层次聚类：结构化与非结构化 Ward#

示例构建了一个瑞士卷数据集，并根据其位置运行层次聚类。

有关更多信息，请参阅层次聚类。

第一步，在结构上没有任何连接约束的情况下执行层次聚类，并且仅基于距离，而在第二步中，聚类被限制在 k 最近邻图中：它是具有结构先验的层次聚类。

一些在没有连接约束的情况下学习到的簇不尊重瑞士卷的结构，并且跨越流形的不同折叠延伸。相反，当反对连接约束时，簇形成瑞士卷的良好分割。

# Authors : Vincent Michel, 2010
#           Alexandre Gramfort, 2010
#           Gael Varoquaux, 2010
# License: BSD 3 clause

import time as time

# The following import is required
# for 3D projection to work with matplotlib < 3.2
import mpl_toolkits.mplot3d  # noqa: F401
import numpy as np

生成数据#

我们首先生成瑞士卷数据集。

from sklearn.datasets import make_swiss_roll

n_samples = 1500
noise = 0.05
X, _ = make_swiss_roll(n_samples, noise=noise)
# Make it thinner
X[:, 1] *= 0.5

计算聚类#

我们执行没有任何连接约束的层次聚类下的 AgglomerativeClustering。

from sklearn.cluster import AgglomerativeClustering

print("Compute unstructured hierarchical clustering...")
st = time.time()
ward = AgglomerativeClustering(n_clusters=6, linkage="ward").fit(X)
elapsed_time = time.time() - st
label = ward.labels_
print(f"Elapsed time: {elapsed_time:.2f}s")
print(f"Number of points: {label.size}")

Compute unstructured hierarchical clustering...
Elapsed time: 0.04s
Number of points: 1500

绘制结果#

绘制非结构化层次聚类。

import matplotlib.pyplot as plt

fig1 = plt.figure()
ax1 = fig1.add_subplot(111, projection="3d", elev=7, azim=-80)
ax1.set_position([0, 0, 0.95, 1])
for l in np.unique(label):
    ax1.scatter(
        X[label == l, 0],
        X[label == l, 1],
        X[label == l, 2],
        color=plt.cm.jet(float(l) / np.max(label + 1)),
        s=20,
        edgecolor="k",
    )
_ = fig1.suptitle(f"Without connectivity constraints (time {elapsed_time:.2f}s)")

Without connectivity constraints (time 0.04s)

我们正在定义具有 10 个邻居的 k 最近邻#

from sklearn.neighbors import kneighbors_graph

connectivity = kneighbors_graph(X, n_neighbors=10, include_self=False)

计算聚类#

我们再次执行具有连接约束的 AgglomerativeClustering。

print("Compute structured hierarchical clustering...")
st = time.time()
ward = AgglomerativeClustering(
    n_clusters=6, connectivity=connectivity, linkage="ward"
).fit(X)
elapsed_time = time.time() - st
label = ward.labels_
print(f"Elapsed time: {elapsed_time:.2f}s")
print(f"Number of points: {label.size}")

Compute structured hierarchical clustering...
Elapsed time: 0.07s
Number of points: 1500

绘制结果#

绘制结构化层次聚类。

fig2 = plt.figure()
ax2 = fig2.add_subplot(121, projection="3d", elev=7, azim=-80)
ax2.set_position([0, 0, 0.95, 1])
for l in np.unique(label):
    ax2.scatter(
        X[label == l, 0],
        X[label == l, 1],
        X[label == l, 2],
        color=plt.cm.jet(float(l) / np.max(label + 1)),
        s=20,
        edgecolor="k",
    )
fig2.suptitle(f"With connectivity constraints (time {elapsed_time:.2f}s)")

plt.show()

With connectivity constraints (time 0.07s)

脚本总运行时间：（0 分 0.402 秒）