機器學習實現手寫數字識別：

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}))

 分類正確率：0.9191

神經網路實現數字識別：反向傳播演算法

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)

正確率：0.9295

卷積神經網路實現手寫數字識別：

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__':
    # 讀入資料
    mnist = input_data.read_data_sets("MNIST_data/", one_hot=True)
    # x為訓練影象的佔位符、y_為訓練影象標籤的佔位符
    x = tf.placeholder(tf.float32, [None, 784])
    y_ = tf.placeholder(tf.float32, [None, 10])

    # 將單張圖片從784維向量重新還原為28x28的矩陣圖片
    x_image = tf.reshape(x, [-1, 28, 28, 1])

    # 第一層卷積層
    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)

    # 第二層卷積層
    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)

    # 全連線層，輸出為1024維的向量
    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是一個佔位符，訓練時為0.5，測試時為1
    keep_prob = tf.placeholder(tf.float32)
    h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

    # 把1024維的向量轉換成10維，對應10個類別
    W_fc2 = weight_variable([1024, 10])
    b_fc2 = bias_variable([10])
    y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2

    # 我們不採用先Softmax再計算交叉熵的方法，而是直接用tf.nn.softmax_cross_entropy_with_logits直接計算
    cross_entropy = tf.reduce_mean(
        tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y_conv))
    # 同樣定義train_step
    train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)

    # 定義測試的準確率
    correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

    # 建立Session和變數初始化
    sess = tf.InteractiveSession()
    sess.run(tf.global_variables_initializer())

    # 訓練20000步
    for i in range(600):
        batch = mnist.train.next_batch(50)
        # 每100步報告一次在驗證集上的準確度
        if i % 100 == 0:
            train_accuracy = accuracy.eval(feed_dict={x: batch[0], y_: batch[1], keep_prob: 1.0})
            print("第%d步, 正確率： %g" % (i, train_accuracy))
        train_step.run(feed_dict={x: batch[0], y_: batch[1], keep_prob: 0.5})

    # 訓練結束後報告在測試集上的準確度
    train_accuracy=accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0})
    print("測試正確率 %g" %train_accuracy)

分類正確率：0.99