转载自：https://blog.****.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：
import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
import numpy as np
tf.reset_default_graph()
mnist = input_data.read_data_sets('./data/mnist',one_hot=True)
print(mnist.validation.num_examples)
print(mnist.train.num_examples)
print(mnist.test.num_examples)
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 def siamese(inputs,keep_prob):
with tf.name_scope('conv1') as scope:
w1 = tf.Variable(tf.truncated_normal(shape=[3,3,1,32],stddev=0.05),name='w1')
b1 = tf.Variable(tf.zeros(32),name='b1')
conv1 = tf.nn.conv2d(inputs,w1,strides=[1,1,1,1],padding='SAME',name='conv1')
with tf.name_scope('relu1') as scope:
relu1 = tf.nn.relu(tf.add(conv1,b1),name='relu1')
with tf.name_scope('conv2') as scope:
w2 = tf.Variable(tf.truncated_normal(shape=[3,3,32,64],stddev=0.05),name='w2')
b2 = tf.Variable(tf.zeros(64),name='b2')
conv2 = tf.nn.conv2d(relu1,w2,strides=[1,2,2,1],padding='SAME',name='conv2')
with tf.name_scope('relu2') as scope:
relu2 = tf.nn.relu(conv2+b2,name='relu2') with tf.name_scope('conv3') as scope: w3 = tf.Variable(tf.truncated_normal(shape=[3,3,64,128],mean=0,stddev=0.05),name='w3')
b3 = tf.Variable(tf.zeros(128),name='b3')
conv3 = tf.nn.conv2d(relu2,w3,strides=[1,2,2,1],padding='SAME')
with tf.name_scope('relu3') as scope:
relu3 = tf.nn.relu(conv3+b3,name='relu3') with tf.name_scope('fc1') as scope:
x_flat = tf.reshape(relu3,shape=[-1,7*7*128])
w_fc1=tf.Variable(tf.truncated_normal(shape=[7*7*128,1024],stddev=0.05,mean=0),name='w_fc1')
b_fc1 = tf.Variable(tf.zeros(1024),name='b_fc1')
fc1 = tf.add(tf.matmul(x_flat,w_fc1),b_fc1)
with tf.name_scope('relu_fc1') as scope:
relu_fc1 = tf.nn.relu(fc1,name='relu_fc1') with tf.name_scope('drop_1') as scope: drop_1 = tf.nn.dropout(relu_fc1,keep_prob=keep_prob,name='drop_1')
with tf.name_scope('bn_fc1') as scope:
bn_fc1 = tf.layers.batch_normalization(drop_1,name='bn_fc1')
with tf.name_scope('fc2') as scope:
w_fc2 = tf.Variable(tf.truncated_normal(shape=[1024,512],stddev=0.05,mean=0),name='w_fc2')
b_fc2 = tf.Variable(tf.zeros(512),name='b_fc2')
fc2 = tf.add(tf.matmul(bn_fc1,w_fc2),b_fc2)
with tf.name_scope('relu_fc2') as scope:
relu_fc2 = tf.nn.relu(fc2,name='relu_fc2')
with tf.name_scope('drop_2') as scope:
drop_2 = tf.nn.dropout(relu_fc2,keep_prob=keep_prob,name='drop_2')
with tf.name_scope('bn_fc2') as scope:
bn_fc2 = tf.layers.batch_normalization(drop_2,name='bn_fc2')
with tf.name_scope('fc3') as scope:
w_fc3 = tf.Variable(tf.truncated_normal(shape=[512,2],stddev=0.05,mean=0),name='w_fc3')
b_fc3 = tf.Variable(tf.zeros(2),name='b_fc3')
fc3 = tf.add(tf.matmul(bn_fc2,w_fc3),b_fc3)
return fc3 lr = 0.01
iterations = 20000
batch_size = 64 with tf.variable_scope('input_x1') as scope:
x1 = tf.placeholder(tf.float32, shape=[None, 784])
x_input_1 = tf.reshape(x1, [-1, 28, 28, 1])
with tf.variable_scope('input_x2') as scope:
x2 = tf.placeholder(tf.float32, shape=[None, 784])
x_input_2 = tf.reshape(x2, [-1, 28, 28, 1])
with tf.variable_scope('y') as scope:
y = tf.placeholder(tf.float32, shape=[batch_size]) with tf.name_scope('keep_prob') as scope:
keep_prob = tf.placeholder(tf.float32) with tf.variable_scope('siamese') as scope:
out1 = siamese(x_input_1,keep_prob)
scope.reuse_variables()
out2 = siamese(x_input_2,keep_prob)
with tf.variable_scope('metrics') as scope:
loss = siamese_loss(out1, out2, y)
optimizer = tf.train.AdamOptimizer(lr).minimize(loss) loss_summary = tf.summary.scalar('loss',loss)
merged_summary = tf.summary.merge_all() with tf.Session() as sess: writer = tf.summary.FileWriter('./graph/siamese',sess.graph)
sess.run(tf.global_variables_initializer()) for itera in range(iterations):
xs_1, ys_1 = mnist.train.next_batch(batch_size)
ys_1 = np.argmax(ys_1,axis=1)
xs_2, ys_2 = mnist.train.next_batch(batch_size)
ys_2 = np.argmax(ys_2,axis=1)
y_s = np.array(ys_1==ys_2,dtype=np.float32)
_,train_loss,summ = sess.run([optimizer,loss,merged_summary],feed_dict={x1:xs_1,x2:xs_2,y:y_s,keep_prob:0.6}) writer.add_summary(summ,itera)
if itera % 1000 == 1 :
print('iter {},train loss {}'.format(itera,train_loss))
embed = sess.run(out1,feed_dict={x1:mnist.test.images,keep_prob:0.6})
test_img = mnist.test.images.reshape([-1,28,28,1])
writer.close()