案例：汽车款式聚类¶

案例背景¶

本案例的数据基于R语言 ISLR 包中的Auto数据集，数据集中共有392个样本， 8个特征，根据每种汽车的参数，利用聚类算法来进行聚类，识别出相似的汽车。

数据读取与划分¶

In [1]:

# 忽略警告信息
import warnings
warnings.filterwarnings("ignore")

# 忽略警告信息 import warnings warnings.filterwarnings("ignore")

In [2]:

import numpy as np
import pandas as pd
from plotnine import *
from sklearn import metrics

import numpy as np import pandas as pd from plotnine import * from sklearn import metrics

In [ ]:

# 读入数据
#auto = pd.read_csv('https://raw.githubusercontent.com/selva86/datasets/master/Auto.csv')
auto = pd.read_csv('Auto.csv')        
auto.head()

# 读入数据 #auto = pd.read_csv('https://raw.githubusercontent.com/selva86/datasets/master/Auto.csv') auto = pd.read_csv('Auto.csv') auto.head()

Out[ ]:

	mpg	cylinders	displacement	horsepower	weight	acceleration	year	origin
0	18.0	8	307.0	130	3504	12.0	70	1
1	15.0	8	350.0	165	3693	11.5	70	1
2	18.0	8	318.0	150	3436	11.0	70	1
3	16.0	8	304.0	150	3433	12.0	70	1
4	17.0	8	302.0	140	3449	10.5	70	1

In [4]:

#对连续变量用Z-score标准化
from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
auto[['mpg','displacement','horsepower','weight','acceleration']] = scaler.fit_transform(auto[['mpg','displacement','horsepower','weight','acceleration']])

#对类别变量进行哑变量编码
auto_scaled = pd.get_dummies(data=auto,columns=['cylinders','year','origin'])

#对连续变量用Z-score标准化 from sklearn.preprocessing import StandardScaler scaler = StandardScaler() auto[['mpg','displacement','horsepower','weight','acceleration']] = scaler.fit_transform(auto[['mpg','displacement','horsepower','weight','acceleration']]) #对类别变量进行哑变量编码 auto_scaled = pd.get_dummies(data=auto,columns=['cylinders','year','origin'])

In [5]:

## 再次查看数据前5行
auto_scaled.head()

## 再次查看数据前5行 auto_scaled.head()

Out[5]:

	mpg	displacement	horsepower	weight	acceleration	cylinders_3	cylinders_4	cylinders_5	cylinders_6	cylinders_8	...	year_76	year_77	year_78	year_79	year_80	year_81	year_82	origin_1	origin_2	origin_3
0	-0.698638	1.077290	0.664133	0.620540	-1.285258	0	0	0	0	1	...	0	0	0	0	0	0	0	1	0	0
1	-1.083498	1.488732	1.574594	0.843334	-1.466724	0	0	0	0	1	...	0	0	0	0	0	0	0	1	0	0
2	-0.698638	1.182542	1.184397	0.540382	-1.648189	0	0	0	0	1	...	0	0	0	0	0	0	0	1	0	0
3	-0.955212	1.048584	1.184397	0.536845	-1.285258	0	0	0	0	1	...	0	0	0	0	0	0	0	1	0	0
4	-0.826925	1.029447	0.924265	0.555706	-1.829655	0	0	0	0	1	...	0	0	0	0	0	0	0	1	0	0

5 rows × 26 columns

K-Means模型搭建与评估¶

In [6]:

#K-means聚类
from sklearn.cluster import KMeans
model = KMeans(n_clusters=3,random_state=42).fit(auto_scaled)    #设置随机种子为42
#样本标签和簇质心
auto_label = model.labels_
auto_cluster = model.cluster_centers_
auto_label

#K-means聚类 from sklearn.cluster import KMeans model = KMeans(n_clusters=3,random_state=42).fit(auto_scaled) #设置随机种子为42 #样本标签和簇质心 auto_label = model.labels_ auto_cluster = model.cluster_centers_ auto_label

Out[6]:

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 2, 2, 2,
       2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
       1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2,
       2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 2, 2, 2, 1,
       1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1,
       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2,
       2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1,
       1, 1, 1, 2, 2, 2, 2, 2, 0, 2, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0,
       1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2,
       2, 2, 2, 2, 2, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0,
       2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 0, 0, 0,
       0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2,
       2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
       2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2])

In [7]:

#画每个簇样本数的柱状图
auto_label_dataframe = pd.DataFrame({'clusters':auto_label})
auto_label_dataframe['clusters'] = auto_label_dataframe['clusters'].astype('category')
ggplot(auto_label_dataframe,aes('clusters',fill='clusters')) + geom_bar()

