传统机器学习之逻辑回归的分类预测，以威斯康辛州乳腺癌数据集为例

传统机器学习之逻辑回归的分类预测，以威斯康辛州乳腺癌数据集为例

1导入基本库

##coding utf-8
# 导入基本数据计算库
import numpy as np 
import pandas as pd 
# 导入基本绘图库
import matplotlib.pyplot as plt
import seaborn as sns 

2读取数据并且变换类型

## 我们利用 sklearn 中自带的breast_cancer数据作为数据载入，并利用Pandas转化为DataFrame格式
from sklearn.datasets import load_breast_cancer
data = load_breast_cancer() #得到数据特征
breast_target = data.target #得到数据对应的标签
breast_features = pd.DataFrame(data=data.data, columns=data.feature_names) #利用Pandas转化为DataFrame格式
print(breast_features)

3输出数据

## 进行简单的数据查看，我们可以利用 .head() 头部.tail()尾部
breast_features.head()

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	…	worst radius	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension
0	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.3001	0.14710	0.2419	0.07871	…	25.38	17.33	184.60	2019.0	0.1622	0.6656	0.7119	0.2654	0.4601	0.11890
1	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.0869	0.07017	0.1812	0.05667	…	24.99	23.41	158.80	1956.0	0.1238	0.1866	0.2416	0.1860	0.2750	0.08902
2	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.1974	0.12790	0.2069	0.05999	…	23.57	25.53	152.50	1709.0	0.1444	0.4245	0.4504	0.2430	0.3613	0.08758
3	11.42	20.38	77.58	386.1	0.14250	0.28390	0.2414	0.10520	0.2597	0.09744	…	14.91	26.50	98.87	567.7	0.2098	0.8663	0.6869	0.2575	0.6638	0.17300
4	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.1980	0.10430	0.1809	0.05883	…	22.54	16.67	152.20	1575.0	0.1374	0.2050	0.4000	0.1625	0.2364	0.07678

5 rows × 30 columns

breast_features.tail()

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	…	worst radius	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension
564	21.56	22.39	142.00	1479.0	0.11100	0.11590	0.24390	0.13890	0.1726	0.05623	…	25.450	26.40	166.10	2027.0	0.14100	0.21130	0.4107	0.2216	0.2060	0.07115
565	20.13	28.25	131.20	1261.0	0.09780	0.10340	0.14400	0.09791	0.1752	0.05533	…	23.690	38.25	155.00	1731.0	0.11660	0.19220	0.3215	0.1628	0.2572	0.06637
566	16.60	28.08	108.30	858.1	0.08455	0.10230	0.09251	0.05302	0.1590	0.05648	…	18.980	34.12	126.70	1124.0	0.11390	0.30940	0.3403	0.1418	0.2218	0.07820
567	20.60	29.33	140.10	1265.0	0.11780	0.27700	0.35140	0.15200	0.2397	0.07016	…	25.740	39.42	184.60	1821.0	0.16500	0.86810	0.9387	0.2650	0.4087	0.12400
568	7.76	24.54	47.92	181.0	0.05263	0.04362	0.00000	0.00000	0.1587	0.05884	…	9.456	30.37	59.16	268.6	0.08996	0.06444	0.0000	0.0000	0.2871	0.07039

5 rows × 30 columns

breast_target

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

4可视化数据

## 合并标签和特征信息
breast_all = breast_features.copy() ##进行浅拷贝，防止对于原始数据的修改
breast_all['target'] = breast_target

for col in breast_features.columns:
    sns.boxplot(x='target', y=col, saturation=0.5,palette='pastel', data=breast_all)
    plt.title(col)
    plt.show()

# 选取其前三个特征绘制三维散点图
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure(figsize=(10,8))
ax = fig.add_subplot(111, projection='3d')

breast_all_class0 = breast_all[breast_all['target']==0].values
breast_all_class1 = breast_all[breast_all['target']==1].values

# 
ax.scatter(breast_all_class0[:,0], breast_all_class0[:,1], breast_all_class0[:,2],label='malignancy')
ax.scatter(breast_all_class1[:,0], breast_all_class1[:,1], breast_all_class1[:,2],label='benign')

plt.legend()# 设置图例

plt.show()

5划分数据集并训练模型

## 为了正确评估模型性能，将数据划分为训练集和测试集，并在训练集上训练模型，在测试集上验证模型性能。
from sklearn.model_selection import train_test_split

## 选择其类别为0和1的样本
breast_features_part = breast_features.iloc[:400]
breast_target_part = breast_target[:400]

## 测试集大小为20%， 80%/20%分
x_train, x_test, y_train, y_test = train_test_split(breast_features_part, breast_target_part, test_size = 0.2, random_state = 2020)

