CNN 卷积神经网络（MNIST 手写数字数据集分类）
数据准备
MNIST 数据集包含 60,000 张训练图像和 10,000 张测试图像，每张图像为 28×28 的灰度手写数字。数据需要预处理为适合 CNN 输入的格式：
import tensorflow as tf
from tensorflow.keras.datasets import mnist
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train = x_train.reshape(-1, 28, 28, 1).astype('float32') / 255.0
x_test = x_test.reshape(-1, 28, 28, 1).astype('float32') / 255.0
y_train = tf.keras.utils.to_categorical(y_train, 10)
y_test = tf.keras.utils.to_categorical(y_test, 10)
模型架构
典型的 CNN 结构包含卷积层、池化层和全连接层：
model = tf.keras.Sequential([
tf.keras.layers.Conv2D(32, (3, 3), activation='relu', input_shape=(28, 28, 1)),
tf.keras.layers.MaxPooling2D((2, 2)),
tf.keras.layers.Conv2D(64, (3, 3), activation='relu'),
tf.keras.layers.MaxPooling2D((2, 2)),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(128, activation='relu'),
tf.keras.layers.Dense(10, activation='softmax')
])
训练配置
使用交叉熵损失函数和 Adam 优化器：
model.compile(optimizer='adam',
loss='categorical_crossentropy',
metrics=['accuracy'])
history = model.fit(x_train, y_train, epochs=5, batch_size=64, validation_split=0.2)
性能评估
测试集上的准确率通常可达 99% 以上：
test_loss, test_acc = model.evaluate(x_test, y_test)
print(f"Test accuracy: {test_acc:.4f}")
关键改进方向
- 数据增强：通过旋转、平移等操作扩充训练数据
- 批归一化：在卷积层后添加 BatchNormalization 加速收敛
- Dropout：在全连接层前加入 Dropout(0.5) 防止过拟合
- 更深的网络：尝试 ResNet 等现代架构
完整代码示例
import tensorflow as tf
from tensorflow.keras import layers
# 数据加载与预处理
(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()
x_train = x_train.reshape(-1, 28, 28, 1).astype('float32') / 255.0
x_test = x_test.reshape(-1, 28, 28, 1).astype('float32') / 255.0
y_train = tf.keras.utils.to_categorical(y_train, 10)
y_test = tf.keras.utils.to_categorical(y_test, 10)
# 模型构建
model = tf.keras.Sequential([
layers.Conv2D(32, 3, activation='relu', input_shape=(28, 28, 1)),
layers.MaxPooling2D(),
layers.Conv2D(64, 3, activation='relu'),
layers.MaxPooling2D(),
layers.Flatten(),
layers.Dense(128, activation='relu'),
layers.Dense(10, activation='softmax')
])
# 训练与评估
model.compile(optimizer='adam',
loss='categorical_crossentropy',
metrics=['accuracy'])
model.fit(x_train, y_train, epochs=5, validation_data=(x_test, y_test))
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