手写数字集相信大家应该很熟悉了，这个程序相当于学一门新语言的“Hello World”，或者mapreduce的“WordCount”：）这里就不多做介绍了，简单给大家看一下：
1 # Author：Charlotte
2 # Plot mnist dataset
3 from keras.datasets import mnist
4 import matplotlib.pyplot as plt
5 # load the MNIST dataset
6 (X_train, y_train), (X_test, y_test) = mnist.load_data()
7 # plot 4 images as gray scale
8 plt.subplot(221)
9 plt.imshow(X_train[0], cmap=plt.get_cmap('PuBuGn_r'))
10 plt.subplot(222)
11 plt.imshow(X_train[1], cmap=plt.get_cmap('PuBuGn_r'))
12 plt.subplot(223)
13 plt.imshow(X_train[2], cmap=plt.get_cmap('PuBuGn_r'))
14 plt.subplot(224)
15 plt.imshow(X_train[3], cmap=plt.get_cmap('PuBuGn_r'))
16 # show the plot
17 plt.show()
图：
1.BaseLine版本
一开始我没有想过用CNN做，因为比较耗时，所以想看看直接用比较简单的算法看能不能得到很好的效果。之前用过机器学习算法跑过一遍，最好的效果是SVM，96.8%（默认参数，未调优），所以这次准备用神经网络做。BaseLine版本用的是MultiLayer Percepton（多层感知机）。这个网络结构比较简单，输入--->隐含--->输出。隐含层采用的rectifier linear unit，输出直接选取的softmax进行多分类。
网络结构：
代码：
1 # coding:utf-8
2 # Baseline MLP for MNIST dataset
3 import numpy
4 from keras.datasets import mnist
5 from keras.models import Sequential
6 from keras.layers import Dense
7 from keras.layers import Dropout
8 from keras.utils import np_utils
9
10 seed = 7
11 numpy.random.seed(seed)
12 #加载数据
13 (X_train, y_train), (X_test, y_test) = mnist.load_data()
14
15 num_pixels = X_train.shape[1] * X_train.shape[2]
16 X_train = X_train.reshape(X_train.shape[0], num_pixels).astype('float32')
17 X_test = X_test.reshape(X_test.shape[0], num_pixels).astype('float32')
18
19 X_train = X_train / 255
20 X_test = X_test / 255
21
22 # 对输出进行one hot编码
23 y_train = np_utils.to_categorical(y_train)
24 y_test = np_utils.to_categorical(y_test)
25 num_classes = y_test.shape[1]
26
27 # MLP模型
28 def baseline_model():
29 model = Sequential()
30 model.add(Dense(num_pixels, input_dim=num_pixels, init='normal', activation='relu'))
31 model.add(Dense(num_classes, init='normal', activation='softmax'))
32 model.summary()
33 model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
34 return model
35
36 # 建立模型
37 model = baseline_model()
38
39 # Fit
40 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=10, batch_size=200, verbose=2)
41
42 #Evaluation
43 scores = model.evaluate(X_test, y_test, verbose=0)
44 print("Baseline Error: %.2f%%" % (100-scores[1]*100))#输出错误率
结果：
1 Layer (type) Output Shape Param # Connected to 2 ==================================================================================================== 3 dense_1 (Dense) (None, 784) 615440 dense_input_1[0][0] 4 ____________________________________________________________________________________________________ 5 dense_2 (Dense) (None, 10) 7850 dense_1[0][0] 6 ==================================================================================================== 7 Total params: 623290 8 ____________________________________________________________________________________________________ 9 Train on 60000 samples, validate on 10000 samples 10 Epoch 1/10 11 3s - loss: 0.2791 - acc: 0.9203 - val_loss: 0.1420 - val_acc: 0.9579 12 Epoch 2/10 13 3s - loss: 0.1122 - acc: 0.9679 - val_loss: 0.0992 - val_acc: 0.9699 14 Epoch 3/10 15 3s - loss: 0.0724 - acc: 0.9790 - val_loss: 0.0784 - val_acc: 0.9745 16 Epoch 4/10 17 3s - loss: 0.0509 - acc: 0.9853 - val_loss: 0.0774 - val_acc: 0.9773 18 Epoch 5/10 19 3s - loss: 0.0366 - acc: 0.9898 - val_loss: 0.0626 - val_acc: 0.9794 20 Epoch 6/10 21 3s - loss: 0.0265 - acc: 0.9930 - val_loss: 0.0639 - val_acc: 0.9797 22 Epoch 7/10 23 3s - loss: 0.0185 - acc: 0.9956 - val_loss: 0.0611 - val_acc: 0.9811 24 Epoch 8/10 25 3s - loss: 0.0150 - acc: 0.9967 - val_loss: 0.0616 - val_acc: 0.9816 26 Epoch 9/10 27 4s - loss: 0.0107 - acc: 0.9980 - val_loss: 0.0604 - val_acc: 0.9821 28 Epoch 10/10 29 4s - loss: 0.0073 - acc: 0.9988 - val_loss: 0.0611 - val_acc: 0.9819 30 Baseline Error: 1.81%
