機器學習做業（三）多類別分類與神經網絡——Python(numpy)實現

題目太長了！下載地址【傳送門】

第1題

簡述：識別圖片上的數字。

 1 import numpy as np  2 import scipy.io as scio  3 import matplotlib.pyplot as plt  4 import scipy.optimize as op  5 
 6 #顯示圖片數據
 7 def displayData(X):  8     m = np.size(X, 0)  #X的行數，即樣本數量
 9     n = np.size(X, 1)  #X的列數，即單個樣本大小
 10     example_width = int(np.round(np.sqrt(n)))  #單張圖片寬度
 11     example_height = int(np.floor(n / example_width))  #單張圖片高度
 12     display_rows = int(np.floor(np.sqrt(m)))  #顯示圖中，一行多少張圖
 13     display_cols = int(np.ceil(m / display_rows))  #顯示圖中，一列多少張圖片
 14     pad = 1  #圖片間的間隔
 15     display_array = - np.ones((pad + display_rows * (example_height + pad),  16                             pad + display_cols * (example_width + pad)))  #初始化圖片矩陣
 17     curr_ex = 0  #當前的圖片計數
 18     #將每張小圖插入圖片數組中
 19     for j in range(0, display_rows):  20         for i in range(0, display_cols):  21             if curr_ex >= m:  22                 break
 23             max_val = np.max(abs(X[curr_ex, :]))  24             jstart = pad + j * (example_height + pad)  25             istart = pad + i * (example_width + pad)  26             display_array[jstart: (jstart + example_height), istart: (istart + example_width)] = \  27                 np.array(X[curr_ex, :]).reshape(example_height, example_width) / max_val  28             curr_ex = curr_ex + 1
 29         if curr_ex >= m:  30             break
 31     display_array = display_array.T  32     plt.imshow(display_array,cmap=plt.cm.gray)  33     plt.axis('off')  34  plt.show()  35 
 36 #計算hθ(z)
 37 def sigmoid(z):  38     g = 1.0 / (1.0 + np.exp(-z))  39     return g  40 
 41 #計算cost
 42 def lrCostFunction(theta, X, y, lamb):  43     theta = np.array(theta).reshape((np.size(theta), 1))  44     m = np.size(y)  45     h = sigmoid(np.dot(X, theta))  46     J = 1 / m * (-np.dot(y.T, np.log(h)) - np.dot((1 - y.T), np.log(1 - h)))  47     theta2 = theta[1:, 0]  48     Jadd = lamb / (2 * m) * np.sum(theta2 ** 2)  49     J = J + Jadd  50     return J.flatten()  51 
 52 #計算梯度
 53 def gradient(theta, X, y, lamb):  54     theta = np.array(theta).reshape((np.size(theta), 1))  55     m = np.size(y)  56     h = sigmoid(np.dot(X, theta))  57     grad = 1/m*np.dot(X.T, h - y)  58     theta[0,0] = 0  59     gradadd = lamb/m*theta  60     grad = grad + gradadd  61     return grad.flatten()  62 
 63 #θ計算
 64 def oneVsAll(X, y, num_labels, lamb):  65     m = np.size(X, 0)  66     n = np.size(X, 1)  67     all_theta = np.zeros((num_labels, n+1))  68     one = np.ones(m)  69     X = np.insert(X, 0, values=one, axis=1)  70     for c in range(0, num_labels):  71         initial_theta = np.zeros(n+1)  72         y_t = (y==c)  73         result = op.minimize(fun=lrCostFunction, x0=initial_theta, args=(X, y_t, lamb), method='TNC', jac=gradient)  74         all_theta[c, :] = result.x  75     return all_theta  76 
 77 #計算準確率
 78 def predictOneVsAll(all_theta, X):  79     m = np.size(X, 0)  80     num_labels = np.size(all_theta, 0)  81     p = np.zeros((m, 1))  #用來保存每行的最大值
 82     g = np.zeros((np.size(X, 0), num_labels))  #用來保存每次分類後的結果（一共分類了10次，每次保存到一列上）
 83     one = np.ones(m)  84     X = np.insert(X, 0, values=one, axis=1)  85     for c in range(0, num_labels):  86         theta = all_theta[c, :]  87         g[:, c] = sigmoid(np.dot(X, theta.T))  88     p = g.argmax(axis=1)  89     # print(p)
 90     return p.flatten()  91 
 92 #加載數據文件
 93 data = scio.loadmat('ex3data1.mat')  94 X = data['X']  95 y = data['y']  96 y = y%10  #由於數據集是考慮了matlab從1開始，把0的結果保存爲了10，這裏進行取餘，將10變回0
 97 m = np.size(X, 0)  98 rand_indices = np.random.randint(0,m,100)  99 sel = X[rand_indices, :] 100 displayData(sel) 101 
102 #計算θ
103 lamb = 0.1
104 num_labels = 10
105 all_theta = oneVsAll(X, y, num_labels, lamb) 106 # print(all_theta)
107 
108 #計算預測的準確性
109 pred = predictOneVsAll(all_theta, X) 110 # np.set_printoptions(threshold=np.inf)
111 #在計算這個上遇到了一個坑：
112 #pred輸出的是[[...]]的形式，須要flatten變成1維向量，y一樣用flatten變成1維向量
113 acc = np.mean(pred == y.flatten())*100
114 print('Training Set Accuracy:',acc,'%')

