First, this is a traditional neural network:
If the input is a 1000 * 1000 pixel images, the input layer nodes v0 there will 1M; 1M with the intermediate hidden layer neurons v1, parameter between the two layers there will 1M * 1M = 10 ^ 12! too much weight, the amount of computation will be enormous, the greater the sample needed. As a result, a convolution neural network played.
Second, the hierarchical structure of the neural network convolution
Seen from the figure, the hierarchical structure of the convolutional neural network into a convolution layer (CONV), pooled layer (the POOL), the excitation layer (RELU), full connectivity layer (FC). And a data input layer.
Third, convolution
eg1:
5 5 * input image, the convolution is multiplied by two and then adding the corresponding elements of the matrix (inner product): 1 * 1 * 1 + 0 + 1 + 1 * 1 * 1 * 1 + 1 = 4, the derived feature value; according to step (Pictured 1) slides, the remaining value is calculated.
EG2:
Figure '3' represents the depth (depth): RGB three-channel image; 32 * 32 pixel image;
Neurons is small circles (filter), each neuron has its own weight matrix for convolution with the input data (multiplied values are added);
Weight matrix is considered as a window (receptive field), according to step (a stride of) slide, successively calculated;
eg3:
Input 7 * 7 * 3, (depth = 3, respectively corresponding to R, G, B); two neurons (W0, W1 of) also has three layers; W0 neuron corresponding to convoluted layer, and then calculating three adding up values + Bias b0, step 2 is moved (pad1: make a circle around 0), results of Output0; W1 calculated Output1 neurons; result two layers. The advantage is that the number of weight reduced.
eg4:
Neurons equivalent filter, only concerned with one of the characteristics of an image and extracting it out.
Fourth, the pooling layer (Pooling Layer)
The main object of the pooled layers of data compression is to reduce the over-fitting.
Reduction from the original 224 * 224 to 112 * 112.
max pooling selected maximum value. mean pooling screened average.
For details, see:
https://www.cnblogs.com/skyfsm/p/6790245.html
https://www.cnblogs.com/fydeblog/p/7450413.html
Fifth, the reference code
1 import tensorflow as tf
2 from tensorflow.examples.tutorials.mnist import input_data
3
4 mnist = input_data.read_data_sets('MNIST_data',one_hot=True)
5
6 #每个批次的大小
7 batch_size = 100
8 #计算一共有多少个批次
9 n_batch = mnist.train.num_examples // batch_size
10
11 #参数概要
12 def variable_summaries(var):
13 with tf.name_scope('summaries'):
14 mean = tf.reduce_mean(var)
15 tf.summary.scalar('mean', mean)#平均值
16 with tf.name_scope('stddev'):
17 stddev = tf.sqrt(tf.reduce_mean(tf.square(var - mean)))
18 tf.summary.scalar('stddev', stddev)#标准差
19 tf.summary.scalar('max', tf.reduce_max(var))#最大值
20 tf.summary.scalar('min', tf.reduce_min(var))#最小值
21 tf.summary.histogram('histogram', var)#直方图
22
23 #初始化权值
24 def weight_variable(shape,name):
25 initial = tf.truncated_normal(shape,stddev=0.1)#生成一个截断的正态分布
26 return tf.Variable(initial,name=name)
27
28 #初始化偏置
29 def bias_variable(shape,name):
30 initial = tf.constant(0.1,shape=shape)
31 return tf.Variable(initial,name=name)
32
33 #卷积层
34 def conv2d(x,W):
35 #x input tensor of shape `[batch, in_height, in_width, in_channels]`
36 #W filter / kernel tensor of shape [filter_height, filter_width, in_channels, out_channels]
37 #`strides[0] = strides[3] = 1`. strides[1]代表x方向的步长，strides[2]代表y方向的步长
38 #padding: A `string` from: `"SAME", "VALID"`
39 return tf.nn.conv2d(x,W,strides=[1,1,1,1],padding='SAME')
40
41 #池化层
42 def max_pool_2x2(x):
43 #ksize [1,x,y,1]
44 return tf.nn.max_pool(x,ksize=[1,2,2,1],strides=[1,2,2,1],padding='SAME')
45
46 #命名空间
47 with tf.name_scope('input'):
48 #定义两个placeholder
49 x = tf.placeholder(tf.float32,[None,784],name='x-input')
50 y = tf.placeholder(tf.float32,[None,10],name='y-input')
51 with tf.name_scope('x_image'):
52 #改变x的格式转为4D的向量[batch, in_height, in_width, in_channels]`
53 x_image = tf.reshape(x,[-1,28,28,1],name='x_image')
54
55
56 with tf.name_scope('Conv1'):
57 #初始化第一个卷积层的权值和偏置
58 with tf.name_scope('W_conv1'):
