转载自：https://blog.csdn.net/qq1483661204/article/details/79039702

 

Learning a Similarity Metric Discriminatively, with Application to Face
Verification 这个siamese文章链接。
本文主要讲解siamese网络，并用tensorflwo实现，在mnist数据集中，siamese网络和其他网络的不同之处在于，首先他是两个输入，它输入的不是标签，而是是否是同一类别，如果是同一类别就是0，否则就是1，文章中是用这个网络来做人脸识别，网络结构图如下：

从图中可以看到，他又两个输入，分别是下x1和x2，左右两个的网咯结构是一样的，并且他们共享权重，最后得到两个输出，分别是Gw(x1)和Gw(x2),这个网络的很好理解，当输入是同一张图片的时候，我们希望他们呢之间的欧式距离很小，当不是一张图片时，我们的欧式距离很大。有了网路结构，接下来就是定义损失函数，这个很重要，而经过我们的分析，我们可以知道，损失函数的特点应该是这样的，
(1) 当我们输入同一张图片时，他们之间的欧式距离越小，损失是越小的，距离越大，损失越大
(2) 当我们的输入是不同的图片的时候，他们之间的距离越大，损失越大
怎么理解呢，很简单，我们就是最小化把相同类的数据之间距离，最大化不同类之间的距离。
然后文章中定义的损失函数如下：
首先是定义距离，使用l2范数，公式如下：

距离其实就是欧式距离，有了距离，我们的损失函数和距离的关系我上面说了，如何包证满足上面的要求呢，文章提出这样的损失函数：

其中我们的Ew就是距离，Lg和L1相当于是一个系数，这个损失函数和交叉熵其实挺像，为了让损失函数满足上面的关系，让Lg满足单调递减，LI满足单调递增就可以。另外一个条件是：同类图片之间的距离必须比不同类之间的距离小，
其他条件如下：

然后作者也给出了证明，最终损失函数为：

Q是一个常数，这个损失函数就满足上面的关系，然后我用tensoflow写了一个损失函数如下：

需要强调的是，这个地方同一类图片是0，不同类图片是1，然后我自己用tensorflow实现的这个损失函数如下：

def siamese_loss(out1,out2,y,Q=5):

    Q = tf.constant(Q, name="Q",dtype=tf.float32)
    E_w = tf.sqrt(tf.reduce_sum(tf.square(out1-out2),1))   
    pos = tf.multiply(tf.multiply(y,2/Q),tf.square(E_w))
    neg = tf.multiply(tf.multiply(1-y,2*Q),tf.exp(-2.77/Q*E_w))                
    loss = pos + neg                 
    loss = tf.reduce_mean(loss)              
    return loss

 

