Tensorflow-交叉熵&过拟合

交叉熵

二次代价函数

原理

缺陷

假如我们目标是收敛到0。A点为0.82离目标比较近,梯度比较大，权值调整比较大。B点为0.98离目标比较远,梯度比较小,权值调整比较小。调整方案不合理。

交叉熵代价函数(cross-entropy)

换一个思路，我们不改变激活函数，而是改变代价函数，改用交叉熵代价函数：

原理

用法

实战

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
tf.compat.v1.disable_eager_execution()
import numpy as np

#载入数据集
mnist=input_data.read_data_sets("MNIST_data",one_hot=True)

#每个批次大小
batch_size=100
#计算一共有多少个批次
n_bath=mnist.train.num_examples // batch_size
print(n_bath)
#定义两个placeholder
x=tf.compat.v1.placeholder(tf.float32,[None,784])
y=tf.compat.v1.placeholder(tf.float32,[None,10])

#创建一个简单的神经网络
W=tf.Variable(tf.zeros([784,10]))
b=tf.Variable(tf.zeros([10]))
prediction=tf.nn.softmax(tf.matmul(x,W)+b)

#交叉熵函数
loss=tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y,logits=prediction))
#梯度下降
train_step=tf.compat.v1.train.GradientDescentOptimizer(0.2).minimize(loss)

#初始化变量
init=tf.compat.v1.global_variables_initializer()

#结果存放在一个布尔型列表中
#返回的是一系列的True或False argmax返回一维张量中最大的值所在的位置，对比两个最大位置是否一致
correct_prediction=tf.equal(tf.argmax(y,1),tf.argmax(prediction,1))

#求准确率
#cast：将布尔类型转换为float，将True为1.0，False为0，然后求平均值
accuracy=tf.reduce_mean(tf.cast(correct_prediction,tf.float32))

with tf.compat.v1.Session() as sess:
    sess.run(init)
    for epoch in range(21):
        for batch in range(n_bath):
            #获得一批次的数据，batch_xs为图片，batch_ys为图片标签
            batch_xs,batch_ys=mnist.train.next_batch(batch_size)
            #进行训练
            sess.run(train_step,feed_dict={x:batch_xs,y:batch_ys})
        #训练完一遍后，测试下准确率的变化

        acc=sess.run(accuracy,feed_dict={x:mnist.test.images,y:mnist.test.labels})
        print("Iter "+str(epoch)+",Testing Accuracy "+str(acc))

输出：明显可以看到有了巨大的变化

拟合

防止过拟合

代码

import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
tf.compat.v1.disable_eager_execution()
import numpy as np

#载入数据集
mnist=input_data.read_data_sets("MNIST_data",one_hot=True)

# 批次的大小
batch_size = 128
n_batch = mnist.train.num_examples // batch_size

x = tf.compat.v1.placeholder(tf.float32, [None,784])
y = tf.compat.v1.placeholder(tf.float32, [None, 10])
keep_prob = tf.compat.v1.placeholder(tf.float32)

# 创建神经网络
W1 = tf.Variable(tf.compat.v1.truncated_normal([784,2000],stddev=0.1))
b1 = tf.Variable(tf.zeros([1, 2000]))
# 激活层
layer1 = tf.nn.relu(tf.matmul(x,W1) + b1)
# drop层
layer1 = tf.nn.dropout(layer1,keep_prob)

# 第二层
W2 = tf.Variable(tf.compat.v1.truncated_normal([2000,500],stddev=0.1))
b2 = tf.Variable(tf.zeros([1, 500]))
layer2 = tf.nn.relu(tf.matmul(layer1,W2) + b2)
layer2 = tf.nn.dropout(layer2,keep_prob)

# 第三层
W3 = tf.Variable(tf.compat.v1.truncated_normal([500,10],stddev=0.1))
b3 = tf.Variable(tf.zeros([1,10]))
prediction = tf.nn.sigmoid(tf.matmul(layer2,W3) + b3)

loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=prediction))

# 梯度下降法
# train_step = tf.train.GradientDescentOptimizer(0.2).minimize(loss)#得到97的正确率
train_step = tf.compat.v1.train.AdadeltaOptimizer(0.1).minimize(loss)

# 初始化变量
init = tf.compat.v1.global_variables_initializer()

prediction_2 = tf.nn.softmax(prediction)
# 得到一个布尔型列表，存放结果是否正确
correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(prediction_2,1)) #argmax 返回一维张量中最大值索引

# 求准确率
accuracy = tf.reduce_mean(tf.cast(correct_prediction,tf.float32)) # 把布尔值转换为浮点型求平均数

with tf.compat.v1.Session() as sess:
    sess.run(init)
    for epoch in range(100):
        for batch in range(n_batch):
            # 获得批次数据
            batch_xs, batch_ys = mnist.train.next_batch(batch_size)
            sess.run(train_step, feed_dict={x:batch_xs, y:batch_ys, keep_prob:0.8})
        test_acc = sess.run(accuracy, feed_dict={x:mnist.test.images,y:mnist.test.labels,keep_prob:1.0} )
        train_acc = sess.run(accuracy, feed_dict={x: mnist.train.images, y: mnist.train.labels, keep_prob: 1.0})
        print("Iter " + str(epoch) + ",Testing Accuracy " + str(test_acc) + ",Train Accuracy " + str(train_acc))