## 从sklearn中导入逻辑回归模型
from sklearn.linear_model import LogisticRegression

## 查看其对应的w
print('the weight of Logistic Regression:',clf.coef_)

## 查看其对应的w0
print('the intercept(w0) of Logistic Regression:',clf.intercept_)

the weight of Logistic Regression: [[ 1.58968483  0.00505748  0.38837107 -0.02644605 -0.06394019 -0.28711873
  -0.37853229 -0.16487063 -0.08104816 -0.02073884  0.03589982  0.74089555
   0.319864   -0.11417749 -0.00675931 -0.05530251 -0.07017069 -0.01922167
  -0.03401847 -0.00483318  1.43728027 -0.293294   -0.44437706 -0.00940775
  -0.1151745  -0.90699784 -1.02800043 -0.31155816 -0.31756381 -0.0902991 ]]
the intercept(w0) of Logistic Regression: [0.27969267]

6进行模型预测和模型评估

## 在训练集和测试集上分布利用训练好的模型进行预测
train_predict = clf.predict(x_train)
test_predict = clf.predict(x_test)

from sklearn import metrics

## 利用accuracy（准确度）【预测正确的样本数目占总预测样本数目的比例】评估模型效果
print('The accuracy of the Logistic Regression is:',metrics.accuracy_score(y_train,train_predict))
print('The accuracy of the Logistic Regression is:',metrics.accuracy_score(y_test,test_predict))

## 查看混淆矩阵 (预测值和真实值的各类情况统计矩阵)
confusion_matrix_result = metrics.confusion_matrix(test_predict,y_test)
print('The confusion matrix result:\n',confusion_matrix_result)

# 利用热力图对于结果进行可视化
plt.figure(figsize=(8, 6))
sns.heatmap(confusion_matrix_result, annot=True, cmap='Blues')
plt.xlabel('Predicted labels')
plt.ylabel('True labels')
plt.show()

## 在训练集和测试集上分布利用训练好的模型进行预测
train_predict = clf.predict(x_train)
test_predict = clf.predict(x_test)

## 由于逻辑回归模型是概率预测模型（p = p(y=1|x,\theta)）,所有我们可以利用 predict_proba 函数预测其概率
train_predict_proba = clf.predict_proba(x_train)
test_predict_proba = clf.predict_proba(x_test)

print('The test predict Probability of each class:\n',test_predict_proba)
## 其中第一列代表预测为0类的概率，第二列代表预测为1类的概率

## 利用accuracy（准确度）【预测正确的样本数目占总预测样本数目的比例】评估模型效果
print('The accuracy of the Logistic Regression is:',metrics.accuracy_score(y_train,train_predict))

