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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_cluster_plot_optics.py>`
        to download the full example code or to run this example in your browser via JupyterLite or Binder

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

Demo of OPTICS clustering algorithm

.. currentmodule:: sklearn

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:`~cluster.OPTICS` is first used with its Xi cluster detection method, and then setting specific thresholds on the reachability, which corresponds to :class:`~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-sg:: /auto_examples/cluster/images/sphx_glr_plot_optics_001.png
   :alt: Reachability Plot, Automatic Clustering OPTICS, Clustering at 0.5 epsilon cut DBSCAN, Clustering at 2.0 epsilon cut DBSCAN
   :srcset: /auto_examples/cluster/images/sphx_glr_plot_optics_001.png
   :class: sphx-glr-single-img





# Authors: Shane Grigsby <[email protected]>
#          Adrin Jalali <[email protected]>
# License: BSD 3 clause

import matplotlib.gridspec as gridspec
import matplotlib.pyplot as plt
import numpy as np

from sklearn.cluster import OPTICS, cluster_optics_dbscan

# Generate sample data

np.random.seed(0)
n_points_per_cluster = 250

C1 = [-5, -2] + 0.8 * np.random.randn(n_points_per_cluster, 2)
C2 = [4, -1] + 0.1 * np.random.randn(n_points_per_cluster, 2)
C3 = [1, -2] + 0.2 * np.random.randn(n_points_per_cluster, 2)
C4 = [-2, 3] + 0.3 * 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=0.05, min_cluster_size=0.05)

# 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, 2.0, 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.", "r.", "b.", "c."]
for klass, color in zip(range(0, 4), colors):
    Xk = X[labels_050 == klass]
    ax3.plot(Xk[:, 0], Xk[:, 1], color, alpha=0.3)
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()

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

   **Total running time of the script:** ( 0 minutes  1.622 seconds)


.. 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_optics.ipynb
        :alt: Launch binder
        :width: 150 px



    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/cluster/plot_optics.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

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

      :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.github.io>`_