数据挖掘与商务分析 - 第2次平时作业¶

信用卡用户聚类¶

利用信用卡用户行为数据 (credit_card.csv)，运用 K 均值方法，开展用户聚类分析，根据聚类结果制定营销策略。

1. 导入需要的库¶

In [1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA

# 让图能显示中文
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False

2. 读取数据并查看基本情况¶

In [2]:
# 读入数据
df = pd.read_csv('credit_card.csv')
print('数据形状：', df.shape)
df.head()

数据形状： (8949, 18)
Out[2]:
CUST_ID BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
0 C10001 40.900749 0.818182 95.40 0.00 95.4 0.000000 0.166667 0.000000 0.083333 0.000000 0 2 1000.0 201.802084 139.509787 0.000000 12
1 C10002 3202.467416 0.909091 0.00 0.00 0.0 6442.945483 0.000000 0.000000 0.000000 0.250000 4 0 7000.0 4103.032597 1072.340217 0.222222 12
2 C10003 2495.148862 1.000000 773.17 773.17 0.0 0.000000 1.000000 1.000000 0.000000 0.000000 0 12 7500.0 622.066742 627.284787 0.000000 12
3 C10004 1666.670542 0.636364 1499.00 1499.00 0.0 205.788017 0.083333 0.083333 0.000000 0.083333 1 1 7500.0 0.000000 0.000000 0.000000 12
4 C10005 817.714335 1.000000 16.00 16.00 0.0 0.000000 0.083333 0.083333 0.000000 0.000000 0 1 1200.0 678.334763 244.791237 0.000000 12
In [3]:
# 查看每列的类型和有多少缺失值
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 8949 entries, 0 to 8948
Data columns (total 18 columns):
 #   Column                            Non-Null Count  Dtype  
---  ------                            --------------  -----  
 0   CUST_ID                           8948 non-null   object 
 1   BALANCE                           8949 non-null   float64
 2   BALANCE_FREQUENCY                 8949 non-null   float64
 3   PURCHASES                         8949 non-null   float64
 4   ONEOFF_PURCHASES                  8949 non-null   float64
 5   INSTALLMENTS_PURCHASES            8949 non-null   float64
 6   CASH_ADVANCE                      8949 non-null   float64
 7   PURCHASES_FREQUENCY               8949 non-null   float64
 8   ONEOFF_PURCHASES_FREQUENCY        8949 non-null   float64
 9   PURCHASES_INSTALLMENTS_FREQUENCY  8949 non-null   float64
 10  CASH_ADVANCE_FREQUENCY            8949 non-null   float64
 11  CASH_ADVANCE_TRX                  8949 non-null   int64  
 12  PURCHASES_TRX                     8949 non-null   int64  
 13  CREDIT_LIMIT                      8949 non-null   float64
 14  PAYMENTS                          8949 non-null   float64
 15  MINIMUM_PAYMENTS                  8949 non-null   float64
 16  PRC_FULL_PAYMENT                  8949 non-null   float64
 17  TENURE                            8949 non-null   int64  
dtypes: float64(14), int64(3), object(1)
memory usage: 1.2+ MB
In [4]:
# 看看缺失值情况
df.isnull().sum()
Out[4]:
CUST_ID                             1
BALANCE                             0
BALANCE_FREQUENCY                   0
PURCHASES                           0
ONEOFF_PURCHASES                    0
INSTALLMENTS_PURCHASES              0
CASH_ADVANCE                        0
PURCHASES_FREQUENCY                 0
ONEOFF_PURCHASES_FREQUENCY          0
PURCHASES_INSTALLMENTS_FREQUENCY    0
CASH_ADVANCE_FREQUENCY              0
CASH_ADVANCE_TRX                    0
PURCHASES_TRX                       0
CREDIT_LIMIT                        0
PAYMENTS                            0
MINIMUM_PAYMENTS                    0
PRC_FULL_PAYMENT                    0
TENURE                              0
dtype: int64
In [5]:
# 看下数值列的统计信息
df.describe()
Out[5]:
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
count 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000 8949.000000
mean 1564.647593 0.877350 1003.316936 592.503572 411.113579 978.959616 0.490405 0.202480 0.364478 0.135141 3.249078 14.711476 4494.449450 1733.336511 834.075035 0.153732 11.517935
std 2081.584016 0.236798 2136.727848 1659.968851 904.378205 2097.264344 0.401360 0.298345 0.397451 0.200132 6.824987 24.858552 3638.815725 2895.168146 2336.104378 0.292511 1.337134
min 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 50.000000 0.000000 0.000000 0.000000 6.000000
25% 128.365782 0.888889 39.800000 0.000000 0.000000 0.000000 0.083333 0.000000 0.000000 0.000000 0.000000 1.000000 1600.000000 383.282850 163.029483 0.000000 12.000000
50% 873.680279 1.000000 361.490000 38.000000 89.000000 0.000000 0.500000 0.083333 0.166667 0.000000 0.000000 7.000000 3000.000000 857.062706 289.686899 0.000000 12.000000
75% 2054.372848 1.000000 1110.170000 577.830000 468.650000 1113.868654 0.916667 0.300000 0.750000 0.222222 4.000000 17.000000 6500.000000 1901.279320 788.721609 0.142857 12.000000
max 19043.138560 1.000000 49039.570000 40761.250000 22500.000000 47137.211760 1.000000 1.000000 1.000000 1.500000 123.000000 358.000000 30000.000000 50721.483360 76406.207520 1.000000 12.000000

