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()
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