聚类分析_客户群聚类分析

聚类是非监督学习的一种算法，我们使用k-means聚类算法，实现客户细分，以及营销战略如何在实际业务中应用。

1.导入数据

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import seaborn as sns
from sklearn.cluster import KMeans

data = pd.read_csv('./Mall_Customers.csv')

2.数据探索

data.head()

	CustomerID	Gender	Age	Annual Income (k$)	Spending Score (1-100)
0	1	Male	19	15	39
1	2	Male	21	15	81
2	3	Female	20	16	6
3	4	Female	23	16	77
4	5	Female	31	17	40

data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 200 entries, 0 to 199
Data columns (total 5 columns):
 #   Column                  Non-Null Count  Dtype 
---  ------                  --------------  ----- 
 0   CustomerID              200 non-null    int64 
 1   Gender                  200 non-null    object
 2   Age                     200 non-null    int64 
 3   Annual Income (k$)      200 non-null    int64 
 4   Spending Score (1-100)  200 non-null    int64 
dtypes: int64(4), object(1)
memory usage: 7.9+ KB

data.isnull().any()

CustomerID                False
Gender                    False
Age                       False
Annual Income (k$)        False
Spending Score (1-100)    False
dtype: bool

data.describe()

	CustomerID	Age	Annual Income (k$)	Spending Score (1-100)
count	200.000000	200.000000	200.000000	200.000000
mean	100.500000	38.850000	60.560000	50.200000
std	57.879185	13.969007	26.264721	25.823522
min	1.000000	18.000000	15.000000	1.000000
25%	50.750000	28.750000	41.500000	34.750000
50%	100.500000	36.000000	61.500000	50.000000
75%	150.250000	49.000000	78.000000	73.000000
max	200.000000	70.000000	137.000000	99.000000

data[['Gender','CustomerID']].groupby('Gender').count()

	CustomerID

|Gender||
|Female|112|
|Male|88|

gender = data['Gender'].value_counts()
labels = ['Female', 'Male']
colors = ['c', 'coral']
explode = [0, 0.05]
plt.figure(figsize=(8,8))
plt.title('Total of customers by gender', fontsize = 16, fontweight='bold') 
plt.pie(gender, colors = colors, autopct = '%1.0f%%', labels = labels, explode = explode, startangle=90, textprops={'fontsize': 16})
plt.savefig('Total of customers by gender.png', bbox_inches = 'tight')
plt.show()

output_11_0.png

plt.figure(figsize=(16,6))
plt.subplot(1,2,1)
sns.distplot(data['Spending Score (1-100)'], color = 'green')
plt.title('Distribution of Spending Score')
plt.subplot(1,2,2)
sns.distplot(data['Annual Income (k$)'], color = 'green')
plt.title('Distribution of Annual Income (k$)')
plt.show()

output_12_0.png

sns.pairplot(data=data[['Spending Score (1-100)','Annual Income (k$)','Age']], diag_kind="kde")
plt.savefig('Distribution.png', bbox_inches = 'tight')

output_13_0.png

plt.figure(figsize=(8,6))
plt.title('Annual Income vs Spending Score', fontsize = 16, fontweight='bold')  
plt.scatter(data['Annual Income (k$)'], data['Spending Score (1-100)'], color = 'indianred', edgecolors = 'crimson')
plt.xlabel('Annual Income', fontsize = 14)
plt.ylabel('Spending Score', fontsize = 14)
plt.savefig('Annual Income vs Spending Score.png', bbox_inches = 'tight')
plt.show()

output_14_0.png

3.模型开发

X1_Matrix = data.iloc[:, [2,4]].values # Age & Spending Score
X2_Matrix = data.iloc[:, [3,4]].values # Annual Income & Spending Score

inertias_1 = []
for i in range(1,20):
    kmeans = KMeans(n_clusters=i, init='k-means++',  max_iter=300, n_init=10,random_state=0)
    kmeans.fit(X1_Matrix)
    inertia = kmeans.inertia_
    inertias_1.append(inertia)
    print('For n_cluster =', i, 'The inertia is:', inertia)

For n_cluster = 1 The inertia is: 171535.5
For n_cluster = 2 The inertia is: 75949.15601023017
For n_cluster = 3 The inertia is: 45840.67661610867
For n_cluster = 4 The inertia is: 28165.58356662934
For n_cluster = 5 The inertia is: 23830.24505228459
For n_cluster = 6 The inertia is: 19502.407839362204
For n_cluster = 7 The inertia is: 15523.684014328752
For n_cluster = 8 The inertia is: 13020.084512948222
For n_cluster = 9 The inertia is: 11517.231348351697
For n_cluster = 10 The inertia is: 10299.698359250398
For n_cluster = 11 The inertia is: 9404.802904325206
For n_cluster = 12 The inertia is: 8659.542579270144
For n_cluster = 13 The inertia is: 7896.277200074606
For n_cluster = 14 The inertia is: 7223.8088214073505
For n_cluster = 15 The inertia is: 6691.75644045497
For n_cluster = 16 The inertia is: 6160.592835350923
For n_cluster = 17 The inertia is: 5552.953625949214
For n_cluster = 18 The inertia is: 5356.265766259883
For n_cluster = 19 The inertia is: 4869.198509239299

