卷積神經網絡入門：LeNet5（手寫體數字識別）詳解

第一張圖包括8層LeNet5卷積神經網絡的結構圖，以及其中最復雜的一層S2到C3的結構處理示意圖。

第二張圖及第三張圖是用tensorflow重寫LeNet5網絡及其注釋。

這是原始的LeNet5網絡：

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
import time

# 聲明輸入圖片數據，類別
x = tf.placeholder('float', [None, 784])
y_ = tf.placeholder('float', [None, 10])
# 輸入圖片數據轉化
x_image = tf.reshape(x, [-1, 28, 28, 1])

#第一層卷積層，初始化卷積核參數、偏置值，該卷積層5*5大小，一個通道，共有6個不同卷積核
filter1 = tf.Variable(tf.truncated_normal([5, 5, 1, 6]))
bias1 = tf.Variable(tf.truncated_normal([6]))
conv1 = tf.nn.conv2d(x_image, filter1, strides=[1, 1, 1, 1], padding='SAME')
h_conv1 = tf.nn.sigmoid(conv1 + bias1)

maxPool2 = tf.nn.max_pool(h_conv1, ksize=[1, 2, 2, 1],strides=[1, 2, 2, 1], padding='SAME')

filter2 = tf.Variable(tf.truncated_normal([5, 5, 6, 16]))
bias2 = tf.Variable(tf.truncated_normal([16]))
conv2 = tf.nn.conv2d(maxPool2, filter2, strides=[1, 1, 1, 1], padding='SAME')
h_conv2 = tf.nn.sigmoid(conv2 + bias2)

maxPool3 = tf.nn.max_pool(h_conv2, ksize=[1, 2, 2, 1],strides=[1, 2, 2, 1], padding='SAME')

filter3 = tf.Variable(tf.truncated_normal([5, 5, 16, 120]))
bias3 = tf.Variable(tf.truncated_normal([120]))
conv3 = tf.nn.conv2d(maxPool3, filter3, strides=[1, 1, 1, 1], padding='SAME')
h_conv3 = tf.nn.sigmoid(conv3 + bias3)



# 全連接層
# 權值參數
W_fc1 = tf.Variable(tf.truncated_normal([7 * 7 * 120, 80]))
# 偏置值
b_fc1 = tf.Variable(tf.truncated_normal([80]))
# 將卷積的產出展開
h_pool2_flat = tf.reshape(h_conv3, [-1, 7 * 7 * 120])
# 神經網絡計算，並添加sigmoid激活函數
h_fc1 = tf.nn.sigmoid(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)


# 輸出層，使用softmax進行多分類
W_fc2 = tf.Variable(tf.truncated_normal([80, 10]))
b_fc2 = tf.Variable(tf.truncated_normal([10]))
y_conv = tf.nn.softmax(tf.matmul(h_fc1, W_fc2) + b_fc2)
# 損失函數
cross_entropy = -tf.reduce_sum(y_ * tf.log(y_conv))
# 使用GDO優化算法來調整參數
train_step = tf.train.GradientDescentOptimizer(0.001).minimize(cross_entropy)

sess = tf.InteractiveSession()
# 測試正確率
correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))

# 所有變量進行初始化
sess.run(tf.initialize_all_variables())

# 獲取mnist數據
mnist_data_set = input_data.read_data_sets('MNIST_data', one_hot=True)

# 進行訓練
start_time = time.time()
for i in range(20000):
    # 獲取訓練數據
    batch_xs, batch_ys = mnist_data_set.train.next_batch(200)

    # 每迭代100個 batch，對當前訓練數據進行測試，輸出當前預測准確率
    if i % 2 == 0:
        train_accuracy = accuracy.eval(feed_dict={x: batch_xs, y_: batch_ys})
        print("step %d, training accuracy %g" % (i, train_accuracy))
        # 計算間隔時間
        end_time = time.time()
        print('time: ', (end_time - start_time))
        start_time = end_time
    # 訓練數據
    train_step.run(feed_dict={x: batch_xs, y_: batch_ys})

# 關閉會話
sess.close()

下面是改進后的LeNet5網絡：

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
import time
import matplotlib.pyplot as plt


# 初始化單個卷積核上的權重
def weight_variable(shape):
    initial = tf.truncated_normal(shape, stddev=0.1)
    return tf.Variable(initial)


# 初始化單個卷積核上的偏置值
def bias_variable(shape):
    initial = tf.constant(0.1, shape=shape)
    return tf.Variable(initial)


# 輸入特征x，用卷積核W進行卷積運算，strides為卷積核移動步長，
# padding表示是否需要補齊邊緣像素使輸出圖像大小不變
def conv2d(x, W):
    return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')


# 對x進行最大池化操作，ksize進行池化的范圍，
def max_pool_2x2(x):
    return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')


sess = tf.InteractiveSession()
# 聲明輸入圖片數據，類別
x = tf.placeholder('float32', [None, 784])
y_ = tf.placeholder('float32', [None, 10])
# 輸入圖片數據轉化
x_image = tf.reshape(x, [-1, 28, 28, 1])

W_conv1 = weight_variable([5, 5, 1, 32])
b_conv1 = bias_variable([32])
h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)
h_pool1 = max_pool_2x2(h_conv1)

W_conv2 = weight_variable([5, 5, 32, 64])
b_conv2 = bias_variable([64])
h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)
h_pool2 = max_pool_2x2(h_conv2)

W_fc1 = weight_variable([7 * 7 * 64, 1024])
# 偏置值
b_fc1 = bias_variable([1024])
# 將卷積的產出展開
h_pool2_flat = tf.reshape(h_pool2, [-1, 7 * 7 * 64])
# 神經網絡計算，並添加relu激活函數
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)

W_fc2 = weight_variable([1024, 128])
b_fc2 = bias_variable([128])
h_fc2 = tf.nn.relu(tf.matmul(h_fc1, W_fc2) + b_fc2)

W_fc3 = weight_variable([128, 10])
b_fc3 = bias_variable([10])
y_conv = tf.nn.softmax(tf.matmul(h_fc2, W_fc3) + b_fc3)
# 代價函數
cross_entropy = -tf.reduce_sum(y_ * tf.log(y_conv))
# 使用Adam優化算法來調整參數
train_step = tf.train.GradientDescentOptimizer(1e-5).minimize(cross_entropy)

# 測試正確率
correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float32"))

# 所有變量進行初始化
sess.run(tf.initialize_all_variables())

# 獲取mnist數據
mnist_data_set = input_data.read_data_sets('MNIST_data', one_hot=True)
c = []

# 進行訓練
start_time = time.time()
for i in range(1000):
    # 獲取訓練數據
    batch_xs, batch_ys = mnist_data_set.train.next_batch(200)

    # 每迭代10個 batch，對當前訓練數據進行測試，輸出當前預測准確率
    if i % 2 == 0:
        train_accuracy = accuracy.eval(feed_dict={x: batch_xs, y_: batch_ys})
        c.append(train_accuracy)
        print("step %d, training accuracy %g" % (i, train_accuracy))
        # 計算間隔時間
        end_time = time.time()
        print('time: ', (end_time - start_time))
        start_time = end_time
    # 訓練數據
    train_step.run(feed_dict={x: batch_xs, y_: batch_ys})

sess.close()
plt.plot(c)
plt.tight_layout()