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纯numpy数值微分法实现手写数字识别
来源:jb51  时间:2022/8/3 12:49:41  对本文有异议

手写数字识别作为深度学习入门经典的识别案例,各种深度学习框架都有这个例子的实现方法。我这里将不用任何深度学习现有框架,例如TensorFlow、Keras、pytorch,直接使用Python语言的numpy实现各种激活函数、损失函数、梯度下降的方法。

程序分为两部分,首先是手写数字数据的准备,直接使用如下mnist.py文件中的方法load_minist即可。文件代码如下:

  1. # coding: utf-8
  2. try:
  3. import urllib.request
  4. except ImportError:
  5. raise ImportError('You should use Python 3.x')
  6. import os.path
  7. import gzip
  8. import pickle
  9. import os
  10. import numpy as np
  11.  
  12.  
  13. url_base = 'http://yann.lecun.com/exdb/mnist/'
  14. key_file = {
  15. 'train_img':'train-images-idx3-ubyte.gz',
  16. 'train_label':'train-labels-idx1-ubyte.gz',
  17. 'test_img':'t10k-images-idx3-ubyte.gz',
  18. 'test_label':'t10k-labels-idx1-ubyte.gz'
  19. }
  20.  
  21. dataset_dir = os.path.dirname(os.path.abspath(__file__))
  22. save_file = dataset_dir + "/mnist.pkl"
  23.  
  24. train_num = 60000
  25. test_num = 10000
  26. img_dim = (1, 28, 28)
  27. img_size = 784
  28.  
  29.  
  30. def _download(file_name):
  31. file_path = dataset_dir + "/" + file_name
  32. if os.path.exists(file_path):
  33. return
  34.  
  35. print("Downloading " + file_name + " ... ")
  36. urllib.request.urlretrieve(url_base + file_name, file_path)
  37. print("Done")
  38. def download_mnist():
  39. for v in key_file.values():
  40. _download(v)
  41. def _load_label(file_name):
  42. file_path = dataset_dir + "/" + file_name
  43. print("Converting " + file_name + " to NumPy Array ...")
  44. with gzip.open(file_path, 'rb') as f:
  45. labels = np.frombuffer(f.read(), np.uint8, offset=8)
  46. print("Done")
  47. return labels
  48.  
  49. def _load_img(file_name):
  50. file_path = dataset_dir + "/" + file_name
  51. print("Converting " + file_name + " to NumPy Array ...")
  52. with gzip.open(file_path, 'rb') as f:
  53. data = np.frombuffer(f.read(), np.uint8, offset=16)
  54. data = data.reshape(-1, img_size)
  55. print("Done")
  56. return data
  57. def _convert_numpy():
  58. dataset = {}
  59. dataset['train_img'] = _load_img(key_file['train_img'])
  60. dataset['train_label'] = _load_label(key_file['train_label'])
  61. dataset['test_img'] = _load_img(key_file['test_img'])
  62. dataset['test_label'] = _load_label(key_file['test_label'])
  63. return dataset
  64.  
  65. def init_mnist():
  66. download_mnist()
  67. dataset = _convert_numpy()
  68. print("Creating pickle file ...")
  69. with open(save_file, 'wb') as f:
  70. pickle.dump(dataset, f, -1)
  71. print("Done!")
  72.  
  73. def _change_one_hot_label(X):
  74. T = np.zeros((X.size, 10))
  75. for idx, row in enumerate(T):
  76. row[X[idx]] = 1
  77. return T
  78.  
  79. def load_mnist(normalize=True, flatten=True, one_hot_label=False):
  80. """读入MNIST数据集
  81. Parameters
  82. ----------
  83. normalize : 将图像的像素值正规化为0.0~1.0
  84. one_hot_label :
  85. one_hot_label为True的情况下,标签作为one-hot数组返回
  86. one-hot数组是指[0,0,1,0,0,0,0,0,0,0]这样的数组
  87. flatten : 是否将图像展开为一维数组
  88. Returns
  89. -------
  90. (训练图像, 训练标签), (测试图像, 测试标签)
  91. """
  92. if not os.path.exists(save_file):
  93. init_mnist()
  94. with open(save_file, 'rb') as f:
  95. dataset = pickle.load(f)
  96. if normalize:
  97. for key in ('train_img', 'test_img'):
  98. dataset[key] = dataset[key].astype(np.float32)
  99. dataset[key] /= 255.0
  100. if one_hot_label:
  101. dataset['train_label'] = _change_one_hot_label(dataset['train_label'])
  102. dataset['test_label'] = _change_one_hot_label(dataset['test_label'])
  103. if not flatten:
  104. for key in ('train_img', 'test_img'):
  105. dataset[key] = dataset[key].reshape(-1, 1, 28, 28)
  106.  
  107. return (dataset['train_img'], dataset['train_label']), (dataset['test_img'], dataset['test_label'])
  108.  
  109.  
  110. if __name__ == '__main__':
  111. init_mnist()
  112.  