#画每个簇样本数的柱状图 auto_label_dataframe = pd.DataFrame({'clusters':auto_label}) auto_label_dataframe['clusters'] = auto_label_dataframe['clusters'].astype('category') ggplot(auto_label_dataframe,aes('clusters',fill='clusters')) + geom_bar()

Out[7]:

<Figure Size: (460 x 345)>

In [8]:

# 轮廓系数评估聚类效果
labels = model.labels_
print("轮廓系数(Silhouette Coefficient): %0.4f"
      % metrics.silhouette_score(auto_scaled, labels))

# 轮廓系数评估聚类效果 labels = model.labels_ print("轮廓系数(Silhouette Coefficient): %0.4f" % metrics.silhouette_score(auto_scaled, labels))

轮廓系数(Silhouette Coefficient): 0.3183

In [9]:

# 选择不同k值比较聚类效果
for i in [2,4,6]:
    model = KMeans(n_clusters=i,random_state=42).fit(auto_scaled)   #设置随机种子为111
    labels = model.labels_
    print("k=%d 轮廓系数(Silhouette Coefficient): %0.4f"% (i,metrics.silhouette_score(auto_scaled, labels)))

# 选择不同k值比较聚类效果 for i in [2,4,6]: model = KMeans(n_clusters=i,random_state=42).fit(auto_scaled) #设置随机种子为111 labels = model.labels_ print("k=%d 轮廓系数(Silhouette Coefficient): %0.4f"% (i,metrics.silhouette_score(auto_scaled, labels)))

k=2 轮廓系数(Silhouette Coefficient): 0.4152
k=4 轮廓系数(Silhouette Coefficient): 0.2548
k=6 轮廓系数(Silhouette Coefficient): 0.2039

层次聚类模型搭建与评估¶

In [10]:

from sklearn.cluster import AgglomerativeClustering

from sklearn.cluster import AgglomerativeClustering

In [11]:

single_model = AgglomerativeClustering(n_clusters=3,linkage="single").fit(auto_scaled)

single_labels = single_model.labels_
print("Single Linkage 轮廓系数(Silhouette Coefficient): %0.4f"
      % metrics.silhouette_score(auto_scaled, single_labels))

single_model = AgglomerativeClustering(n_clusters=3,linkage="single").fit(auto_scaled) single_labels = single_model.labels_ print("Single Linkage 轮廓系数(Silhouette Coefficient): %0.4f" % metrics.silhouette_score(auto_scaled, single_labels))

Single Linkage 轮廓系数(Silhouette Coefficient): 0.0111

In [12]:

complete_model = AgglomerativeClustering(n_clusters=3, linkage='complete').fit(auto_scaled)

complete_labels = complete_model.labels_
print("Complete Linkage 轮廓系数(Silhouette Coefficient): %0.4f"
      % metrics.silhouette_score(auto_scaled, complete_labels))

complete_model = AgglomerativeClustering(n_clusters=3, linkage='complete').fit(auto_scaled) complete_labels = complete_model.labels_ print("Complete Linkage 轮廓系数(Silhouette Coefficient): %0.4f" % metrics.silhouette_score(auto_scaled, complete_labels))

Complete Linkage 轮廓系数(Silhouette Coefficient): 0.2297

In [13]:

average_model = AgglomerativeClustering(n_clusters=3, linkage='average').fit(auto_scaled)

average_labels = average_model.labels_
print("Average Linkage轮廓系数(Silhouette Coefficient): %0.4f"
      % metrics.silhouette_score(auto_scaled, average_labels))

average_model = AgglomerativeClustering(n_clusters=3, linkage='average').fit(auto_scaled) average_labels = average_model.labels_ print("Average Linkage轮廓系数(Silhouette Coefficient): %0.4f" % metrics.silhouette_score(auto_scaled, average_labels))

Average Linkage轮廓系数(Silhouette Coefficient): 0.3075

In [14]:

#画每个簇样本数的柱状图
auto_label = average_model.labels_
auto_label_dataframe = pd.DataFrame({'clusters':auto_label})
auto_label_dataframe['clusters'] = auto_label_dataframe['clusters'].astype('category')
ggplot(auto_label_dataframe,aes('clusters',fill='clusters')) + geom_bar()

#画每个簇样本数的柱状图 auto_label = average_model.labels_ auto_label_dataframe = pd.DataFrame({'clusters':auto_label}) auto_label_dataframe['clusters'] = auto_label_dataframe['clusters'].astype('category') ggplot(auto_label_dataframe,aes('clusters',fill='clusters')) + geom_bar()

Out[14]:

<Figure Size: (640 x 480)>

In [15]:

# 绘制谱系图
from scipy.spatial.distance import pdist
from scipy.cluster.hierarchy import linkage, dendrogram
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei']