 

運行結果：

 

 

第2題

簡介：使用神經網絡實現數字識別（Θ已提供）

 1 import numpy as np  2 import scipy.io as scio  3 import matplotlib.pyplot as plt  4 import scipy.optimize as op  5 
 6 #顯示圖片數據
 7 def displayData(X):  8     m = np.size(X, 0)  #X的行數，即樣本數量
 9     n = np.size(X, 1)  #X的列數，即單個樣本大小
10     example_width = int(np.round(np.sqrt(n)))  #單張圖片寬度
11     example_height = int(np.floor(n / example_width))  #單張圖片高度
12     display_rows = int(np.floor(np.sqrt(m)))  #顯示圖中，一行多少張圖
13     display_cols = int(np.ceil(m / display_rows))  #顯示圖中，一列多少張圖片
14     pad = 1  #圖片間的間隔
15     display_array = - np.ones((pad + display_rows * (example_height + pad), 16                             pad + display_cols * (example_width + pad)))  #初始化圖片矩陣
17     curr_ex = 0  #當前的圖片計數
18     #將每張小圖插入圖片數組中
19     for j in range(0, display_rows): 20         for i in range(0, display_cols): 21             if curr_ex >= m: 22                 break
23             max_val = np.max(abs(X[curr_ex, :])) 24             jstart = pad + j * (example_height + pad) 25             istart = pad + i * (example_width + pad) 26             display_array[jstart: (jstart + example_height), istart: (istart + example_width)] = \ 27                 np.array(X[curr_ex, :]).reshape(example_height, example_width) / max_val 28             curr_ex = curr_ex + 1
29         if curr_ex >= m: 30             break
31     display_array = display_array.T 32     plt.imshow(display_array,cmap=plt.cm.gray) 33     plt.axis('off') 34  plt.show() 35 
36 #計算hθ(z)
37 def sigmoid(z): 38     g = 1.0 / (1.0 + np.exp(-z)) 39     return g 40 
41 #實現神經網絡
42 def predict(theta1, theta2, X): 43     m = np.size(X,0) 44     p = np.zeros((np.size(X, 0), 1)) 45     #第二層計算
46     one = np.ones(m) 47     X = np.insert(X, 0, values=one, axis=1) 48     a2 = sigmoid(np.dot(X, theta1.T)) 49     #第三層計算
50     one = np.ones(np.size(a2,0)) 51     a2 = np.insert(a2, 0, values=one, axis=1) 52     a3 = sigmoid(np.dot(a2, theta2.T)) 53     p = a3.argmax(axis=1) + 1  #y的值爲1-10，因此此處0-9要加1
54     return p.flatten() 55 
56 #讀取數據文件
57 data = scio.loadmat('ex3data1.mat') 58 X = data['X'] 59 y = data['y'] 60 m = np.size(X, 0) 61 rand_indices = np.random.randint(0,m,100) 62 sel = X[rand_indices, :] 63 # displayData(sel)
64 
65 theta = scio.loadmat('ex3weights.mat') 66 theta1 = theta['Theta1'] 67 theta2 = theta['Theta2'] 68 
69 #預測準確率
70 pred = predict(theta1, theta2, X) 71 acc = np.mean(pred == y.flatten())*100
72 print('Training Set Accuracy:',acc,'%') 73 
74 #識別單張圖片
75 for i in range(0, m): 76     it = np.random.randint(0, m, 1) 77     it = it[0] 78     displayData(X[it:it+1, :]) 79     pred = predict(theta1, theta2, X[it:it+1, :]) 80     print('Neural Network Prediction:', pred) 81     print('input q to exit:') 82     cin = input() 83     if cin == 'q': 84         break

神經網絡的矩陣表示分析：

運行結果：