3. 数据预处理¶

主要做三件事：

  1. 删掉用户ID列（聚类用不到）
  2. 处理缺失值（用中位数填充）
  3. 标准化（因为不同字段量纲差太大，比如余额几千和频率0-1）
In [6]:
# 删掉CUST_ID列
data = df.drop('CUST_ID', axis=1)

# 用中位数填充缺失值
data = data.fillna(data.median())

print('处理后还有缺失值吗？', data.isnull().sum().sum())

处理后还有缺失值吗？ 0
In [7]:
# 标准化
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

# 转回DataFrame方便查看
data_scaled = pd.DataFrame(data_scaled, columns=data.columns)
data_scaled.head()
Out[7]:
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
0 -0.732054 -0.249881 -0.424934 -0.356957 -0.349114 -0.466805 -0.806649 -0.678716 -0.707409 -0.675294 -0.476083 -0.511381 -0.960380 -0.529026 -0.297334 -0.525588 0.360541
1 0.786858 0.134049 -0.469584 -0.356957 -0.454607 2.605438 -1.221928 -0.678716 -0.917090 0.573949 0.110032 -0.591841 0.688601 0.818546 0.101998 0.234159 0.360541
2 0.447041 0.517980 -0.107716 0.108843 -0.454607 -0.466805 1.269742 2.673295 -0.917090 -0.675294 -0.476083 -0.109082 0.826016 -0.383857 -0.088524 -0.525588 0.360541
3 0.049015 -1.017743 0.231995 0.546123 -0.454607 -0.368678 -1.014290 -0.399383 -0.917090 -0.258882 -0.329554 -0.551611 0.826016 -0.598733 -0.357057 -0.525588 0.360541
4 -0.358849 0.517980 -0.462095 -0.347317 -0.454607 -0.466805 -1.014290 -0.399383 -0.917090 -0.675294 -0.476083 -0.551611 -0.905414 -0.364421 -0.252265 -0.525588 0.360541

4. 用肘部法则确定最佳K值¶

通过画出不同K值下的SSE（簇内平方和），找拐点位置的K作为最佳聚类数。

In [8]:
# 试K从2到10
sse = []
k_range = range(2, 11)

for k in k_range:
    km = KMeans(n_clusters=k, random_state=42, n_init=10)
    km.fit(data_scaled)
    sse.append(km.inertia_)  # inertia_就是SSE

# 画肘部图
plt.figure(figsize=(8, 5))
plt.plot(k_range, sse, marker='o')
plt.xlabel('K值（聚类数）')
plt.ylabel('SSE（簇内平方和）')
plt.title('肘部法则确定最佳K值')
plt.grid(True)
plt.show()
No description has been provided for this image

从上图看，K=4时曲线下降变缓，所以选 K=4 比较合适。

5. 用K=4进行聚类¶

In [9]:
# 训练K-means模型
kmeans = KMeans(n_clusters=4, random_state=42, n_init=10)
labels = kmeans.fit_predict(data_scaled)

# 把聚类结果加回原数据
data['cluster'] = labels

# 看每个簇有多少人
print('每个簇的用户数：')
print(data['cluster'].value_counts().sort_index())

每个簇的用户数：
cluster
0     409
1    3366
2    1197
3    3977
Name: count, dtype: int64

