Datawhale机器学习算法（一）: 基于逻辑回归的分类预测
#基础函数库的导入
import numpy as np
#常用的两个画图库
import matplotlib.pyplot as plt
import seaborn as sns
#逻辑回归函数的导入
from sklearn.linear_model import LogisticRegression
造数据集
x_fearures=np.array([[-1,-2],[-2,-1],[-3,-2],[1,3],[2,1],[3,2]])
y_label=np.array([0,0,0,1,1,1])
#逻辑回归函数模型
lr_clf=LogisticRegression()
#拟合构造的数据集
lr_clf=lr_clf.fit(x_fearures,y_label)
查看逻辑回归函数拟合后的权重和截距
print("逻辑回归的权重：",lr_clf.coef_)
print("逻辑回归的截距：",lr_clf.intercept_)
逻辑回归的权重： [[ 0.73462087 0.6947908 ]]
逻辑回归的截距： [-0.03643213]
对构造出的数据集进行可视化处理
plt.figure()
#s表示画出的圆点大小，c表示圆点色彩或颜色序列,写成如下表示按照y_label分配不同颜色
plt.scatter(x_fearures[:,0],x_fearures[:,1],c=y_label,s=50,cmap='viridis')
plt.title('Dataset')
plt.show()
可视化决策边界
plt.figure()
plt.scatter(x_fearures[:,0],x_fearures[:,1],c=y_label,s=50,cmap='viridis')
plt.title('Dataset')
nx,ny=200,100
x_min,x_max=plt.xlim()
y_min,y_max=plt.ylim()
x_grid,y_grid=np.meshgrid(np.linspace(x_min,x_max,nx),np.linspace(y_min,y_max,ny))
z_proba=lr_clf.predict_proba(np.c_[x_grid.ravel(),y_grid.ravel()])
z_proba=z_proba[:,1].reshape(x_grid.shape)
plt.contour(x_grid,y_grid,z_proba,[0.5],linewidths=2,colors='blue')
plt.show()
### 可视化预测新样本
plt.figure()
## new point 1
x_fearures_new1 = np.array([[0, -1]])
plt.scatter(x_fearures_new1[:,0],x_fearures_new1[:,1], s=50, cmap='viridis')
plt.annotate(s='New point 1',xy=(0,-1),xytext=(-2,0),color='blue',arrowprops=dict(arrowstyle='-|>',connectionstyle='arc3',color='red'))
## new point 2
x_fearures_new2 = np.array([[1, 2]])
plt.scatter(x_fearures_new2[:,0],x_fearures_new2[:,1], s=50, cmap='viridis')
plt.annotate(s='New point 2',xy=(1,2),xytext=(-1.5,2.5),color='red',arrowprops=dict(arrowstyle='-|>',connectionstyle='arc3',color='red'))
## 训练样本
plt.scatter(x_fearures[:,0],x_fearures[:,1], c=y_label, s=50, cmap='viridis')
plt.title('Dataset')
# 可视化决策边界
plt.contour(x_grid, y_grid, z_proba, [0.5], linewidths=2., colors='blue')
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
y_label_new1_predict=lr_clf.predict(x_fearures_new1)
y_label_new2_predict=lr_clf.predict(x_fearures_new2)
print('The New point 1 predict class:\n',y_label_new1_predict)
print('The New point 2 predict class:\n',y_label_new2_predict)
##由于逻辑回归模型是概率预测模型（前文介绍的p = p(y=1|x,\theta)）,所有我们可以利用predict_proba函数预测其概率
y_label_new1_predict_proba=lr_clf.predict_proba(x_fearures_new1)
y_label_new2_predict_proba=lr_clf.predict_proba(x_fearures_new2)
print('The New point 1 predict Probability of each class:\n',y_label_new1_predict_proba)
print('The New point 2 predict Probability of each class:\n',y_label_new2_predict_proba)
运行结果
The New point 1 predict class:
[0]
The New point 2 predict class:
[1]
The New point 1 predict Probability of each class:
[[ 0.67507358 0.32492642]]
The New point 2 predict Probability of each class:
[[ 0.11029117 0.88970883]]
可以发现训练好的回归模型将X_new1预测为了类别0（判别面左下侧），X_new2预测为了类别1（判别面右上侧）。其训练得到的逻辑回归模型的概率为0.5的判别面为上图中蓝色的线。
基于鸢尾花（iris）数据集的逻辑回归分类实践
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
##我们利用sklearn中自带的iris数据作为数据载入，并利用Pandas转化为DataFrame格式
from sklearn.datasets import load_iris
data = load_iris() #得到数据特征
iris_target = data.target #得到数据对应的标签