使用上述文件中的函数就可以直接得到手写数字的训练数据、训练标签,测试样本以及测试标签。
接下里使用如下代码就可以进行手写数字的训练,代码如下:

  1. import numpy as np
  2. from numpy.lib.function_base import select
  3. from dataset.mnist import load_mnist
  4. import matplotlib.pylab as plt
  5.  
  6.  
  7. def sigmoid(x):
  8. return 1 / (1 + np.exp(-x))
  9.  
  10. def sigmoid_grad(x):
  11. return (1.0 - sigmoid(x)) * sigmoid(x)
  12.  
  13. def softmax(x):
  14. if x.ndim == 2:
  15. x = x.T
  16. x = x - np.max(x, axis=0)
  17. y = np.exp(x) / np.sum(np.exp(x), axis=0)
  18. return y.T
  19.  
  20. x = x - np.max(x) # 溢出对策
  21. return np.exp(x) / np.sum(np.exp(x))
  22.  
  23. def cross_entropy_error(y, t):
  24. if y.ndim == 1:
  25. t = t.reshape(1, t.size)
  26. y = y.reshape(1, y.size)
  27. # 监督数据是one-hot-vector的情况下,转换为正确解标签的索引
  28. if t.size == y.size:
  29. t = t.argmax(axis=1)
  30. batch_size = y.shape[0]
  31. return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size
  32.  
  33. def numerical_gradient(f, x):
  34. h = 1e-4 # 0.0001
  35. grad = np.zeros_like(x)
  36. it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
  37. while not it.finished:
  38. idx = it.multi_index
  39. tmp_val = x[idx]
  40. x[idx] = float(tmp_val) + h
  41. fxh1 = f(x) # f(x+h)
  42. x[idx] = tmp_val - h
  43. fxh2 = f(x) # f(x-h)
  44. grad[idx] = (fxh1 - fxh2) / (2*h)
  45. x[idx] = tmp_val # 还原值
  46. it.iternext()
  47. return grad
  48.  
  49. #(x_train,t_train),(x_test,t_test)=load_mnist(normalize=True,one_hot_label=True)
  50. #两层神经网络的类
  51. class TwoLayerNet:
  52. def __init__(self,input_size,hidden_size,output_size,weight_init_std=0.01):
  53. #初始化权重
  54. self.params={}
  55. self.params['W1']=weight_init_std*np.random.randn(input_size,hidden_size)
  56. self.params['b1']=np.zeros(hidden_size)
  57. self.params['W2']=weight_init_std*np.random.randn(hidden_size,output_size)
  58. self.params['b2']=np.zeros(output_size)
  59. def predict(self,x):
  60. W1,W2=self.params['W1'],self.params['W2']
  61. b1,b2=self.params['b1'],self.params['b2']
  62.  
  63. a1=np.dot(x,W1)+b1
  64. z1=sigmoid(a1)
  65. a2=np.dot(z1,W2)+b2
  66. y=softmax(a2)
  67.  
  68. return y
  69. #损失函数
  70. def loss(self,x,t):
  71. y=self.predict(x)
  72. return cross_entropy_error(y,t)
  73. #数值微分法
  74. def numerical_gradient(self,x,t):
  75. loss_W=lambda W:self.loss(x,t)
  76. grads={}
  77. grads['W1']=numerical_gradient(loss_W,self.params['W1'])
  78. grads['b1']=numerical_gradient(loss_W,self.params['b1'])
  79. grads['W2']=numerical_gradient(loss_W,self.params['W2'])
  80. grads['b2']=numerical_gradient(loss_W,self.params['b2'])
  81. return grads
  82.  
  83. #误差反向传播法
  84. def gradient(self, x, t):
  85. W1, W2 = self.params['W1'], self.params['W2']
  86. b1, b2 = self.params['b1'], self.params['b2']
