深度学习6（多分类+交叉熵损失原理+手写数字识别案例TensorFlow）

目录

多分类

softmax回归

多分类

        我们已经接触过二分类问题，神经网络输出层只有一个神经元，表示预测输出是正类的概率P(y =1m),g>0.5则判断为正类，反之判断为负类。那么对于多分类问题怎么办?

        对于多分类问题，用 N表示种类个数，那么神经网络的输出层的神经元个数必须为L[output]=N,每个神经元的输出依次对应属于N个类别当中某个具体类别的概率，即 P(y=N1|),…,P(y= Nn|z)。

softmax回归

        Softmax回归（也称为多项逻辑回归）是逻辑回归在多分类问题上的自然扩展，它是深度学习中最基础也是最重要的多分类方法之一。与二分类的逻辑回归不同，Softmax回归可以同时处理多个类别的分类问题，并且将输出转化为概率分布，满足 0 ≤ P ≤ 1

交叉熵损失

        对于softmax回归(逻辑回归代价函数的推广，都可称之为交叉损失)，它的代价函数公式为:

        其实将逻辑回归看作是一个多分类（两个分类），它的表达形式也可以与之统一，

手写数字识别案例

        本次代码没有手写实现正向传播、反向传播等细节，都使用tensorflow包调用其API来实现，

封装更简洁，大大增加了代码可读性。这里引入的tensorflow的版本可能落后，完全复制可能不一定复现成功。

        本次使用的样本是通过下载网上的数据集，并通过mnist = tf.keras.datasets.mnist.load_data()引入数据。

import tensorflow.compat.v1 as tf
tf.disable_v2_behavior()
mnist = tf.keras.datasets.mnist.load_data()

def fc_nn():
    # 获取数据
    mnist = tf.keras.datasets.mnist.load_data()

    with tf.variable_scope("resource"):
        # 特征X
        x = tf.placeholder(tf.float32, [None, 784], name="X_data")
        # 目标值Y（修正：改为float32以匹配one-hot编码）
        y = tf.placeholder(tf.float32, [None, 10], name="label")

    with tf.variable_scope("hidden"):
        # [none,784] * [784 ,64] + [64] = [none , 64]
        # 修正：将mean和stddev参数移到random_normal函数内部
        weight_hidden = tf.Variable(tf.random_normal([784,64], mean=0.0, stddev=1.0), name="weight_hidden")
        bias_hidden = tf.Variable(tf.random_normal([64], mean=0.0, stddev=1.0), name="bias_hidden")
        A1 = tf.matmul(x, weight_hidden) + bias_hidden

    with tf.variable_scope("fc"):
        # [none , 64] * [64 , 10] + [10] = [none , 10]
        weight_fc = tf.Variable(tf.random_normal([64,10], mean=0.0, stddev=1.0), name="weight_fc")
        bias_fc = tf.Variable(tf.random_normal([10], mean=0.0, stddev=1.0), name="bias_fc")
        y_pred = tf.matmul(A1, weight_fc) + bias_fc

    with tf.variable_scope("compute_loss"):
       # 计算损失
       all_loss = tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=y_pred)
       loss = tf.reduce_mean(all_loss)

    with tf.variable_scope("optimize"):
        train_op = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

    with tf.Session() as sess:
        # 运行初始化变量(必须做)
        sess.run(tf.global_variables_initializer())
        # 循环
        for i in range(2000):
            # 修正：添加批量数据获取
            batch_x, batch_y = mnist.train.next_batch(100)
            # 修正：添加feed_dict参数传递数据
            loss_run, _ = sess.run([loss, train_op], feed_dict={x: batch_x, y: batch_y})
            print("迭代第%d步，损失为：%f"%(i, loss_run))

if __name__ == '__main__':
    fc_nn()

这里是通过AI修改后，符合版本的代码，谨慎尝试

import tensorflow.compat.v1 as tf
tf.disable_v2_behavior()

def fc_nn():
    # 获取数据
    (x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()
    # 预处理数据
    x_train = x_train.reshape(-1, 784).astype('float32') / 255.0
    y_train = tf.keras.utils.to_categorical(y_train, 10)

    with tf.variable_scope("resource"):
        # 特征X
        x = tf.placeholder(tf.float32, [None, 784], name="X_data")
        # 目标值Y
        y = tf.placeholder(tf.float32, [None, 10], name="label")

    with tf.variable_scope("hidden"):
        # [none,784] * [784 ,64] + [64] = [none , 64]
        weight_hidden = tf.Variable(tf.random_normal([784,64], mean=0.0, stddev=1.0), name="weight_hidden")
        bias_hidden = tf.Variable(tf.random_normal([64], mean=0.0, stddev=1.0), name="bias_hidden")
        A1 = tf.matmul(x, weight_hidden) + bias_hidden

