Machine learning operations (b) logistic regression --Python (numpy) to achieve

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Question 1

Description: Implementing logistic regression.

Here minimize the use of Matlab function instead of fminunc function, refer to the blog [ Portal ].

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 import scipy.optimize as op
 4 
 5 #S函数
 6 def sigmoid(z):
 7     g = 1/(1+np.exp(-z))
 8     return g
 9 
10 #cost计算函数
11 def costFunction(theta, X, y):
12     theta = np.array(theta).reshape((np.size(theta),1))
13     m = np.size(y)
14     h = sigmoid(np.dot(X, theta))
15     . 1 = J / m * (- np.dot (yT, np.log (H)) - np.dot ((. 1-yT), np.log (l- H)))
 16      return J.flatten ()
 . 17  
18 is  DEF gradient (Theta, X-, Y):
 . 19      Theta = np.array (Theta) .reshape ((np.size (Theta),. 1 ))
 20 is      m = np.size (Y)
 21 is      H = Sigmoid (NP. DOT (X-, Theta))
 22 is      Grad = 1 / m * np.dot (XT, H - Y)
 23 is      return grad.flatten ()
 24  
25  
26 is  # read data, score 1 is the first column, the second column is score 2, the third column is Yes / NO 
27 Data = np.loadtxt ( ' ex2data1.txt ' , DELIMITER = ',', dtype='float')
28 m = np.size(data[:, 0])
29 # print(data)
30 
31 #绘制样本点
32 X = data[:, 0:2]
33 y = data[:, 2:3]
34 pos = np.where(y == 1)[0]
35 neg = np.where(y == 0)[0]
36 X1 = X[pos, 0:2]
37 X0 = X[neg, 0:2]
38 plt.plot(X1[:, 0], X1[:, 1], 'k+')
39 plt.plot(X0[:, 0], X0[:, 1], 'yo')
40 plt.xlabel('Exam 1 score')
41 plt.ylabel('Exam 2 score')
42 
43 #求解最优解
44 one = np.ones(m)
45 X = np.insert(X, 0, values=one, axis=1)
46 initial_theta = np.zeros(np.size(X, 1))
47 result = op.minimize(fun=costFunction, x0=initial_theta, args=(X, y), method='TNC', jac=gradient)
48 # print(result)
49 theta = result.x
50 cost = result.fun
51 print('theta:', theta)
52 print('cost:', cost)
53 
54 #绘制决策边界
55 plot_x = np.array([np.min(X[:, 1]), np.max(X[:, 2])])
56 # print(plot_x)
57 plot_y = (-1/theta[2])*(theta[1]*plot_x+theta[0])
58 # print(plot_y)
59 plt.plot(plot_x,plot_y)
60 plt.legend(labels=['Admitted', 'Not admitted' ])
 61 is plt.axis ([30, 100, 30, 100 ])
 62 is  plt.show ()
 63 is  
64  # forecast [4585] student performance, and accuracy of calculation 
65 Theta = np.array (Theta). the RESHAPE ((np.size (Theta),. 1 ))
 66 Z = np.dot ([. 1, 45, 85 ], Theta)
 67 Prob = Sigmoid (Z)
 68  Print ( ' the For A Student Scores with 45 and 85, Predict AN Admission Probability of WE ' , Prob)
 69 P = np.round (Sigmoid (np.dot (X-, Theta)))
 70 ACC = np.mean (P == Y) * 100
 71 is  Print ( ' Train the Accuracy:',acc,'%')

operation result:

 

Problem 2

Description: normalization implemented by logistic regression.

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 import scipy.optimize as op
 4 
 5 #S函数
 6 def sigmoid(z):
 7     g = 1/(1+np.exp(-z))
 8     return g
 9 
10 #cost计算函数
11 def costFunction(theta, X, y, lamb):
12     theta = np.array(theta).reshape((np.size(theta), 1))
13     m = np.size(y)
14     h = sigmoid(np.dot(X, theta))
15     J = 1/m*(-np.dot(y.T, np.log(h)) - np.dot((1-y.T), np.log(1-h)))
16     # 添加项
17     theta2 = theta[1:, 0]
18     Jadd = lamb/(2*m)*np.sum(theta2**2)
19     J = J + Jadd
20     return J.flatten()
21 
22 #求梯度
23 def gradient(theta, X, y, lamb):
24     theta = np.array(theta).reshape((np.size(theta), 1))
25     m = np.size(y)
26     h = sigmoid(np.dot(X, theta))
27     grad = 1/m*np.dot(X.T, h - y)
28     #添加项
29     theta[0,0] = 0
30     gradadd = lamb/m*theta
31     grad = grad + gradadd
32     return grad.flatten()
33 
34 #求特征矩阵
35 def mapFeature(X1, X2):
36     degree = 6
37     out = np.ones((np.size(X1),1))
38     for i in range(1, degree+1):
39         for j in range(0, i+1):
40             res = np.multiply(np.power(X1, i-J), np.power (an X2, J))
 41 is              OUT = np.insert (OUT, np.size (OUT [0,:]), values RES =, = Axis. 1 )
 42 is      return OUT
 43 is  
44 is  
45  
46 is  # read data fetch, score 1 is the first column, the second column is the score 2, the third column is Yes / NO 
47 data = np.loadtxt ( ' ex2data2.txt ' , DELIMITER = ' , ' , DTYPE = ' a float ' )
 48 = m np.size (Data [:, 0])
 49  
50  # draw sample point 
51 is X-= Data [:, 0: 2 ]
 52 is Y = Data [2 :,:. 3 ]
 53 is pos = np.where(y == 1)[0]
54 neg = np.where(y == 0)[0]
55 X1 = X[pos, 0:2]
56 X0 = X[neg, 0:2]
57 plt.plot(X1[:, 0], X1[:, 1], 'k+')
58 plt.plot(X0[:, 0], X0[:, 1], 'yo')
59 plt.xlabel('Microchip Test 1')
60 plt.ylabel('Microchip Test 2')
61 plt.legend(labels=['y = 1', 'y = 0'])
 62 is  
63 is  # initialized data 
64 X-mapFeature = (X-[:, 0], X-[:,. 1 ])
 65  # Print (X-) 
66 Lamb. 1 =
 67 initial_theta = np.zeros (np.size (X-,. 1 ))
 68  
69  # to find the optimal solution 
70 Result = op.minimize (Fun = costFunction, X0 = initial_theta, args = (X-, Y, Lamb), Method = ' the TNC ' , JAC = gradient)
 71 is  # Print (Result) 
72 cost = result.fun
 73 is Theta = result.x
 74  Print ( ' Theta: ', theta)
75 print('cost:', cost)
76 
77 #绘制决策边界
78 u = np.linspace(-1, 1.5, 50)
79 v = np.linspace(-1, 1.5, 50)
80 z = np.zeros((np.size(u),np.size(v)))
81 theta = np.array(theta).reshape((np.size(theta), 1))
82 for i in range(0, np.size(u)):
83     for j in range(0, np.size(v)):
84         z[i, j] = np.dot(mapFeature(u[i], v[j]), theta)
85 #Print (Z) 
86  plt.contour (U, V, zT, [0])
 87  plt.show ()
 88  
89  # calculation accuracy of 
90 P = np.round (Sigmoid (np.dot (X-, Theta)))
 91 is ACC = np.mean (P == Y) * 100
 92  Print ( ' Train the Accuracy: ' , ACC, ' % ' )

operation result: