逻辑回归的介绍和应用

##  基础函数库
import numpy as np 
 
## 导入画图库
import matplotlib.pyplot as plt
import seaborn as sns
 
## 导入逻辑回归模型函数
from sklearn.linear_model import LogisticRegression

##Demo演示LogisticRegression分类
 
## 构造数据集
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])
 
## 调用逻辑回归模型
lr_clf = LogisticRegression()
 
## 用逻辑回归模型拟合构造的数据集
lr_clf = lr_clf.fit(x_fearures, y_label) #其拟合方程为 y=w0+w1*x1+w2*x2

## 查看其对应模型的w
print('the weight of Logistic Regression:',lr_clf.coef_)
 
## 查看其对应模型的w0
print('the intercept(w0) of Logistic Regression:',lr_clf.intercept_)

## 可视化构造的数据样本点
plt.figure()
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别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)）,所以我们可以利用 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)

import numpy as np
import matplotlib.pyplot as plt
x = np.arange(-5,5,0.01)
y = 1/(1+np.exp(-x))
 
plt.plot(x,y)
plt.xlabel('z')
plt.ylabel('y')
plt.grid()
plt.show()