    with tf.variable_scope("fc"):
        # [none , 64] * [64 , 10] + [10] = [none , 10]
        weight_fc = tf.Variable(tf.random_normal([64,10], mean=0.0, stddev=1.0), name="weight_fc")
        bias_fc = tf.Variable(tf.random_normal([10], mean=0.0, stddev=1.0), name="bias_fc")
        y_pred = tf.matmul(A1, weight_fc) + bias_fc

    with tf.variable_scope("compute_loss"):
       # 计算损失
       all_loss = tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=y_pred)
       loss = tf.reduce_mean(all_loss)

    with tf.variable_scope("optimize"):
        train_op = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

    with tf.Session() as sess:
        # 运行初始化变量(必须做)
        sess.run(tf.global_variables_initializer())
        # 循环
        for i in range(2000):
            # 获取批量数据
            start = (i * 100) % (len(x_train) - 100)
            end = start + 100
            batch_x = x_train[start:end]
            batch_y = y_train[start:end]

            loss_run, _ = sess.run([loss, train_op], feed_dict={x: batch_x, y: batch_y})
            print("迭代第%d步，损失为：%f"%(i, loss_run))

if __name__ == '__main__':
    fc_nn()

改进代码（数据保存+TensorBoard显示图像）

import tensorflow.compat.v1 as tf
import os

tf.disable_v2_behavior()

def fc_nn():
    # 获取数据
    (x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()
    # 预处理数据
    x_train = x_train.reshape(-1, 784).astype('float32') / 255.0
    y_train = tf.keras.utils.to_categorical(y_train, 10)

    # 创建日志目录
    log_dir = "./logs/fc_nn"
    if not os.path.exists(log_dir):
        os.makedirs(log_dir)

    with tf.variable_scope("resource"):
        # 特征X
        x = tf.placeholder(tf.float32, [None, 784], name="X_data")
        # 目标值Y
        y = tf.placeholder(tf.float32, [None, 10], name="label")

    with tf.variable_scope("hidden"):
        # [none,784] * [784 ,64] + [64] = [none , 64]
        weight_hidden = tf.Variable(tf.random_normal([784,64], mean=0.0, stddev=1.0), name="weight_hidden")
        bias_hidden = tf.Variable(tf.random_normal([64], mean=0.0, stddev=1.0), name="bias_hidden")
        A1 = tf.matmul(x, weight_hidden) + bias_hidden
        # 添加激活函数和直方图记录
        A1 = tf.nn.relu(A1)
        tf.summary.histogram("hidden_activations", A1)

    with tf.variable_scope("fc"):
        # [none , 64] * [64 , 10] + [10] = [none , 10]
        weight_fc = tf.Variable(tf.random_normal([64,10], mean=0.0, stddev=1.0), name="weight_fc")
        bias_fc = tf.Variable(tf.random_normal([10], mean=0.0, stddev=1.0), name="bias_fc")
        y_pred = tf.matmul(A1, weight_fc) + bias_fc
        # 记录权重和偏置
        tf.summary.histogram("fc_weights", weight_fc)
        tf.summary.histogram("fc_biases", bias_fc)

    with tf.variable_scope("compute_loss"):
       # 计算损失
       all_loss = tf.nn.softmax_cross_entropy_with_logits(labels=y, logits=y_pred)
       loss = tf.reduce_mean(all_loss)
       # 记录损失
       tf.summary.scalar("loss", loss)

    with tf.variable_scope("accuracy"):
        # 计算准确率
        correct_pred = tf.equal(tf.argmax(y_pred, 1), tf.argmax(y, 1))
        accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32))
        tf.summary.scalar("accuracy", accuracy)

    with tf.variable_scope("optimize"):
        train_op = tf.train.GradientDescentOptimizer(0.1).minimize(loss)

    # 合并所有summary
    merged = tf.summary.merge_all()

    with tf.Session() as sess:
        # 创建FileWriter
        train_writer = tf.summary.FileWriter(log_dir, sess.graph)

        # 运行初始化变量
        sess.run(tf.global_variables_initializer())

        # 训练循环
        for i in range(2000):
            # 获取批量数据
            start = (i * 100) % (len(x_train) - 100)
            end = start + 100
            batch_x = x_train[start:end]
            batch_y = y_train[start:end]

            # 运行训练并记录summary
            _, loss_run, summary = sess.run([train_op, loss, merged],
                                          feed_dict={x: batch_x, y: batch_y})

            # 写入summary
            train_writer.add_summary(summary, i)

            # 每100步打印一次信息
            if i % 100 == 0:
                acc = sess.run(accuracy, feed_dict={x: batch_x, y: batch_y})
                print(f"迭代第{i}步，损失: {loss_run:.4f}, 准确率: {acc:.4f}")

        # 关闭FileWriter
        train_writer.close()

if __name__ == '__main__':
    fc_nn()

        该代码运行一次后会创建log文件保存数据，然后再python终端里输入

tensorboard --logdir=./logs

        就能看到该神经网络拟合过程的图像。本代码只保存了accuracy和loss，当然自己也可以增加保存的变量看看图像。记得清理日志。