MNIST手写数字识别数据集是NIST数据集的一个子集（介绍），常用于深度学习的入门样例。
该数据集包含60000张图片作为训练数据（为验证模型效果，一般从验证数据中划分出一部分作为验证数据，一般为5000），10000张图片作为测试数据。MNIST数据集中每张图片代表0-9中的一个数字，图片大小为28 × 28 ，且数字都位于图片中央。
（1） 加载数据
Tensorflow提供了一个类来处理MNIST数据，这个类会自动下载并转化MNIST数据的格式，将原始数据解析成可直接进行训练和测试的数据格式。代码如下：
mnist = input_data.read_data_sets("datasets/MNIST_data/", one_hot=True) print("Training data size: ", mnist.train.num_examples) #55000 print("Validating data size: ", mnist.validation.num_examples) #5000 print("Testing data size: ", mnist.test.num_examples) #10000
（2）设置参数
learning_rate = 0.0001 # 学习率 num_epochs = 1000 # 迭代次数 BATCH_SIZE = 100 #每轮迭代的训练数据个数
（3）前向传播
定义神经网络，输入层为784 ( 对 应 像 素 28 × 28 ) 784(对应像素28 )784(对应像素28×28)，隐藏层为500 ，输出层为10 （对应10 个类别）。代码如下：
(m,n_x) = mnist.train.images.shape #784 n_y = mnist.train.labels.shape[1] #10 n_1 = 500 X = tf.placeholder(tf.float32, shape=(None,n_x), name="X") #(55000,784) Y = tf.placeholder(tf.float32, shape=(None,n_y), name="Y") #(55000,10) W1 = tf.get_variable("w1",[n_x,n_1],initializer = tf.contrib.layers.xavier_initializer(seed = 1)) #(784,500) b1 = tf.get_variable("b1",[1,n_1], initializer = tf.zeros_initializer()) #(1,500) W2 = tf.get_variable("w2",[n_1,n_y],initializer = tf.contrib.layers.xavier_initializer(seed = 1)) #(500,10) b2 = tf.get_variable("b2",[1,n_y], initializer = tf.zeros_initializer()) #(1,10) Z1 = tf.nn.relu(tf.matmul(X,W1) + b1) #(55000,500) Z2 = tf.matmul(Z1,W2) + b2 #(55000,10)
（4）定义损失函数
使用交叉熵损失函数，代码如下：
cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits = Z2, labels = Y))
（5） 优化器
使用Adam优化器，代码如下
optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost)
（6）模型训练
with tf.Session() as sess: tf.initialize_all_variables().run() for i in range(num_epochs): x,y = mnist.train.next_batch(BATCH_SIZE) sess.run(optimizer,feed_dict={X:x,Y:y}) if i%500 == 0: cost_v = sess.run(cost,feed_dict={X:x,Y:y}) costs.append(cost_v) print(i,cost_v) # Calculate the correct accuracy correct_prediction = tf.equal(tf.argmax(Z2,1), tf.argmax(Y,1)) accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float")) print ("Train Accuracy:", accuracy.eval({X:mnist.train.images, Y: mnist.train.labels})) #Train Accuracy: 0.98807275 print ("Test Accuracy:", accuracy.eval({X: mnist.test.images, Y: mnist.test.labels})) #Test Accuracy: 0.9756
（7）模型评估
代码如下：
plt.plot(np.squeeze(costs)) plt.ylabel('cost') plt.xlabel('iterations (per tens)') plt.title("Learning rate =" + str(learning_rate)) plt.show()
生成图形如下：
可以看出损失值随迭代轮数增加而减小。
import numpy as np import matplotlib.pyplot as plt import tensorflow as tf from tensorflow.python.framework import ops from tensorflow.examples.tutorials.mnist import input_data mnist = input_data.read_data_sets("datasets/MNIST_data/", one_hot=True) learning_rate = 0.0001 num_epochs = 10000 BATCH_SIZE = 100 (m,n_x) = mnist.train.images.shape #784 n_y = mnist.train.labels.shape[1] #10 n_1 = 500 costs = [] tf.set_random_seed(1) # to keep consistent results ops.reset_default_graph() # to be able to rerun the model without overwriting tf variables X = tf.placeholder(tf.float32, shape=(None,n_x), name="X") #(55000,784) Y = tf.placeholder(tf.float32, shape=(None,n_y), name="Y") #(55000,10) W1 = tf.get_variable("w1",[n_x,n_1],initializer = tf.contrib.layers.xavier_initializer(seed = 1)) #(784,500) b1 = tf.get_variable("b1",[1,n_1], initializer = tf.zeros_initializer()) #(1,500) W2 = tf.get_variable("w2",[n_1,n_y],initializer = tf.contrib.layers.xavier_initializer(seed = 1)) #(500,10) b2 = tf.get_variable("b2",[1,n_y], initializer = tf.zeros_initializer()) #(1,10) Z1 = tf.nn.relu(tf.matmul(X,W1) + b1) #(55000,500) Z2 = tf.matmul(Z1,W2) + b2 #(55000,10) cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits = Z2, labels = Y)) optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost) with tf.Session() as sess: tf.initialize_all_variables().run() for i in range(num_epochs): x,y = mnist.train.next_batch(BATCH_SIZE) sess.run(optimizer,feed_dict={X:x,Y:y}) if i%500 == 0: cost_v = sess.run(cost,feed_dict={X:x,Y:y}) costs.append(cost_v) print(i,cost_v) # Calculate the correct accuracy correct_prediction = tf.equal(tf.argmax(Z2,1), tf.argmax(Y,1)) accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float")) print ("Train Accuracy:", accuracy.eval({X:mnist.train.images, Y: mnist.train.labels})) #Train Accuracy: 0.98807275 print ("Test Accuracy:", accuracy.eval({X: mnist.test.images, Y: mnist.test.labels})) #Test Accuracy: 0.9756 plt.plot(np.squeeze(costs)) plt.ylabel('cost') plt.xlabel('iterations (per tens)') plt.title("Learning rate =" + str(learning_rate)) plt.show()
