数学模型

Wang Haihua

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卷积神经网络基础

基础的卷积神经网络CNN: CNN类似于多层感知器模型MLP因为它们都是前向神经网络,但CNN有几个不同特点

• 卷积层 :在一个小的接收域(即过滤器)中处理数据
• 池化层 : 沿2个维度向下采样(通常是宽度和高度)
• 全连接层 :类似于MLP中的隐含层

创建模型

卷积层

一般使用二维卷积处理图像数据

• 过滤器的大小(由'kernel_size'参数指定)定义了接收字段的宽度和高度
• 过滤器的数量(由'filters'参数指定)等于下一层的深度**
• 步幅(由“步幅”参数指定)是过滤器在每次移动中改变位置的距离
• 图像可以被“零填充”，以防止变得太小(由“padding”参数指定)

激活层

和MLP中的激活层相同

池化层

用于所见参数数量

全连接层

-卷积和池化层可以连接到全连接层。

模型编译和训练

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import numpy as np
import matplotlib.pyplot as plt

from sklearn import datasets
from sklearn.model_selection import train_test_split
from keras.utils.np_utils import to_categorical

data = datasets.load_digits()

plt.imshow(data.images[0])    # show first number in the dataset
plt.show()
print('label: ', data.target[0])    # label = '0'

label:  0

X_data = data.images
y_data = data.target

# shape of data
print(X_data.shape)    # (8 X 8) format
print(y_data.shape)

(1797, 8, 8)
(1797,)

# reshape X_data into 3-D format
# note that this follows image format of Tensorflow backend
X_data = X_data.reshape((X_data.shape[0], X_data.shape[1], X_data.shape[2], 1))

# one-hot encoding of y_data
y_data = to_categorical(y_data)

# partition data into train/test sets
X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, test_size = 0.3, random_state = 777)

from keras.models import Sequential
from keras import optimizers
from keras.layers import Dense, Activation, Flatten, Conv2D, MaxPooling2D

model = Sequential()
# convolution layer
model.add(Conv2D(input_shape = (X_data.shape[1], X_data.shape[2], X_data.shape[3]), filters = 10, kernel_size = (3,3), strides = (1,1), padding = 'valid'))

model.add(Activation('relu'))

model.add(MaxPooling2D(pool_size = (2,2)))

# prior layer should be flattend to be connected to dense layers
model.add(Flatten())

# dense layer with 50 neurons
model.add(Dense(50, activation = 'relu'))

# final layer with 10 neurons to classify the instances
model.add(Dense(10, activation = 'softmax'))

adam = optimizers.Adam(lr = 0.001)
model.compile(loss = 'categorical_crossentropy', optimizer = adam, metrics = ['accuracy'])
history = model.fit(X_train, y_train, batch_size = 50, validation_split = 0.2, epochs = 100, verbose = 0)

history.history.keys()

dict_keys(['val_loss', 'val_accuracy', 'loss', 'accuracy'])

plt.plot(history.history['accuracy'])
plt.plot(history.history['val_accuracy'])
plt.legend(['training', 'validation'], loc = 'upper left')
plt.show()

results = model.evaluate(X_test, y_test)

540/540 [==============================] - 0s 22us/step

print('Test accuracy: ', results[1])

Test accuracy:  0.9870370626449585

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