in zip(range(0, 6), colors):
        Xk = X[labels_050 == klass]
        ax3.plot(Xk[:, 0], Xk[:, 1], color, alpha=0.3, marker='.')
    ax3.plot(X[labels_050 == -1, 0], X[labels_050 == -1, 1], 'k+', alpha=0.1)
    ax3.set_title('Clustering at 0.5 epsilon cut\nDBSCAN')

    # DBSCAN at 2.
    colors = ['g.', 'm.', 'y.', 'c.']
    for klass, color in zip(range(0, 4), colors):
        Xk = X[labels_200 == klass]
        ax4.plot(Xk[:, 0], Xk[:, 1], color, alpha=0.3)
    ax4.plot(X[labels_200 == -1, 0], X[labels_200 == -1, 1], 'k+', alpha=0.1)
    ax4.set_title('Clustering at 2.0 epsilon cut\nDBSCAN')

    plt.tight_layout()
    plt.show()

**Total running time of the script:** ( 0 minutes  0.935 seconds)


.. _sphx_glr_download_auto_examples_cluster_plot_optics.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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