Plot Dbscan¶
=================================== Demo of DBSCAN clustering algorithm¶
DBSCAN (Density-Based Spatial Clustering of Applications with Noise) finds core samples in regions of high density and expands clusters from them. This algorithm is good for data which contains clusters of similar density.
See the :ref:sphx_glr_auto_examples_cluster_plot_cluster_comparison.py example
for a demo of different clustering algorithms on 2D datasets.
Imports for DBSCAN Density-Based Clustering¶
DBSCAN (Density-Based Spatial Clustering of Applications with Noise) discovers clusters by finding regions where data points are densely packed, controlled by two parameters: eps (the maximum distance between neighbors) and min_samples (the minimum number of points required to form a dense region). Points that satisfy the density criterion become “core samples,” which are expanded into clusters by transitively connecting nearby core samples and their neighbors. Points that fall within eps of a core sample but are not themselves core samples become “border points,” while points that belong to no cluster are labeled as noise (label = -1).
Why DBSCAN matters in practice: Unlike K-Means, DBSCAN does not require specifying the number of clusters in advance, can discover clusters of arbitrary shape (not just spherical), and naturally identifies outliers as noise points. This makes it well-suited for spatial data analysis, anomaly detection, and any domain where clusters have irregular geometry. The StandardScaler preprocessing step is critical here because DBSCAN’s eps parameter defines an absolute distance threshold – without standardization, features on different scales would distort the neighborhood definition. The evaluation metrics used (homogeneity, completeness, V-measure, Adjusted Rand Index, silhouette score) demonstrate both supervised and unsupervised approaches to assessing cluster quality.
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
# %%
# Data generation
# ---------------
#
# We use :class:`~sklearn.datasets.make_blobs` to create 3 synthetic clusters.
from sklearn.datasets import make_blobs
from sklearn.preprocessing import StandardScaler
centers = [[1, 1], [-1, -1], [1, -1]]
X, labels_true = make_blobs(
n_samples=750, centers=centers, cluster_std=0.4, random_state=0
)
X = StandardScaler().fit_transform(X)
# %%
# We can visualize the resulting data:
import matplotlib.pyplot as plt
plt.scatter(X[:, 0], X[:, 1])
plt.show()
# %%
# Compute DBSCAN
# --------------
#
# One can access the labels assigned by :class:`~sklearn.cluster.DBSCAN` using
# the `labels_` attribute. Noisy samples are given the label :math:`-1`.
import numpy as np
from sklearn import metrics
from sklearn.cluster import DBSCAN
db = DBSCAN(eps=0.3, min_samples=10).fit(X)
labels = db.labels_
# Number of clusters in labels, ignoring noise if present.
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
n_noise_ = list(labels).count(-1)
print("Estimated number of clusters: %d" % n_clusters_)
print("Estimated number of noise points: %d" % n_noise_)
# %%
# Clustering algorithms are fundamentally unsupervised learning methods.
# However, since :class:`~sklearn.datasets.make_blobs` gives access to the true
# labels of the synthetic clusters, it is possible to use evaluation metrics
# that leverage this "supervised" ground truth information to quantify the
# quality of the resulting clusters. Examples of such metrics are the
# homogeneity, completeness, V-measure, Rand-Index, Adjusted Rand-Index and
# Adjusted Mutual Information (AMI).
#
# If the ground truth labels are not known, evaluation can only be performed
# using the model results itself. In that case, the Silhouette Coefficient comes
# in handy.
#
# For more information, see the
# :ref:`sphx_glr_auto_examples_cluster_plot_adjusted_for_chance_measures.py`
# example or the :ref:`clustering_evaluation` module.
print(f"Homogeneity: {metrics.homogeneity_score(labels_true, labels):.3f}")
print(f"Completeness: {metrics.completeness_score(labels_true, labels):.3f}")
print(f"V-measure: {metrics.v_measure_score(labels_true, labels):.3f}")
print(f"Adjusted Rand Index: {metrics.adjusted_rand_score(labels_true, labels):.3f}")
print(
"Adjusted Mutual Information:"
f" {metrics.adjusted_mutual_info_score(labels_true, labels):.3f}"
)
print(f"Silhouette Coefficient: {metrics.silhouette_score(X, labels):.3f}")
# %%
# Plot results
# ------------
#
# Core samples (large dots) and non-core samples (small dots) are color-coded
# according to the assigned cluster. Samples tagged as noise are represented in
# black.
unique_labels = set(labels)
core_samples_mask = np.zeros_like(labels, dtype=bool)
core_samples_mask[db.core_sample_indices_] = True
colors = [plt.cm.Spectral(each) for each in np.linspace(0, 1, len(unique_labels))]
for k, col in zip(unique_labels, colors):
if k == -1:
# Black used for noise.
col = [0, 0, 0, 1]
class_member_mask = labels == k
xy = X[class_member_mask & core_samples_mask]
plt.plot(
xy[:, 0],
xy[:, 1],
"o",
markerfacecolor=tuple(col),
markeredgecolor="k",
markersize=14,
)
xy = X[class_member_mask & ~core_samples_mask]
plt.plot(
xy[:, 0],
xy[:, 1],
"o",
markerfacecolor=tuple(col),
markeredgecolor="k",
markersize=6,
)
plt.title(f"Estimated number of clusters: {n_clusters_}")
plt.show()