#利用scipy中pdist,linkage,dendrogram函数绘制谱系图
#pdist函数返回距离矩阵，linkage函数返回一个ndarray对象，描述了簇合并的过程
#dendrogram函数用来绘制谱系图
row_clusters = linkage(pdist(auto_scaled,metric='euclidean'),method='ward')
fig = plt.figure(figsize=(12,10))
#参数p和参数truncate_mode用来将谱系图截断，部分结点的子树被剪枝，横轴显示的是该结点包含的样本数
row_dendr = dendrogram(row_clusters,p=50,truncate_mode='lastp',color_threshold=5)
plt.tight_layout()
plt.xticks(fontsize=15)
plt.title('谱系图', fontsize=15)

# 绘制谱系图 from scipy.spatial.distance import pdist from scipy.cluster.hierarchy import linkage, dendrogram import matplotlib.pyplot as plt plt.rcParams['font.sans-serif'] = ['SimHei'] #利用scipy中pdist,linkage,dendrogram函数绘制谱系图 #pdist函数返回距离矩阵，linkage函数返回一个ndarray对象，描述了簇合并的过程 #dendrogram函数用来绘制谱系图 row_clusters = linkage(pdist(auto_scaled,metric='euclidean'),method='ward') fig = plt.figure(figsize=(12,10)) #参数p和参数truncate_mode用来将谱系图截断，部分结点的子树被剪枝，横轴显示的是该结点包含的样本数 row_dendr = dendrogram(row_clusters,p=50,truncate_mode='lastp',color_threshold=5) plt.tight_layout() plt.xticks(fontsize=15) plt.title('谱系图', fontsize=15)

Out[15]:

Text(0.5, 1.0, '谱系图')

DBSCAN模型搭建与评估¶

In [16]:

from sklearn.cluster import DBSCAN

from sklearn.cluster import DBSCAN

In [17]:

model = DBSCAN(eps=1.5,min_samples=4).fit(auto_scaled)

model = DBSCAN(eps=1.5,min_samples=4).fit(auto_scaled)

In [19]:

#绘制不同簇的样本数柱状图
auto_label = model.labels_
auto_label_dataframe = pd.DataFrame({'clusters':auto_label})
auto_label_dataframe['clusters'] = auto_label_dataframe['clusters'].astype('category')
ggplot(auto_label_dataframe,aes('clusters',fill='clusters')) + geom_bar()

#绘制不同簇的样本数柱状图 auto_label = model.labels_ auto_label_dataframe = pd.DataFrame({'clusters':auto_label}) auto_label_dataframe['clusters'] = auto_label_dataframe['clusters'].astype('category') ggplot(auto_label_dataframe,aes('clusters',fill='clusters')) + geom_bar()

Out[19]:

<Figure Size: (640 x 480)>

In [20]:

# 样本的类别标签
labels = model.labels_

# 标签中的簇数，忽略噪声点
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)

print('簇数: %d' % n_clusters_)
print("轮廓系数(Silhouette Coefficient): %0.4f"
      % metrics.silhouette_score(auto_scaled, labels))

# 样本的类别标签 labels = model.labels_ # 标签中的簇数，忽略噪声点 n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0) print('簇数: %d' % n_clusters_) print("轮廓系数(Silhouette Coefficient): %0.4f" % metrics.silhouette_score(auto_scaled, labels))

簇数: 3
轮廓系数(Silhouette Coefficient): 0.1476

In [21]:

# 不同最小样本数下的簇个数
## 设置参数取值范围
min_samples_grid = [1, 3, 5, 7, 9]

## 训练模型并输出簇个数
cluster_number = []
slt_score = []

for item in min_samples_grid:
    model = DBSCAN(min_samples=item).fit(auto_scaled)
    cluster_number.append(len(np.unique(model.labels_))-1)
    
## 绘图
plt.plot(min_samples_grid, cluster_number, 'r-*', linewidth=2)
plt.xlabel('最小样本数')
plt.ylabel('簇个数')
plt.title('不同最小样本数下聚类的簇个数')

# 不同最小样本数下的簇个数 ## 设置参数取值范围 min_samples_grid = [1, 3, 5, 7, 9] ## 训练模型并输出簇个数 cluster_number = [] slt_score = [] for item in min_samples_grid: model = DBSCAN(min_samples=item).fit(auto_scaled) cluster_number.append(len(np.unique(model.labels_))-1) ## 绘图 plt.plot(min_samples_grid, cluster_number, 'r-*', linewidth=2) plt.xlabel('最小样本数') plt.ylabel('簇个数') plt.title('不同最小样本数下聚类的簇个数')

Out[21]:

Text(0.5, 1.0, '不同最小样本数下聚类的簇个数')