这就是损失函数，其他的代码如下：

  1 import tensorflow as tf
  2 from tensorflow.examples.tutorials.mnist import input_data
  3 import numpy as np
  4 tf.reset_default_graph()
  5 mnist = input_data.read_data_sets('./data/mnist',one_hot=True)
  6 print(mnist.validation.num_examples)
  7 print(mnist.train.num_examples)
  8 print(mnist.test.num_examples)
  9 def siamese_loss(out1,out2,y,Q=5):
 10 
 11     Q = tf.constant(Q, name="Q",dtype=tf.float32)
 12     E_w = tf.sqrt(tf.reduce_sum(tf.square(out1-out2),1))   
 13     pos = tf.multiply(tf.multiply(y,2/Q),tf.square(E_w))
 14     neg = tf.multiply(tf.multiply(1-y,2*Q),tf.exp(-2.77/Q*E_w))                
 15     loss = pos + neg                 
 16     loss = tf.reduce_mean(loss)              
 17     return loss
 18 
 19 def siamese(inputs,keep_prob):
 20         with tf.name_scope('conv1') as scope:
 21             w1 = tf.Variable(tf.truncated_normal(shape=[3,3,1,32],stddev=0.05),name='w1')
 22             b1 = tf.Variable(tf.zeros(32),name='b1')
 23             conv1 = tf.nn.conv2d(inputs,w1,strides=[1,1,1,1],padding='SAME',name='conv1')
 24         with tf.name_scope('relu1') as scope:
 25             relu1 = tf.nn.relu(tf.add(conv1,b1),name='relu1')
 26         with tf.name_scope('conv2') as scope:
 27             w2 = tf.Variable(tf.truncated_normal(shape=[3,3,32,64],stddev=0.05),name='w2')
 28             b2 = tf.Variable(tf.zeros(64),name='b2')
 29             conv2 = tf.nn.conv2d(relu1,w2,strides=[1,2,2,1],padding='SAME',name='conv2')
 30         with tf.name_scope('relu2') as scope:
 31             relu2 = tf.nn.relu(conv2+b2,name='relu2')
 32 
 33         with tf.name_scope('conv3') as scope:
 34 
 35             w3 = tf.Variable(tf.truncated_normal(shape=[3,3,64,128],mean=0,stddev=0.05),name='w3')
 36             b3 = tf.Variable(tf.zeros(128),name='b3')
 37             conv3 = tf.nn.conv2d(relu2,w3,strides=[1,2,2,1],padding='SAME')
 38         with tf.name_scope('relu3') as scope:
 39             relu3 = tf.nn.relu(conv3+b3,name='relu3')
 40 
 41         with tf.name_scope('fc1') as scope:
 42             x_flat = tf.reshape(relu3,shape=[-1,7*7*128])
 43             w_fc1=tf.Variable(tf.truncated_normal(shape=[7*7*128,1024],stddev=0.05,mean=0),name='w_fc1')
 44             b_fc1 = tf.Variable(tf.zeros(1024),name='b_fc1')
 45             fc1 = tf.add(tf.matmul(x_flat,w_fc1),b_fc1)
 46         with tf.name_scope('relu_fc1') as scope:
 47             relu_fc1 = tf.nn.relu(fc1,name='relu_fc1')
 48 
 49 
 50 
 51         with tf.name_scope('drop_1') as scope:
 52 
 53             drop_1 = tf.nn.dropout(relu_fc1,keep_prob=keep_prob,name='drop_1')
 54         with tf.name_scope('bn_fc1') as scope:
 55             bn_fc1 = tf.layers.batch_normalization(drop_1,name='bn_fc1')
 56         with tf.name_scope('fc2') as scope:
 57             w_fc2 = tf.Variable(tf.truncated_normal(shape=[1024,512],stddev=0.05,mean=0),name='w_fc2')
 58             b_fc2 = tf.Variable(tf.zeros(512),name='b_fc2')
 59             fc2 = tf.add(tf.matmul(bn_fc1,w_fc2),b_fc2)
 60         with tf.name_scope('relu_fc2') as scope:
 61             relu_fc2 = tf.nn.relu(fc2,name='relu_fc2')
 62         with tf.name_scope('drop_2') as scope:
 63             drop_2 = tf.nn.dropout(relu_fc2,keep_prob=keep_prob,name='drop_2')
 64         with tf.name_scope('bn_fc2') as scope:
 65             bn_fc2 = tf.layers.batch_normalization(drop_2,name='bn_fc2')
 66         with tf.name_scope('fc3') as scope:
 67             w_fc3 = tf.Variable(tf.truncated_normal(shape=[512,2],stddev=0.05,mean=0),name='w_fc3')
 68             b_fc3 = tf.Variable(tf.zeros(2),name='b_fc3')
 69             fc3 = tf.add(tf.matmul(bn_fc2,w_fc3),b_fc3)
 70         return fc3
 71 
 72 lr = 0.01
 73 iterations = 20000
 74 batch_size = 64
 75 
 76 with tf.variable_scope('input_x1') as scope:
 77     x1 = tf.placeholder(tf.float32, shape=[None, 784])
 78     x_input_1 = tf.reshape(x1, [-1, 28, 28, 1])
 79 with tf.variable_scope('input_x2') as scope:
 80     x2 = tf.placeholder(tf.float32, shape=[None, 784])
 81     x_input_2 = tf.reshape(x2, [-1, 28, 28, 1])
 82 with tf.variable_scope('y') as scope:
 83     y = tf.placeholder(tf.float32, shape=[batch_size])
 84 
 85 with tf.name_scope('keep_prob') as scope:
 86     keep_prob = tf.placeholder(tf.float32)
 87 
 88 with tf.variable_scope('siamese') as scope:
 89     out1 = siamese(x_input_1,keep_prob)
 90     scope.reuse_variables()
 91     out2 = siamese(x_input_2,keep_prob)
 92 with tf.variable_scope('metrics') as scope:
 93     loss = siamese_loss(out1, out2, y)
 94     optimizer = tf.train.AdamOptimizer(lr).minimize(loss)
 95 
 96 loss_summary = tf.summary.scalar('loss',loss)
 97 merged_summary = tf.summary.merge_all()
 98 
 99 with tf.Session() as sess:
100 
101     writer = tf.summary.FileWriter('./graph/siamese',sess.graph)
102     sess.run(tf.global_variables_initializer())
103 
104     for itera in range(iterations):
105         xs_1, ys_1 = mnist.train.next_batch(batch_size)
106         ys_1 = np.argmax(ys_1,axis=1)
107         xs_2, ys_2 = mnist.train.next_batch(batch_size)
108         ys_2 = np.argmax(ys_2,axis=1)
109         y_s = np.array(ys_1==ys_2,dtype=np.float32)
110         _,train_loss,summ = sess.run([optimizer,loss,merged_summary],feed_dict={x1:xs_1,x2:xs_2,y:y_s,keep_prob:0.6})
111 
112         writer.add_summary(summ,itera)
113         if itera % 1000 == 1 :
114             print('iter {},train loss {}'.format(itera,train_loss))
115     embed = sess.run(out1,feed_dict={x1:mnist.test.images,keep_prob:0.6})
116     test_img = mnist.test.images.reshape([-1,28,28,1])
117     writer.close()