机器学习实现手写数字识别：
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
mnist=input_data.read_data_sets('MNIST_data/',one_hot=True)
x=tf.placeholder(tf.float32,[None,784])
w=tf.Variable(tf.zeros([784,10]))
b=tf.Variable(tf.zeros([10]))
y=tf.nn.softmax(tf.matmul(x,w)+b)
y_=tf.placeholder(tf.float32,[None,10])
cross_entropy=tf.reduce_mean(-tf.reduce_sum(y_*tf.log(y)))
train_step=tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)
sess=tf.InteractiveSession()
tf.global_variables_initializer().run()
for i in range(1000):
batch_xs,batch_ys=mnist.train.next_batch(100)
sess.run(train_step,feed_dict={x:batch_xs,y_:batch_ys})
correct_prediction=tf.equal(tf.argmax(y,1),tf.argmax(y_,1))
accuracy=tf.reduce_mean(tf.cast(correct_prediction,tf.float32))
print(sess.run(accuracy,feed_dict={x:mnist.test.images,y_:mnist.test.labels}))
分类正确率：0.9191
神经网络实现数字识别：反向传播算法
import numpy as np
import random
import mnist_loader
class Network(object):
def __init__(self, sizes):
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
def sigmoid(self,z):
return 1.0 / (1.0 + np.exp(-z))
def feedforward(self, a):
for b, w in zip(self.biases, self.weights):
a = self.sigmoid(np.dot(w,a)+b)
return a
def SGD(self, training_data, epochs, mini_batch_size, eta,test_data=None):
if test_data: n_test = len(test_data)
n = len(training_data)
for j in range(epochs):
random.shuffle(training_data)
mini_batches = [
training_data[k:k + mini_batch_size]
for k in range(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print("Epoch {0}: {1} / {2}".format(j, self.evaluate(test_data), n_test))
else:
print("Epoch {0} complete".format(j))
def update_mini_batch(self, mini_batch, eta):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb + dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw + dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w - (eta / len(mini_batch)) * nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b - (eta / len(mini_batch)) * nb
for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation) + b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for l in range(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l + 1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l - 1].transpose())
return (nabla_b, nabla_w)
def evaluate(self, test_data):
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
def cost_derivative(self, output_activations, y):
return (output_activations - y)
def sigmoid(z):
return 1.0 / (1.0 + np.exp(-z))
def sigmoid_prime(z):
return sigmoid(z) * (1 - sigmoid(z))
if __name__=="__main__":
training_data, validation_data, test_data = mnist_loader.load_data_wrapper()
net = Network([784, 20, 10])
net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
正确率：0.9295
卷积神经网络实现手写数字识别：
from tensorflow.examples.tutorials.mnist import input_data import tensorflow as tf def weight_variable(shape): initial=tf.truncated_normal(shape,stddev=0.1) return tf.Variable(initial) def bias_variable(shape): initial=tf.constant(0.1,shape=shape) return tf.Variable(initial) def conv2d(x,w): return tf.nn.conv2d(x,w,strides=[1,1,1,1],padding='SAME') def max_pool_2x2(x): return tf.nn.max_pool(x,ksize=[1,2,2,1],strides=[1,2,2,1],padding='SAME') if __name__ == '__main__': # 读入数据 mnist = input_data.read_data_sets("MNIST_data/", one_hot=True) # x为训练图像的占位符、y_为训练图像标签的占位符 x = tf.placeholder(tf.float32, [None, 784]) y_ = tf.placeholder(tf.float32, [None, 10]) # 将单张图片从784维向量重新还原为28x28的矩阵图片 x_image = tf.reshape(x, [-1, 28, 28, 1]) # 第一层卷积层 W_conv1 = weight_variable([5, 5, 1, 32]) b_conv1 = bias_variable([32]) h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1) h_pool1 = max_pool_2x2(h_conv1) # 第二层卷积层 W_conv2 = weight_variable([5, 5, 32, 64]) b_conv2 = bias_variable([64]) h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2) h_pool2 = max_pool_2x2(h_conv2) # 全连接层，输出为1024维的向量 W_fc1 = weight_variable([7 * 7 * 64, 1024]) b_fc1 = bias_variable([1024]) h_pool2_flat = tf.reshape(h_pool2, [-1, 7 * 7 * 64]) h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1) # 使用Dropout，keep_prob是一个占位符，训练时为0.5，测试时为1 keep_prob = tf.placeholder(tf.float32) h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob) # 把1024维的向量转换成10维，对应10个类别 W_fc2 = weight_variable([1024, 10]) b_fc2 = bias_variable([10]) y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2 # 我们不采用先Softmax再计算交叉熵的方法，而是直接用tf.nn.softmax_cross_entropy_with_logits直接计算 cross_entropy = tf.reduce_mean( tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y_conv)) # 同样定义train_step train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy) # 定义测试的准确率 correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1)) accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32)) # 创建Session和变量初始化 sess = tf.InteractiveSession() sess.run(tf.global_variables_initializer()) # 训练20000步 for i in range(600): batch = mnist.train.next_batch(50) # 每100步报告一次在验证集上的准确度 if i % 100 == 0: train_accuracy = accuracy.eval(feed_dict={x: batch[0], y_: batch[1], keep_prob: 1.0}) print("第%d步, 正确率： %g" % (i, train_accuracy)) train_step.run(feed_dict={x: batch[0], y_: batch[1], keep_prob: 0.5}) # 训练结束后报告在测试集上的准确度 train_accuracy=accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}) print("测试正确率 %g" %train_accuracy)
分类正确率：0.99