每个神经元不再与下一层的所有的神经元相连，只和一部分神经元连接，同时这一部分神经元具有相关性（邻近的几个神经元），针对图像的空间关系，一般是局部的像素联系比较紧密，而距离比较远的像素之间的关联性比较弱，也因此没有相连的必要，只需对图像空间中联系比较紧密的局部信息进行感知，然后在更深层网络中继续提取图像的局部特征。

随着网络层次的深入，图像的尺寸逐渐缩小，对图像特征的提取也从片面到整体，综合起来便能够得到图像的全局信息。

4.2.权值共享

一组连接可以共享一个参数，或者多组连接也可以共享同一个卷积核，不再是每条连接都有自己的权重。

比如，一个卷积核在图像的局部区域中抽取了纹理特征，那么在类似图像的类似特征依然可以使用该卷积核，这样就大大的减小了卷积核的数目，也就减小的参数的数目。

4.3.下采样技术

通过pooling技术对输入的数据进行下采样压缩操作，减少输出节点。

方式：Max Pooling和Mean Pooling

优点：

1、减少过拟合的可能性，当网络中权重参数过多的时候，很容易在训练阶段造成过拟合；

2、缩减图像的尺寸，减少计算量，提升计算速度；

3、进一步提取图像高维的统计特征。

5.可视化手写字体的网络特征

5.1.LeNet5的训练


from keras.datasets import mnist
from keras.utils import to_categorical
from keras.layers import MaxPool2D, Input, Flatten, Conv2D, Dropout, Dense
from keras.models import Model
from tensorflow.examples.tutorials.mnist import input_data
from keras.callbacks import ModelCheckpoint
import os
import keras
 
 
num_classes = 10
img_rows, img_cols = (28, 28)
 
 
def get_mnist_data():    
    (x_train, y_train), (x_test, y_test)  = mnist.load_data()
    x_train = x_train.reshape(x_train.shape[0], img_rows, img_cols, 1)
    x_test = x_test.reshape(x_test.shape[0], img_rows, img_cols, 1)
    
    x_train = x_train.astype('float32')
    x_test = x_test.astype('float32')
    x_train /= 255
    x_test /= 255
    
    y_train = to_categorical(y_train, num_classes)
    y_test = to_categorical(y_test, num_classes)
    
    return x_train, y_train, x_test, y_test
 
def LeNet5_model(w_path=None):
    input_shape = (img_rows, img_cols, 1)
    img_input = Input(shape=input_shape)
    x = Conv2D(32, (3, 3), activation='relu', padding='same', name='conv1')(img_input)
    x = MaxPool2D((2, 2), strides=(2, 2), name='pool1')(x)
    x = Conv2D(64, (5, 5), activation='relu', name='conv2')(x)
    x = MaxPool2D((2, 2), strides=(2, 2), name='pool2')(x)
    x = Dropout(0.25)(x)
    
    x = Flatten(name='Flatten')(x)
    
    x = Dense(120, activation='relu', name='fc1')(x)
    x = Dropout(0.5)(x)
    x = Dense(84, activation='relu', name='fc2')(x)
    x = Dropout(0.5)(x)
    x = Dense(10, activation='softmax', name='predictions')(x)
    
    model = Model(img_input, x, name='LeNet5')
    if w_path:
        model.load_weights(w_path)
    model.summary()
    model.compile(loss=keras.losses.categorical_crossentropy, optimizer=keras.optimizers.Adadelta(), metrics=['accuracy'])
    return model
    
if __name__ == '__main__':
    x_train, y_train, x_test, y_test = get_mnist_data()
    print(x_train.shape)
    print(x_test.shape)
    if not os.path.exists('letnet5_checkpoints'):
        os.mkdir('letnet5_checkpoints')
    model = LeNet5_model()
    checkpoint = ModelCheckpoint(monitor='val_acc', filepath='letnet5_checkpoints/model_{epoch:02d}_{val_acc:.3f}.h5',
                                 save_best_only=True)
    model.fit(x_train, 
              y_train, 
              batch_size=128, 
              epochs=30, 
              verbose=1, 
              validation_data=(x_test, y_test), 
              callbacks=[checkpoint])
 
    score = model.evaluate(x_test, y_test, verbose=0)
    print('Test loss:', score[0])
    print('Test accuracy:', score[1])

5.2.可视化特征向量

5.3.获取最好的保存的模型


lenet5 = load_model('letnet5_checkpoints/model_21_0.995.h5')
layer1 = lenet5.get_layer("conv1")
w = layer1.get_weights()
print(w[0].shape)
print(np.squeeze(w[0]).shape)

5.4.获取特征的输出


def get_activations(model, model_input, layer_name = None):
    activations = []
    inp = [model.input]
    
    # 所有层的输出 
    model_layers = [layer.output for layer in model.layers if 
               layer.name == layer_name or layer_name is None]
    pprint.pprint(model_layers)
    
    newmodel_layers = []
    newmodel_layers.append(model_layers[0])
    newmodel_layers.append(model_layers[1])
    newmodel_layers.append(model_layers[2])
    newmodel_layers.append(model_layers[3])
    newmodel_layers.append(model_layers[4])
    newmodel_layers.append(model_layers[7])
    newmodel_layers.append(model_layers[9])
    newmodel_layers.append(model_layers[11])
 
    funcs = [K.function(inp + [K.learning_phase()], [layer]) for layer in newmodel_layers]
    
    list_inputs = model_input.reshape(1,28,28,1)
    print(list_inputs.shape)
    
        
    layer_outputs = [func([list_inputs]) for func in funcs]
    for activation in layer_outputs:
        activations.append(activation)
        
    return activations
 
activations = get_activations(lenet5, x_test[i])
def display_tensor(tensors):
    if tensors.shape == (1, 1, 28, 28):
        tt = np.hstack(np.transpose(tensors[0], (0, 1, 2)))
        plt.figure(figsize=(15,1))
        plt.imshow(tt, interpolation='None', cmap='gray')
        plt.show()
    else:
        tt = np.hstack(np.transpose(tensors[0], (0, 1, 2)))
        plt.figure(figsize=(15,1))
        plt.imshow(tt, interpolation='None', cmap='hot')
        plt.show()        
        
def display_matrix(matrix):
    num_activations = len(matrix)
    tt = np.repeat(matrix, 10, axis=0)
    
    plt.figure(figsize=(20,2))
    plt.imshow(tt, interpolation='None', cmap='hot')
    plt.colorbar()
    plt.show()
 
    
def display_activations(activations_tensor):
    img_size = activations_tensor[0][0].shape[0]
    assert img_size == 1, 'One image at a time to visualize!'
 
    for i, activation_map in enumerate(activations_tensor):
        print('Displaying activation: {} {}'.format(i, activation_map[0].shape))
        activation_map = activation_map[0]
        shape = activation_map.shape
        if len(shape) == 4:
            display_tensor(activation_map)
            pass
        if len(shape) == 2:
            display_matrix(activation_map)
        
display_activations(activations)

参考：

《深度学习原理与实践》.陈仲铭，彭凌西
《统计学习方法》李航
《深度学习》古德费洛

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