一、聚类目标

簇内相似度高，且簇间相似度低（高内聚，低耦合）（high-intra-class,low-inter-class）

1.K-Means(K均值)聚类

算法步骤：

(1) 首先我们选择一些类/组，并随机初始化它们各自的中心点。中心点是与每个数据点向量长度相同的位置。这需要我们提前预知类的数量(即中心点的数量)。
(2) 计算每个数据点到中心点的距离，数据点距离哪个中心点最近就划分到哪一类中。
(3) 计算每一类中中心点作为新的中心点。
(4) 重复以上步骤，直到每一类中心在每次迭代后变化不大为止。也可以多次随机初始化中心点，然后选择运行结果最好的一个。

优点：

速度快，计算简便

缺点：

必须提前知道数据有多少类/组。
K-Medians是K-Means的一种变体，是用数据集的中位数而不是均值来计算数据的中心点。
K-Medians的优势是使用中位数来计算中心点不受异常值的影响；缺点是计算中位数时需要对数据集中的数据进行排序，速度相对于K-Means较慢。

二、使用步骤

1.生成数据

#导入需要的库
from numpy import unique
from numpy import where
from sklearn.datasets import make_classification
from sklearn.preprocessing import LabelEncoder, StandardScaler
from matplotlib import pyplot

# 将生成的分类数据集用图形化显示
X,y = make_classification(n_samples=5000, n_features=2,n_informative=2, 
                          n_redundant=0,n_classes=3,n_clusters_per_class=1,
                          random_state=1)
# 数据集标准化操作
X = StandardScaler().fit_transform(X)
clusters_temp = unique(y)
for cluster_temp in clusters_temp:
    row_ix = where(y == cluster_temp)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()#显示数据集分布情况
# y.shape

2.使用K-means算法进行聚类

from sklearn.cluster import KMeans
from matplotlib import pyplot
from numpy import unique
from numpy import where
from matplotlib import pyplot

model = KMeans(n_clusters=3)#聚类类别为2
yhat = model.fit_predict(X)
clusters = unique(yhat)
for cluster in clusters:
    row_ix = where(yhat == cluster)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()

分类后是这个样子：

3.评价聚类结果

from sklearn import metrics
from sklearn.metrics import davies_bouldin_score
print("Adjusted Rand-Index: %.3f" % metrics.adjusted_rand_score(y,yhat))
print("davies bouldin index: %.3f"% metrics.davies_bouldin_score(X,yhat))

评价结果如下：

4.用silhouette选择K-means聚类的簇数：

import numpy as np
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score

range_n_clusters = [2, 3, 4, 5, 6]

for n_clusters in range_n_clusters:
   
    clusterer = KMeans(n_clusters=n_clusters, random_state=10)
    cluster_labels = clusterer.fit_predict(X)

    silhouette_avg = silhouette_score(X, cluster_labels)
    print(
        "For n_clusters =",
        n_clusters,
        "The average silhouette_score is :",
        silhouette_avg,
    )

结果显示分成3簇的时候效果最好

5.使用不同聚类方法

from sklearn.cluster import Birch

model = Birch(n_clusters=3)

yhat = model.fit_predict(X)
clusters = unique(yhat)
for cluster in clusters:
    row_ix = where(yhat == cluster)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()

print("The Birch adjusted_rand_score is:",metrics.adjusted_rand_score(y,yhat))
print("The Birch davies_bouldin_score is:",metrics.davies_bouldin_score(X,yhat))

结果如下：

完整代码

#导入库
import numpy as np
from numpy import unique
from numpy import where
from matplotlib import pyplot
from sklearn.datasets import make_classification
from sklearn.preprocessing import LabelEncoder, StandardScaler
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score

# 生成数据集
X,y = make_classification(n_samples=5000, n_features=2,n_informative=2, 
                          n_redundant=0,n_classes=3,n_clusters_per_class=1,
                          random_state=1)
X = StandardScaler().fit_transform(X)
################################################################################
range_n_clusters = [2, 3, 4, 5, 6]
for n_clusters in range_n_clusters:   
    clusterer = KMeans(n_clusters=n_clusters, random_state=10)
    cluster_labels = clusterer.fit_predict(X)
    silhouette_avg = silhouette_score(X, cluster_labels)
    print(
        "For n_clusters =",
        n_clusters,
        "The average silhouette_score is :",
        silhouette_avg,
    )
################################################################################
model = KMeans(n_clusters=3)#聚类类别为2
yhat = model.fit_predict(X)
clusters = unique(yhat)
for cluster in clusters:
    row_ix = where(yhat == cluster)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()
print("The KMeans Adjusted Rand-Index: %.3f" % metrics.adjusted_rand_score(y,yhat))
print("The KMeans davies bouldin index: %.3f"% metrics.davies_bouldin_score(X,yhat))
################################################################################
from sklearn.cluster import AgglomerativeClustering
model = AgglomerativeClustering(n_clusters=3)
yhat = model.fit_predict(X)
clusters = unique(yhat)
for cluster in clusters:
    row_ix = where(yhat == cluster)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()
print("The AgglomerativeClustering adjusted_rand_score is:",metrics.adjusted_rand_score(y,yhat))
print("The AgglomerativeClustering davies_bouldin_score is:",metrics.davies_bouldin_score(X,yhat))
################################################################################
from sklearn.cluster import SpectralClustering
model = SpectralClustering(n_clusters=3)
yhat = model.fit_predict(X)
clusters = unique(yhat)
for cluster in clusters:
    row_ix = where(yhat == cluster)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()
print("The SpectralClustering adjusted_rand_score is:",metrics.adjusted_rand_score(y,yhat))
print("The SpectralClustering davies_bouldin_score is:",metrics.davies_bouldin_score(X,yhat))
################################################################################
from sklearn.cluster import Birch
model = Birch(n_clusters=3)
yhat = model.fit_predict(X)
clusters = unique(yhat)
for cluster in clusters:
    row_ix = where(yhat == cluster)
    pyplot.scatter(X[row_ix,0],X[row_ix,1])
pyplot.show()
print("The Birch adjusted_rand_score is:",metrics.adjusted_rand_score(y,yhat))
print("The Birch davies_bouldin_score is:",metrics.davies_bouldin_score(X,yhat))

结果如下：

总结

以上是关于聚类方法实例的一种实现方法，供大家参考。

参考

常见的六大聚类算法