  87. grads = {}
  88. batch_num = x.shape[0]
  89. # forward
  90. a1 = np.dot(x, W1) + b1
  91. z1 = sigmoid(a1)
  92. a2 = np.dot(z1, W2) + b2
  93. y = softmax(a2)
  94. # backward
  95. dy = (y - t) / batch_num
  96. grads['W2'] = np.dot(z1.T, dy)
  97. grads['b2'] = np.sum(dy, axis=0)
  98. da1 = np.dot(dy, W2.T)
  99. dz1 = sigmoid_grad(a1) * da1
  100. grads['W1'] = np.dot(x.T, dz1)
  101. grads['b1'] = np.sum(dz1, axis=0)
  102.  
  103. return grads
  104. #准确率
  105. def accuracy(self,x,t):
  106. y=self.predict(x)
  107. y=np.argmax(y,axis=1)
  108. t=np.argmax(t,axis=1)
  109.  
  110. accuracy=np.sum(y==t)/float(x.shape[0])
  111. return accuracy
  112.  
  113. if __name__=='__main__':
  114. (x_train,t_train),(x_test,t_test)=load_mnist(normalize=True,one_hot_label=True)
  115. net=TwoLayerNet(input_size=784,hidden_size=50,output_size=10)
  116.  
  117. train_loss_list=[]
  118.  
  119. #超参数
  120. iter_nums=10000
  121. train_size=x_train.shape[0]
  122. batch_size=100
  123. learning_rate=0.1
  124.  
  125. #记录准确率
  126. train_acc_list=[]
  127. test_acc_list=[]
  128. #平均每个epoch的重复次数
  129. iter_per_epoch=max(train_size/batch_size,1)
  130.  
  131. for i in range(iter_nums):
  132. #小批量数据
  133. batch_mask=np.random.choice(train_size,batch_size)
  134. x_batch=x_train[batch_mask]
  135. t_batch=t_train[batch_mask]
  136.  
  137. #计算梯度
  138. #数值微分 计算很慢
  139. #grad=net.numerical_gradient(x_batch,t_batch)
  140. #误差反向传播法 计算很快
  141. grad=net.gradient(x_batch,t_batch)
  142.  
  143. #更新参数 权重W和偏重b
  144. for key in ['W1','b1','W2','b2']:
  145. net.params[key]-=learning_rate*grad[key]
  146. #记录学习过程
  147. loss=net.loss(x_batch,t_batch)
  148. print('训练次数:'+str(i)+' loss:'+str(loss))
  149. train_loss_list.append(loss)
  150.  
  151. #计算每个epoch的识别精度
  152. if i%iter_per_epoch==0:
  153. #测试在所有训练数据和测试数据上的准确率
  154. train_acc=net.accuracy(x_train,t_train)
  155. test_acc=net.accuracy(x_test,t_test)
  156. train_acc_list.append(train_acc)
  157. test_acc_list.append(test_acc)
  158. print('train acc:'+str(train_acc)+' test acc:'+str(test_acc))
  159. print(train_acc_list)
  160. print(test_acc_list)
  161.  
  162. # 绘制图形
  163. markers = {'train': 'o', 'test': 's'}
  164. x = np.arange(len(train_acc_list))
  165. plt.plot(x, train_acc_list, label='train acc')
  166. plt.plot(x, test_acc_list, label='test acc', linestyle='--')
  167. plt.xlabel("epochs")
  168. plt.ylabel("accuracy")
  169. plt.ylim(0, 1.0)
  170. plt.legend(loc='lower right')
  171. plt.show()

训练完成后,查看绘制准确率的图片,可以获取到成功实现了手写数字识别。

在这里插入图片描述

随着训练批次的增加,准确率逐渐增大接近于1,说明训练过程按着正确拟合的方向前进。

到此这篇关于纯numpy实现数值微分法实现手写数字识别的文章就介绍到这了,更多相关numpy 手写数字识别内容请搜索w3xue以前的文章或继续浏览下面的相关文章希望大家以后多多支持w3xue!

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