59 W_conv1 = weight_variable([5,5,1,32],name='W_conv1')#5*5的采样窗口，32个卷积核从1个平面抽取特征
60 with tf.name_scope('b_conv1'):
61 b_conv1 = bias_variable([32],name='b_conv1')#每一个卷积核一个偏置值
62
63 #把x_image和权值向量进行卷积，再加上偏置值，然后应用于relu激活函数
64 with tf.name_scope('conv2d_1'):
65 conv2d_1 = conv2d(x_image,W_conv1) + b_conv1
66 with tf.name_scope('relu'):
67 h_conv1 = tf.nn.relu(conv2d_1)
68 with tf.name_scope('h_pool1'):
69 h_pool1 = max_pool_2x2(h_conv1)#进行max-pooling
70
71 with tf.name_scope('Conv2'):
72 #初始化第二个卷积层的权值和偏置
73 with tf.name_scope('W_conv2'):
74 W_conv2 = weight_variable([5,5,32,64],name='W_conv2')#5*5的采样窗口，64个卷积核从32个平面抽取特征
75 with tf.name_scope('b_conv2'):
76 b_conv2 = bias_variable([64],name='b_conv2')#每一个卷积核一个偏置值
77
78 #把h_pool1和权值向量进行卷积，再加上偏置值，然后应用于relu激活函数
79 with tf.name_scope('conv2d_2'):
80 conv2d_2 = conv2d(h_pool1,W_conv2) + b_conv2
81 with tf.name_scope('relu'):
82 h_conv2 = tf.nn.relu(conv2d_2)
83 with tf.name_scope('h_pool2'):
84 h_pool2 = max_pool_2x2(h_conv2)#进行max-pooling
85
86 #28*28的图片第一次卷积后还是28*28，第一次池化后变为14*14
87 #第二次卷积后为14*14，第二次池化后变为了7*7
88 #进过上面操作后得到64张7*7的平面
89
90 with tf.name_scope('fc1'):
91 #初始化第一个全连接层的权值
92 with tf.name_scope('W_fc1'):
93 W_fc1 = weight_variable([7*7*64,1024],name='W_fc1')#上一场有7*7*64个神经元，全连接层有1024个神经元
94 with tf.name_scope('b_fc1'):
95 b_fc1 = bias_variable([1024],name='b_fc1')#1024个节点
96
97 #把池化层2的输出扁平化为1维
98 with tf.name_scope('h_pool2_flat'):
99 h_pool2_flat = tf.reshape(h_pool2,[-1,7*7*64],name='h_pool2_flat')
100 #求第一个全连接层的输出
101 with tf.name_scope('wx_plus_b1'):
102 wx_plus_b1 = tf.matmul(h_pool2_flat,W_fc1) + b_fc1
103 with tf.name_scope('relu'):
104 h_fc1 = tf.nn.relu(wx_plus_b1)
105
106 #keep_prob用来表示神经元的输出概率
107 with tf.name_scope('keep_prob'):
108 keep_prob = tf.placeholder(tf.float32,name='keep_prob')
109 with tf.name_scope('h_fc1_drop'):
110 h_fc1_drop = tf.nn.dropout(h_fc1,keep_prob,name='h_fc1_drop')
111
112 with tf.name_scope('fc2'):
113 #初始化第二个全连接层
114 with tf.name_scope('W_fc2'):
115 W_fc2 = weight_variable([1024,10],name='W_fc2')
116 with tf.name_scope('b_fc2'):
117 b_fc2 = bias_variable([10],name='b_fc2')
118 with tf.name_scope('wx_plus_b2'):
119 wx_plus_b2 = tf.matmul(h_fc1_drop,W_fc2) + b_fc2
120 with tf.name_scope('softmax'):
121 #计算输出
122 prediction = tf.nn.softmax(wx_plus_b2)
123
124 #交叉熵代价函数
125 with tf.name_scope('cross_entropy'):
126 cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y,logits=prediction),name='cross_entropy')
127 tf.summary.scalar('cross_entropy',cross_entropy)
128
129 #使用AdamOptimizer进行优化
130 with tf.name_scope('train'):
131 train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)
132
133 #求准确率
134 with tf.name_scope('accuracy'):
135 with tf.name_scope('correct_prediction'):
136 #结果存放在一个布尔列表中
137 correct_prediction = tf.equal(tf.argmax(prediction,1),tf.argmax(y,1))#argmax返回一维张量中最大的值所在的位置
138 with tf.name_scope('accuracy'):
139 #求准确率
140 accuracy = tf.reduce_mean(tf.cast(correct_prediction,tf.float32))
141 tf.summary.scalar('accuracy',accuracy)
142
143 #合并所有的summary
144 merged = tf.summary.merge_all()
145
146 with tf.Session() as sess:
147 sess.run(tf.global_variables_initializer())
148 train_writer = tf.summary.FileWriter('logs/train',sess.graph)
149 test_writer = tf.summary.FileWriter('logs/test',sess.graph)
150 for i in range(1001):
151 #训练模型
152 batch_xs,batch_ys = mnist.train.next_batch(batch_size)
153 sess.run(train_step,feed_dict={x:batch_xs,y:batch_ys,keep_prob:0.5})
154 #记录训练集计算的参数
155 summary = sess.run(merged,feed_dict={x:batch_xs,y:batch_ys,keep_prob:1.0})
156 train_writer.add_summary(summary,i)
157 #记录测试集计算的参数
158 batch_xs,batch_ys = mnist.test.next_batch(batch_size)
159 summary = sess.run(merged,feed_dict={x:batch_xs,y:batch_ys,keep_prob:1.0})
160 test_writer.add_summary(summary,i)
161
162 if i%100==0:
163 test_acc = sess.run(accuracy,feed_dict={x:mnist.test.images,y:mnist.test.labels,keep_prob:1.0})
164 train_acc = sess.run(accuracy,feed_dict={x:mnist.train.images[:10000],y:mnist.train.labels[:10000],keep_prob:1.0})
165 print ("Iter " + str(i) + ", Testing Accuracy= " + str(test_acc) + ", Training Accuracy= " + str(train_acc))
2019-06-11 18:59:16