基于examdata.csv数据，建立逻辑回归模型 预测Exam1 = 75, Exam2 = 60时，该同学在Exam3是 passed or failed; 建立二阶边界，提高模型准确度
（1）load the data
import pandas as pd
import numpy as np
data = pd.read_csv('examdata.csv')
data.head()
查看数据信息
（2）#visualize the data
%matplotlib inline
from matplotlib import pyplot as plt
fig1 = plt.figure()
plt.scatter(data.loc[:,'Exam1'],data.loc[:,'Exam2'])
plt.title('Exam1-Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.show()
(3)add label mask
mask=data.loc[:,'Pass']==1
print(~mask)
(4) 数据分类可视化
fig2 = plt.figure()
passed=plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed=plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.title('Exam1-Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()
#define X,y
X = data.drop(['Pass'],axis=1)
y = data.loc[:,'Pass']
X1 = data.loc[:,'Exam1']
X2 = data.loc[:,'Exam2']
X1.head()
（5）训练
#establish the model and train it
from sklearn.linear_model import LogisticRegression
LR = LogisticRegression()
LR.fit(X,y)
（6）预测
#show the predicted result and its accuracy
y_predict = LR.predict(X)
print(y_predict)
from sklearn.metrics import accuracy_score
accuracy = accuracy_score(y,y_predict)
print(accuracy)
赋值theta0，theta1,theta2
theta0 = LR.intercept_
theta1,theta2 = LR.coef_[0][0],LR.coef_[0][1]
print(theta0,theta1,theta2)
X2_new = -(theta0+theta1*X1)/theta2
print(X2_new)
拟合数据
fig3 = plt.figure()
passed=plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed=plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.plot(X1,X2_new)
plt.title('Exam1-Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()
下面将使用边界函数进行优化
边界函数： 𝜃0+𝜃1𝑋1+𝜃2𝑋2=0θ0+θ1X1+θ2X2=0
二阶边界函数：𝜃0+𝜃1𝑋1+𝜃2𝑋2+𝜃3𝑋21+𝜃4𝑋22+𝜃5𝑋1𝑋2=0
对数据重新整合
#create new data
X1_2 = X1*X1
X2_2 = X2*X2
X1_X2 = X1*X2
#生成X_new集合
X_new = {'X1':X1,'X2':X2,'X1_2':X1_2,'X2_2':X2_2,'X1_X2':X1_X2}
X_new = pd.DataFrame(X_new)
print(X_new)
#建立新模型并训练
#establish new model and train
LR2 = LogisticRegression()
LR2.fit(X_new,y)
y2_predict = LR2.predict(X_new)
accuracy2 = accuracy_score(y,y2_predict)
print(accuracy2)
对X1_new 进行排序
X1_new = X1.sort_values()
边界函数： 𝜃0+𝜃1𝑋1+𝜃2𝑋2=0θ0+θ1X1+θ2X2=0
二阶边界函数：𝜃0+𝜃1𝑋1+𝜃2𝑋2+𝜃3𝑋21+𝜃4𝑋22+𝜃5𝑋1𝑋2=0θ0+θ1X1+θ2X2+θ3X12+θ4X22+θ5X1X2=0
𝑎𝑥2+𝑏𝑥+𝑐=0:𝑥1=(−𝑏+(𝑏2−4𝑎𝑐).5)/2𝑎,𝑥1=(−𝑏−(𝑏2−4𝑎𝑐).5)/2𝑎ax2+bx+c=0:x1=(−b+(b2−4ac).5)/2a,x1=(−b−(b2−4ac).5)/2a
𝜃4𝑋22+(𝜃5𝑋1++𝜃2)𝑋2+(𝜃0+𝜃1𝑋1+𝜃3𝑋21)=0
theta0 = LR2.intercept_
theta1,theta2,theta3,theta4,theta5 = LR2.coef_[0][0],LR2.coef_[0][1],LR2.coef_[0][2],LR2.coef_[0][3],LR2.coef_[0][4]
a = theta4
b = theta5*X1_new+theta2
c = theta0+theta1*X1_new+theta3*X1_new*X1_new
X2_new_boundary = (-b+np.sqrt(b*b-4*a*c))/(2*a)
print(X2_new_boundary)
优化拟合可视化
fig5 = plt.figure()
passed=plt.scatter(data.loc[:,'Exam1'][mask],data.loc[:,'Exam2'][mask])
failed=plt.scatter(data.loc[:,'Exam1'][~mask],data.loc[:,'Exam2'][~mask])
plt.plot(X1_new,X2_new_boundary)
plt.title('Exam1-Exam2')
plt.xlabel('Exam1')
plt.ylabel('Exam2')
plt.legend((passed,failed),('passed','failed'))
plt.show()
plt.plot(X1_new,X2_new_boundary)
plt.show()
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