iris_features = pd.DataFrame(data=data.data, co
iris_features.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 150 entries, 0 to 149
Data columns (total 4 columns):
sepal length (cm) 150 non-null float64
sepal width (cm) 150 non-null float64
petal length (cm) 150 non-null float64
petal width (cm) 150 non-null float64
dtypes: float64(4)
memory usage: 4.8 KB
iris_features.head()
##其对应的类别标签为，其中0，1，2分别代表'setosa','versicolor','virginica'三种不同花的类别
iris_target
pd.Series(iris_target).value_counts()
iris_features.describe()
iris_all=iris_features.copy()
iris_all['target']=iris_target
sns.pairplot(data=iris_all,diag_kind='hist',hue='target')
plt.show()
for col in iris_features.columns:
sns.boxplot(x='target',y=col,saturation=0.5,palette='pastel',data=iris_all)
plt.title(col)
plt.show()
iris_all.head()
from mpl_toolkits.mplot3d import Axes3D
fig=plt.figure(figsize=(10,8))
ax=fig.add_subplot(111,projection='3d')
iris_all_class0 = iris_all[iris_all['target']==0].values
iris_all_class1 = iris_all[iris_all['target']==1].values
iris_all_class2 = iris_all[iris_all['target']==2].values
# 'setosa'(0), 'versicolor'(1), 'virginica'(2)
ax.scatter(iris_all_class0[:,0], iris_all_class0[:,1], iris_all_class0[:,2],label='setosa')
ax.scatter(iris_all_class1[:,0], iris_all_class1[:,1], iris_all_class1[:,2],label='versicolor')
ax.scatter(iris_all_class2[:,0], iris_all_class2[:,1], iris_all_class2[:,2],label='virginica')
plt.legend()
plt.show()
iris_all[iris_all['target']==0]
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm) target
0 5.1 3.5 1.4 0.2 0
1 4.9 3.0 1.4 0.2 0
2 4.7 3.2 1.3 0.2 0
3 4.6 3.1 1.5 0.2 0
4 5.0 3.6 1.4 0.2 0
5 5.4 3.9 1.7 0.4 0
6 4.6 3.4 1.4 0.3 0
7 5.0 3.4 1.5 0.2 0
8 4.4 2.9 1.4 0.2 0
9 4.9 3.1 1.5 0.1 0
10 5.4 3.7 1.5 0.2 0
11 4.8 3.4 1.6 0.2 0
12 4.8 3.0 1.4 0.1 0
13 4.3 3.0 1.1 0.1 0
14 5.8 4.0 1.2 0.2 0
15 5.7 4.4 1.5 0.4 0
16 5.4 3.9 1.3 0.4 0
17 5.1 3.5 1.4 0.3 0
18 5.7 3.8 1.7 0.3 0
19 5.1 3.8 1.5 0.3 0
20 5.4 3.4 1.7 0.2 0
21 5.1 3.7 1.5 0.4 0
22 4.6 3.6 1.0 0.2 0
23 5.1 3.3 1.7 0.5 0
24 4.8 3.4 1.9 0.2 0
25 5.0 3.0 1.6 0.2 0
26 5.0 3.4 1.6 0.4 0
27 5.2 3.5 1.5 0.2 0
28 5.2 3.4 1.4 0.2 0
29 4.7 3.2 1.6 0.2 0
30 4.8 3.1 1.6 0.2 0
31 5.4 3.4 1.5 0.4 0
32 5.2 4.1 1.5 0.1 0
33 5.5 4.2 1.4 0.2 0
34 4.9 3.1 1.5 0.1 0
35 5.0 3.2 1.2 0.2 0
36 5.5 3.5 1.3 0.2 0
37 4.9 3.1 1.5 0.1 0
38 4.4 3.0 1.3 0.2 0
39 5.1 3.4 1.5 0.2 0
40 5.0 3.5 1.3 0.3 0
41 4.5 2.3 1.3 0.3 0
42 4.4 3.2 1.3 0.2 0
43 5.0 3.5 1.6 0.6 0
44 5.1 3.8 1.9 0.4 0
45 4.8 3.0 1.4 0.3 0
46 5.1 3.8 1.6 0.2 0
47 4.6 3.2 1.4 0.2 0
48 5.3 3.7 1.5 0.2 0
49 5.0 3.3 1.4 0.2 0
##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（不包括类别为2的样本）
iris_features_part=iris_features.iloc[:100]
iris_target_part=iris_target[:100]
##测试集大小为20%，80%/20%分
x_train,x_test,y_train,y_test=train_test_split(iris_features_part,iris_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
##定义逻辑回归模型
clf=LogisticRegression(random_state=0,solver='lbfgs')
##在训练集上训练逻辑回归模型
clf.fit(x_train,y_train)
##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_)
运行结果
the weight of Logistic Regression: [[ 0.45244919 -0.81010583 2.14700385 0.90450733]]
