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 OPTICS is first used with its Xi cluster detection method, and then setting specific thresholds on the reachability, which corresponds to DBSCAN. We can see that the different clusters of OPTICS’s Xi method can be recovered with different choices of thresholds in DBSCAN.

# Authors: The scikit-learn developers
# SPDX-License-Identifier: 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 enumerate(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 enumerate(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 enumerate(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 enumerate(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 1.744 seconds)

Download Jupyter notebook: plot_optics.ipynb

Download Python source code: plot_optics.py

Download zipped: plot_optics.zip

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