逻辑斯蒂回归实现手写字的识别

import tensorflow as tf
import matplotlib.pyplot as plt
import numpy as np
from tensorflow.keras.datasets import mnist
#MNIST数据集参数
num_classes = 10
num_features = 784 #28*28
#训练参数
learning_rate = 0.01
training_steps = 1000
batch_size = 256
display_step = 50
#加载MNIST数据
(x_train,y_train),(x_test,y_test) = mnist.load_data()
#转换为float32
x_train,x_test = np.array(x_train,np.float32),np.array(x_test,np.float32)
#将图像平铺成784个特征的一维向量（28*28）
x_train,x_test = x_train.reshape([-1,num_features]),x_test.reshape([-1,num_features])
#将像素值从[0,255]归一化为[0,1]
x_train,x_test = x_train/255,x_test/255
#使用tf.data api 对数据随机分布和批处理
train_data = tf.data.Dataset.from_tensor_slices((x_train,y_train))
train_data = train_data.repeat().shuffle(5000).batch(batch_size).prefetch(1)
# 权值矩阵形状[784,10]，28 * 28图像特征数和类别数目
W = tf.Variable(tf.ones([num_features, num_classes]), name="weight")
# 偏置形状[10], 类别数目
b = tf.Variable(tf.zeros([num_classes]), name="bias")
# 逻辑斯谛回归（Wx+b)
def logistic_regression(x):
    #应用softmax将logits标准化为概率分布
    return tf.nn.softmax(tf.matmul(x,W) + b)
# 交叉熵损失函数
def cross_entropy(y_pred, y_true):
    # 将标签编码为一个独热编码向量
    y_true = tf.one_hot(y_true, depth=num_classes)
    # 压缩预测值以避免log（0）错误
    y_pred = tf.clip_by_value(y_pred, 1e-9, 1.)
    # 计算交叉熵
    return tf.reduce_mean(-tf.reduce_sum(y_true * tf.math.log(y_pred)))
# 准确率度量
def accuracy(y_pred, y_true):
    # 预测的类别是预测向量中最高分的索引（即argmax）
    correct_prediction = tf.equal(tf.argmax(y_pred, 1), tf.cast(y_true, tf.int64))
    return tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
# 随机梯度下降优化器
optimizer = tf.optimizers.SGD(learning_rate)
# 优化过程
def run_optimization(x, y):
    # 将计算封装在GradientTape中以实现自动微分
    with tf.GradientTape() as g:
        pred = logistic_regression(x)
        loss = cross_entropy(pred, y)
    # 计算梯度
    gradients = g.gradient(loss, [W, b])
    # 根据gradients更新 W 和 b
    optimizer.apply_gradients(zip(gradients, [W, b]))
# 针对给定训练步骤数开始训练
for step, (batch_x, batch_y) in enumerate(train_data.take(training_steps), 1):
    # 运行优化以更新W和b值
    run_optimization(batch_x, batch_y)
    if step % display_step == 0:
        pred = logistic_regression(batch_x)
        loss = cross_entropy(pred, batch_y)
        acc = accuracy(pred, batch_y)
        print("step: %i, loss: %f, accuracy: %f" % (step, loss, acc))
# 在验证集上测试模型
pred = logistic_regression(x_test)
print("Test Accuracy: %f" % accuracy(pred, y_test))
#可视化预测,在测试集中预测5张图片
n_images = 5
test_images = x_test[:n_images]
predictions = logistic_regression(test_images)
for i in range(n_images):
    plt.imshow(np.reshape(test_images[i],[28,28]))
    plt.show()
    print("Model prediction: %i" % np.argmax(predictions.numpy()[i]))