the intercept(w0) of Logistic Regression: [-6.57504448]
##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('Predictedlabels')
plt.ylabel('Truelabels')
plt.show()
运行结果
The accuracy of the Logistic Regression is: 1.0
The accuracy of the Logistic Regression is: 1.0
The confusion matrix result:
[[ 9 0]
[ 0 11]]
##测试集大小为20%，80%/20%分
x_train,x_test,y_train,y_test=train_test_split(iris_features,iris_target,test_size=0.2,random_state=2020)
##定义逻辑回归模型
clf=LogisticRegression(random_state=0,solver='lbfgs')
##在训练集上训练逻辑回归模型
clf.fit(x_train,y_train)
运行结果
LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=0, solver='lbfgs', tol=0.0001,
verbose=0, warm_start=False)
##查看其对应的w
print('the weight of Logistic Regression:\n',clf.coef_)
##查看其对应的w0
print('the intercept(w0) of Logistic Regression:\n',clf.intercept_)
运行结果
the weight of Logistic Regression:
[[-0.43538857 0.87888013 -2.19176678 -0.94642091]
[-0.39434234 -2.6460985 0.76204684 -1.35386989]
[-0.00806312 0.11304846 2.52974343 2.3509289 ]]
the intercept(w0) of Logistic Regression:
[ 6.30620875 8.25761672 -16.63629247]
##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（前文介绍的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，第三列代表预测为2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))
print('The accuracy of the Logistic Regression is:',metrics.accuracy_score(y_test,test_predict))
运行结果
The test predict Probability of each class:
[[ 1.32525870e-04 2.41745142e-01 7.58122332e-01]
[ 7.02970475e-01 2.97026349e-01 3.17667822e-06]
[ 3.37367886e-02 7.25313901e-01 2.40949311e-01]
[ 5.66207138e-03 6.53245545e-01 3.41092383e-01]
[ 1.06817066e-02 6.72928600e-01 3.16389693e-01]
[ 8.98402870e-04 6.64470713e-01 3.34630884e-01]
[ 4.06382037e-04 3.86192249e-01 6.13401369e-01]
[ 1.26979439e-01 8.69440588e-01 3.57997319e-03]
[ 8.75544317e-01 1.24437252e-01 1.84312617e-05]
[ 9.11209514e-01 8.87814689e-02 9.01671605e-06]
[ 3.86067682e-04 3.06912689e-01 6.92701243e-01]
[ 6.23261939e-03 7.19220636e-01 2.74546745e-01]
[ 8.90760124e-01 1.09235653e-01 4.22292409e-06]
[ 2.32339490e-03 4.47236837e-01 5.50439768e-01]
[ 8.59945211e-04 4.22804376e-01 5.76335679e-01]
[ 9.24814068e-01 7.51814638e-02 4.46852786e-06]
[ 2.01307999e-02 9.35166320e-01 4.47028801e-02]
[ 1.71215635e-02 5.07246971e-01 4.75631465e-01]
[ 1.83964097e-04 3.17849048e-01 6.81966988e-01]
[ 5.69461042e-01 4.30536566e-01 2.39269631e-06]
[ 8.26025475e-01 1.73971556e-01 2.96936737e-06]
[ 3.05327704e-04 5.15880492e-01 4.83814180e-01]
[ 4.69978972e-03 2.90561777e-01 7.04738434e-01]
[ 8.61077168e-01 1.38915993e-01 6.83858427e-06]
[ 6.99887637e-04 2.48614010e-01 7.50686102e-01]
[ 5.33421842e-02 8.31557126e-01 1.15100690e-01]
[ 2.34973018e-02 3.54915328e-01 6.21587370e-01]
[ 1.63311193e-03 3.48301765e-01 6.50065123e-01]
[ 7.72156866e-01 2.27838662e-01 4.47157219e-06]
[ 9.30816593e-01 6.91640361e-02 1.93708074e-05]]
The accuracy of the Logistic Regression is: 0.958333333333
The accuracy of the Logistic Regression is: 0.8
##查看混淆矩阵
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()
运行结果
The confusion matrix result:
[[10 0 0]
[ 0 7 3]
[ 0 3 7]]