The test predict Probability of each class:
 [[1.00000000e+00 1.74550212e-20]
 [1.39048275e-01 8.60951725e-01]
 [5.93137883e-03 9.94068621e-01]
 [9.99928649e-01 7.13512878e-05]
 [1.10598806e-02 9.88940119e-01]
 [1.51763229e-02 9.84823677e-01]
 [9.99999976e-01 2.40399407e-08]
 [6.62445901e-01 3.37554099e-01]
 [9.99998635e-01 1.36531478e-06]
 [9.99999937e-01 6.26178303e-08]
 [6.90866554e-03 9.93091334e-01]
 [5.05999535e-01 4.94000465e-01]
 [9.99286913e-01 7.13086781e-04]
 [1.76610793e-03 9.98233892e-01]
 [2.80400461e-02 9.71959954e-01]
 [1.24867157e-02 9.87513284e-01]
 [2.83215334e-02 9.71678467e-01]
 [1.15554505e-01 8.84445495e-01]
 [1.00000000e+00 2.80618965e-19]
 [9.53877184e-01 4.61228156e-02]
 [9.99981034e-01 1.89663222e-05]
 [9.99999998e-01 1.77364899e-09]
 [9.99784834e-01 2.15165875e-04]
 [9.49142700e-04 9.99050857e-01]
 [1.64447085e-02 9.83555291e-01]
 [2.33740738e-01 7.66259262e-01]
 [6.99567302e-01 3.00432698e-01]
 [3.04170042e-01 6.95829958e-01]
 [1.44626331e-01 8.55373669e-01]
 [1.00000000e+00 5.02507240e-26]
 [9.97623824e-01 2.37617614e-03]
 [2.58153192e-01 7.41846808e-01]
 [3.06528727e-02 9.69347127e-01]
 [2.36651118e-03 9.97633489e-01]
 [9.99999630e-01 3.70006531e-07]
 [1.38031809e-02 9.86196819e-01]
 [8.14914321e-01 1.85085679e-01]
 [9.99964597e-01 3.54026953e-05]
 [2.63450870e-03 9.97365491e-01]
 [1.00392014e-03 9.98996080e-01]
 [8.71662147e-01 1.28337853e-01]
 [4.38761196e-03 9.95612388e-01]
 [8.36873412e-03 9.91631266e-01]
 [1.06161420e-02 9.89383858e-01]
 [9.99999997e-01 3.31516428e-09]
 [9.94734026e-01 5.26597408e-03]
 [5.13494043e-03 9.94865060e-01]
 [9.99999939e-01 6.09370477e-08]
 [9.99999998e-01 2.05445256e-09]
 [2.46967502e-02 9.75303250e-01]
 [1.00000000e+00 9.38730719e-11]
 [1.77617121e-02 9.82238288e-01]
 [1.60523832e-02 9.83947617e-01]
 [9.99987835e-01 1.21654996e-05]
 [9.82051340e-01 1.79486596e-02]
 [4.18451580e-03 9.95815484e-01]
 [1.00000000e+00 1.09319254e-11]
 [6.97450777e-05 9.99930255e-01]
 [1.37259706e-01 8.62740294e-01]
 [1.00000000e+00 2.49456197e-12]
 [7.97894321e-02 9.20210568e-01]
 [5.37893016e-03 9.94621070e-01]
 [1.96820584e-02 9.80317942e-01]
 [1.17207761e-01 8.82792239e-01]
 [7.35320492e-02 9.26467951e-01]
 [9.99673213e-01 3.26787395e-04]
 [2.57482071e-02 9.74251793e-01]
 [1.71958276e-03 9.98280417e-01]
 [9.97528713e-01 2.47128671e-03]
 [9.80976661e-01 1.90233388e-02]
 [6.21099876e-03 9.93789001e-01]
 [8.15132942e-03 9.91848671e-01]
 [9.23436304e-01 7.65636959e-02]
 [4.19986782e-03 9.95800132e-01]
 [1.27804652e-03 9.98721953e-01]
 [1.87243107e-03 9.98127569e-01]
 [1.85282178e-01 8.14717822e-01]
 [6.44246823e-02 9.35575318e-01]
 [9.99998455e-01 1.54502928e-06]
 [6.62652442e-03 9.93373476e-01]
 [8.57651190e-01 1.42348810e-01]
 [7.16548957e-01 2.83451043e-01]
 [3.06459764e-03 9.96935402e-01]
 [9.96314395e-01 3.68560463e-03]
 [1.47485316e-01 8.52514684e-01]
 [9.99999787e-01 2.12826060e-07]
 [1.18626317e-02 9.88137368e-01]
 [1.57873994e-01 8.42126006e-01]
 [3.78928093e-03 9.96210719e-01]
 [1.29844105e-02 9.87015589e-01]
 [9.99793895e-01 2.06105131e-04]
 [9.99066816e-01 9.33183505e-04]
 [9.29672666e-01 7.03273335e-02]
 [3.54993590e-02 9.64500641e-01]
 [9.99998018e-01 1.98162222e-06]
 [1.40153070e-02 9.85984693e-01]
 [1.13682784e-02 9.88631722e-01]
 [9.99999974e-01 2.62916142e-08]
 [1.00000000e+00 9.16315813e-13]
 [5.19135133e-03 9.94808649e-01]
 [1.85001642e-02 9.81499836e-01]
 [2.35600902e-02 9.76439910e-01]
 [5.37148641e-02 9.46285136e-01]
 [6.41665354e-02 9.35833465e-01]
 [7.27446091e-04 9.99272554e-01]
 [7.95455974e-04 9.99204544e-01]
 [2.91957313e-03 9.97080427e-01]
 [8.42552515e-04 9.99157447e-01]
 [9.28348894e-02 9.07165111e-01]
 [9.98976712e-01 1.02328806e-03]
 [9.99710759e-01 2.89240705e-04]
 [1.00000000e+00 4.26245383e-16]
 [9.98616497e-01 1.38350344e-03]
 [9.65916735e-04 9.99034083e-01]]
The accuracy of the Logistic Regression is: 0.9516483516483516
```![在这里插入图片描述](https://img-blog.csdnimg.cn/f33fccd63ca0432d96566ec9fb1cc58a.bmp#pic_center)
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