6. 各簇用户特征分析¶

In [10]:
# 计算每个簇各字段的平均值
cluster_mean = data.groupby('cluster').mean()
cluster_mean
Out[10]:
BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
cluster
0 3551.153761 0.986879 7681.620098 5095.878826 2587.208264 653.638891 0.946418 0.739031 0.788060 0.071290 2.085575 89.359413 9696.943765 7288.739497 1970.476256 0.286707 11.951100
1 894.768927 0.934715 1236.263333 593.995933 642.541696 209.816318 0.885255 0.297109 0.711930 0.042487 0.789067 22.092692 4214.013741 1331.325429 633.801648 0.269313 11.594474
2 4602.449658 0.968389 501.862982 320.188797 181.759123 4521.509581 0.287832 0.138911 0.185671 0.484792 14.294904 7.665831 7546.160857 3484.054216 2000.543192 0.034888 11.386800
3 1012.995969 0.790134 270.281184 210.068828 60.479311 597.154288 0.170292 0.086343 0.080662 0.114888 2.126226 2.907971 3278.263348 975.328059 535.626389 0.078002 11.448076
In [11]:
# 画热力图直观看每个簇的特点
# 这里先把均值标准化一下，方便对比
cluster_mean_scaled = (cluster_mean - cluster_mean.mean()) / cluster_mean.std()

plt.figure(figsize=(10, 8))
sns.heatmap(cluster_mean_scaled.T, annot=True, cmap='RdBu_r', center=0, fmt='.2f')
plt.title('各簇用户特征热力图（标准化后）')
plt.xlabel('簇')
plt.ylabel('特征')
plt.show()
No description has been provided for this image

7. 用PCA降维可视化聚类结果¶

因为数据有17个特征不好画图，用PCA降到2维就能可视化了。

In [12]:
# PCA降维到2个主成分
pca = PCA(n_components=2)
data_pca = pca.fit_transform(data_scaled)

# 画散点图
plt.figure(figsize=(10, 6))
for i in range(4):
    plt.scatter(data_pca[labels == i, 0], data_pca[labels == i, 1],
                label=f'簇 {i}', alpha=0.5)
plt.xlabel('主成分1')
plt.ylabel('主成分2')
plt.title('K-means聚类结果（PCA降维到2维）')
plt.legend()
plt.grid(True)
plt.show()

print(f'两个主成分一共解释了 {pca.explained_variance_ratio_.sum()*100:.2f}% 的方差')
No description has been provided for this image 
两个主成分一共解释了 47.62% 的方差

8. 聚类结果解读与营销策略¶

结合上面的均值表和热力图，对 4 个簇分别画像如下（簇编号和上面表格一致）：

簇 0：高端购物达人（409 人，约 4.6%）¶

  • 特征：购买金额最高（约 7681），一次性购买（5095）和分期购买（2587）都遥遥领先
  • 购买频率 0.95，购买交易笔数 89 笔，活跃度极高
  • 信用额度最高（约 9696），还款金额最高（7288）
  • 营销策略：推荐联名高端信用卡、积分加倍、商旅权益，绑定他们的忠诚度；可推大额免息分期

簇 1：日常活跃用户（3366 人，约 37.6%）¶

  • 特征：购买金额中等（1236），但购买频率高达 0.88，分期付款频率 0.71
  • 现金预借很少，行为健康
  • 信用额度中等（4214）
  • 营销策略：日常消费返现、商超联合优惠、小额免息分期，挖掘他们的消费潜力

簇 2：预借现金重度用户（1197 人，约 13.4%）¶

  • 特征：现金预借金额最高（4521），现金预借频率最高（0.48），交易次数 14 次
  • 购买金额却很低（501），余额最高（4602）
  • 全额还款比例最低（仅 0.03），有较高的逾期风险
  • 营销策略：重点风险监控，限制额度提升；可定向推现金分期产品，但要严格审核还款能力

簇 3：低活跃沉睡用户（3977 人，约 44.4%）¶

  • 特征：用户数最多，但购买金额最低（270），购买频率最低（0.17）
  • 信用额度也最低（3278），整体不活跃
  • 营销策略：发新人优惠券、首刷礼、生日礼等激励活动，唤醒他们多刷卡

总结¶

通过 K-means 聚类把信用卡用户分成 4 类：

  • 高端购物达人（簇 0）和日常活跃用户（簇 1）是优质客户，应重点维护
  • 预借现金重度用户（簇 2）需要重点风险管控
  • 低活跃用户（簇 3）人数最多，需要通过营销活动激活

针对不同人群制定不同的营销策略，可以在提高营销效率的同时，更好地控制信用风险。