采用胶囊网络分类mnist数据集 使用python并给出完整代码

胶囊网络（Capsule Network）是一种相对较新的深度学习模型，它尝试解决传统神经网络在处理物体识别中局部对齐的问题。在MNIST数据集上应用胶囊网络可以提高手写数字识别的准确性。

以下是使用Keras库（Python）构建一个简单的胶囊网络分类MNIST数据集的示例代码：

# 导入所需库
from keras import layers, models, backend
from keras.datasets import mnist
from keras.layers import Input, Lambda
import numpy as np

# 定义Squash函数（胶囊网络的核心部分）
def squash(x, axis=-1):
    s_squared_norm = backend.sum(backend.square(x), axis=axis)
    scale = 1 / (1 + s_squared_norm)
    return scale * x

# 构建胶囊层
def caps_layer-routing(num_capsules, num_route_nodes, in_dim, out_dim):
    def layer(x):
        capsules = []
        for i in range(num_capsules):
            c = layers.Dense(num_route_nodes, kernel_initializer='glorot_uniform')(x)
            b = layers.Lambda(lambda z: z[:, None])(np.zeros((num_route_nodes, out_dim))) # route bias
            c = layers.Softmax(axis=1)(c)  # 软max路由
            capsules.append(layers.Multiply()([c, b]))
        capsules = layers.Concatenate(axis=1)(capsules)
        output = layers.Reshape((num_capsules, out_dim))(capsules)
        return squash(output)
    return layer

# 准备数据
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train, x_test = x_train.reshape(-1, 28, 28, 1).astype('float32') / 255., x_test.reshape(-1, 28, 28, 1).astype('float32') / 255.

# 将输入扁平化，以便适应胶囊网络
input_shape = (None, 28, 28, 1)
inputs = layers.Input(shape=input_shape)

# 创建第一个胶囊层
primary_caps = caps_layer-routing(256, 16, 28 * 28, 8)(inputs)

# 输出层
digit_caps = caps_layer-routing(10, 16, 8, 16)(primary_caps)

# 定义损失函数（动态路由的Margin Loss）
def margin_loss(y_true, y_pred):
    L = y_true * backend.square(kron(y_pred, y_pred) - y_pred) \
         + 0.5 * (1 - y_true) * (backend.square(kron(1 - y_pred, 1 - y_pred) - (1 - y_pred)))
    return backend.mean(L, axis=[1,2])

# 计算准确率
def accuracy(y_true, y_pred):
    batch_size = tf.shape(y_true)[0]
    pred_digits = tf.argmax(y_pred, axis=1)
    true_labels = tf.argmax(y_true, axis=1)
    correct = tf.cast(tf.equal(pred_digits, true_labels), tf.float32)
    return backend.mean(correct)

# 模型编译
margin_loss_value = layers.Lambda(margin_loss)
accuracy_value = layers.Lambda(accuracy)
capsule_model = models.Model(inputs=inputs, outputs=[margin_loss_value, accuracy_value])
capsule_model.compile(optimizer='adam', loss=[lambda y_true, y_pred: 0., 'accuracy'])

# 训练模型
capsule_model.fit(x_train, [y_train, y_train],
                  epochs=5,
                  validation_data=(x_test, [y_test, y_test]))