# Creating the figure
figure = plt.figure(1, figsize=(15,6), dpi=300)
plt.plot(np.arange(1,20), inertias_1, alpha=0.8, marker='o')
plt.xlabel("K")
plt.ylabel("Inertia ")

Text(0, 0.5, 'Inertia ')

output_18_1.png

Kmeans = KMeans(n_clusters=5, init='k-means++',  max_iter=300, n_init=10,random_state=0)
labels = Kmeans.fit_predict(X1_Matrix)
centroids1 = Kmeans.cluster_centers_ 
# the centroid points in each cluster
# Visualizing the 5 clusters
plt.scatter(x=X1_Matrix[labels==0, 0], y=X1_Matrix[labels==0, 1], s=20, c='red', marker='o')
plt.scatter(x=X1_Matrix[labels==1, 0], y=X1_Matrix[labels==1, 1], s=20, c='blue', marker='^')
plt.scatter(x=X1_Matrix[labels==2, 0], y=X1_Matrix[labels==2, 1], s=20, c='grey', marker='s')
plt.scatter(x=X1_Matrix[labels==3, 0], y=X1_Matrix[labels==3, 1], s=20, c='orange', marker='p')
plt.scatter(x=X1_Matrix[labels==4, 0], y=X1_Matrix[labels==4, 1], s=20, c='green', marker='*')
#Visualizing every centroids in different cluster.
plt.scatter(x=centroids1[:,0], y=centroids1[:,1], s=300, alpha=0.8, marker='+', label='Centroids')
#Style Setting
plt.title("Cluster Of Customers", fontsize=20)
plt.xlabel("Age")
plt.ylabel("Spending Score (1-100)")
plt.legend(loc=0)

<matplotlib.legend.Legend at 0x228401f81c8>

output_19_1.png

pd.Series(labels).value_counts()

0    57
1    41
2    37
3    34
4    31
dtype: int64

inertias_2 = []
for i in range(1,8):
    kmeans = KMeans(n_clusters=i, init='k-means++',  max_iter=300, n_init=10,random_state=1)
    kmeans.fit(X2_Matrix)
    inertia = kmeans.inertia_
    inertias_2.append(inertia)
    print('For n_cluster =', i, 'The inertia is:', inertia)

For n_cluster = 1 The inertia is: 269981.28
For n_cluster = 2 The inertia is: 181363.59595959596
For n_cluster = 3 The inertia is: 106348.37306211118
For n_cluster = 4 The inertia is: 73679.78903948834
For n_cluster = 5 The inertia is: 44448.45544793371
For n_cluster = 6 The inertia is: 37233.81451071001
For n_cluster = 7 The inertia is: 30227.606513152015

# Creating the figure
figure = plt.figure(1, figsize=(15,6), dpi=80)
plt.plot(np.arange(1,8), inertias_2, alpha=0.8, marker='o')
plt.xlabel("K")
plt.ylabel("Inertia ")
Kmeans = KMeans(n_clusters=5, init='k-means++',  max_iter=300, n_init=10,random_state=1)
labels = Kmeans.fit_predict(X2_Matrix)
centroids2 = Kmeans.cluster_centers_ 

output_22_0.png

# the centroid points in each cluster
# Visualizing the 5 clusters
plt.scatter(x=X2_Matrix[labels==0, 0], y=X1_Matrix[labels==0, 1], s=20, c='red', marker='o')
plt.scatter(x=X2_Matrix[labels==1, 0], y=X1_Matrix[labels==1, 1], s=20, c='blue', marker='^')
plt.scatter(x=X2_Matrix[labels==2, 0], y=X1_Matrix[labels==2, 1], s=20, c='grey', marker='s')
plt.scatter(x=X2_Matrix[labels==3, 0], y=X1_Matrix[labels==3, 1], s=20, c='orange', marker='p')
plt.scatter(x=X2_Matrix[labels==4, 0], y=X1_Matrix[labels==4, 1], s=20, c='green', marker='*')
#Visualizing every centroids in different cluster.
plt.scatter(x=centroids2[:,0], y=centroids2[:,1], s=300, alpha=0.8, marker='+', label='Centroids')
#Style Setting
plt.title("Cluster Of Customers", fontsize=20)
plt.xlabel("Annual Income (k$)")
plt.ylabel("Spending Score (1-100)")
plt.legend(loc=7)

<matplotlib.legend.Legend at 0x22840569d88>

output_23_1.png

5.总结

聚类结果显示：
在年龄方面，我们可以将客户分为5类，其中一类年轻人消费能力特别强，需要重点关注。
在年收入方面，我们可以将客户分为5类，有高收入低消费、高收入消费、中等收入中端消费、低收入第消费以及低收入高消费，可以针对他们做有针对性的营销策略。