DBSCAN集群算法演示#

DBSCAN（含噪应用程序基于密度的空间集群）在高密度区域中查找核心样本，并从中扩展集群。该算法适合包含相似密度集群的数据。

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

数据生成#

我们使用 make_blobs 创建3个合成集群。

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)

我们可以将结果数据可视化：

import matplotlib.pyplot as plt

plt.scatter(X[:, 0], X[:, 1])
plt.show()

计算DBSCAN#

可以访问由指定的标签 DBSCAN 使用 labels_ 属性有噪音的样品都有标签 \(-1\) .

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_)

Estimated number of clusters: 3
Estimated number of noise points: 18

聚类算法基本上是无监督的学习方法。但由于 make_blobs 由于可以访问合成聚类的真实标签，因此可以使用评估度量，该评估度量利用该“监督”地面真实信息来量化所得到的聚类的质量。这种度量的例子是同质性、完整性、V-度量、随机指数、调整后的随机指数和调整后的互信息（AMI）。

如果基础事实标签未知，则只能使用模型结果本身执行评估。在这种情况下，剪影系数就派上了用场。

更多详见集群绩效评估中的机会调整示例或第集群绩效评估 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}")

Homogeneity: 0.953
Completeness: 0.883
V-measure: 0.917
Adjusted Rand Index: 0.952
Adjusted Mutual Information: 0.916
Silhouette Coefficient: 0.626

图结果#

核心样本（大点）和非核心样本（小点）根据指定的聚类进行颜色编码。标记为噪声的样本以黑色表示。

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()

Total running time of the script: （0分0.144秒）