机器学习吴恩达-线性回归笔记（1）

 1 import pandas as pd
 2 import numpy as np
 3 def CostFunction(x,y,theta):
 4     med_var=np.power((x*theta)-y,2)
 5     return np.sum(med_var)/(2*len(x))
 6 
 7 def Grandent(x,y,theta,alphl,maxcircle):
 8     m = x.shape[0]
 9     print(‘m=‘,m)
10     print(‘theta shape‘,theta.shape)
11     temp = np.matrix(np.zeros(theta.shape))
12     print(‘temp shape‘,temp.shape)
13     cost = np.zeros(maxcircle)  # 初始化一个ndarray，包含每次迭代的cost
14     for k in range(maxcircle):
15         # print(theta)
16         temp=theta-(alphl/m)*(x.T)*(x*theta-y)
17         cost[k]=CostFunction(x,y,theta)
18         theta=temp
19     return theta,cost
20 
21 
22 data=pd.read_csv(‘ex1data1.txt‘,names=[‘feature‘,‘price‘])   #(97, 2)
23 data.insert(0,‘x0‘,1)
24 X_dataframe=data.drop([‘price‘],axis=1)
25 y_dataframe=data.price
26 X=np.matrix(X_dataframe.values)  #专程矩阵格式
27 y=np.matrix(y_dataframe.values)
28 y=y.T
29 m,n=X_dataframe.shape
30 theta=np.zeros((n,1))
31 alphl=0.01  #开始设置为0.1,会一直报溢出，导致梯度下降方法不收敛
32 maxcircle=1000
33 
34 theta_fin,cost=Grandent(X,y,theta,alphl,maxcircle)
35 
36 import matplotlib.pyplot as plt
37 
38 fig,ax = plt.subplots()
39 
40 ax.plot(np.arange(maxcircle), cost, ‘red‘)  # np.arange()返回等差数组
41 ax.set_xlabel(‘Iterations‘)
42 ax.set_ylabel(‘Cost‘)
43 ax.set_title(‘Cost vs. num_Iterations‘)
44 
45 #np.linspace()在指定的间隔内返回均匀间隔的数字
46 x = np.linspace(data.feature.min(), data.feature.max(), 100) # 横坐标
47 f = theta_fin[0,0] + (theta_fin[1,0] * x)  # 纵坐标
48 fig,ax = plt.subplots()
49 ax.plot(x, f, ‘r‘, label=‘Prediction‘)
50 ax.scatter(data[‘feature‘], data.price, label=‘Traning Data‘)
51 ax.legend(loc=2)  # 2表示在左上角
52 ax.set_xlabel(‘feature‘)
53 ax.set_ylabel(‘price‘)
54 ax.set_title(‘Predicted Profit vs. Population Size‘)
55 plt.show()