可以看到结果还是不错的，正确率98.19%，错误率只有1.81%，而且只迭代十次效果也不错。这个时候我还是没想到去用CNN，而是想如果迭代100次，会不会效果好一点？于是我迭代了100次，结果如下：
Epoch 100/100
8s - loss: 4.6181e-07 - acc: 1.0000 - val_loss: 0.0982 - val_acc: 0.9854
Baseline Error: 1.46%
从结果中可以看出，迭代100次也只提高了0.35%，没有突破99%，所以就考虑用CNN来做。
2.简单的CNN网络
keras的CNN模块还是很全的，由于这里着重讲CNN的结果，对于CNN的基本知识就不展开讲了。
网络结构：
代码：
1 #coding: utf-8
2 #Simple CNN
3 import numpy
4 from keras.datasets import mnist
5 from keras.models import Sequential
6 from keras.layers import Dense
7 from keras.layers import Dropout
8 from keras.layers import Flatten
9 from keras.layers.convolutional import Convolution2D
10 from keras.layers.convolutional import MaxPooling2D
11 from keras.utils import np_utils
12
13 seed = 7
14 numpy.random.seed(seed)
15
16 #加载数据
17 (X_train, y_train), (X_test, y_test) = mnist.load_data()
18 # reshape to be [samples][channels][width][height]
19 X_train = X_train.reshape(X_train.shape[0], 1, 28, 28).astype('float32')
20 X_test = X_test.reshape(X_test.shape[0], 1, 28, 28).astype('float32')
21
22 # normalize inputs from 0-255 to 0-1
23 X_train = X_train / 255
24 X_test = X_test / 255
25
26 # one hot encode outputs
27 y_train = np_utils.to_categorical(y_train)
28 y_test = np_utils.to_categorical(y_test)
29 num_classes = y_test.shape[1]
30
31 # define a simple CNN model
32 def baseline_model():
33 # create model
34 model = Sequential()
35 model.add(Convolution2D(32, 5, 5, border_mode='valid', input_shape=(1, 28, 28), activation='relu'))
36 model.add(MaxPooling2D(pool_size=(2, 2)))
37 model.add(Dropout(0.2))
38 model.add(Flatten())
39 model.add(Dense(128, activation='relu'))
40 model.add(Dense(num_classes, activation='softmax'))
41 # Compile model
42 model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
43 return model
44
45 # build the model
46 model = baseline_model()
47
48 # Fit the model
49 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=10, batch_size=128, verbose=2)
50
51 # Final evaluation of the model
52 scores = model.evaluate(X_test, y_test, verbose=0)
53 print("CNN Error: %.2f%%" % (100-scores[1]*100))
结果：
1 ____________________________________________________________________________________________________ 2 Layer (type) Output Shape Param # Connected to 3 ==================================================================================================== 4 convolution2d_1 (Convolution2D) (None, 32, 24, 24) 832 convolution2d_input_1[0][0] 5 ____________________________________________________________________________________________________ 6 maxpooling2d_1 (MaxPooling2D) (None, 32, 12, 12) 0 convolution2d_1[0][0] 7 ____________________________________________________________________________________________________ 8 dropout_1 (Dropout) (None, 32, 12, 12) 0 maxpooling2d_1[0][0] 9 ____________________________________________________________________________________________________ 10 flatten_1 (Flatten) (None, 4608) 0 dropout_1[0][0] 11 ____________________________________________________________________________________________________ 12 dense_1 (Dense) (None, 128) 589952 flatten_1[0][0] 13 ____________________________________________________________________________________________________ 14 dense_2 (Dense) (None, 10) 1290 dense_1[0][0] 15 ==================================================================================================== 16 Total params: 592074 17 ____________________________________________________________________________________________________ 18 Train on 60000 samples, validate on 10000 samples 19 Epoch 1/10 20 32s - loss: 0.2412 - acc: 0.9318 - val_loss: 0.0754 - val_acc: 0.9766 21 Epoch 2/10 22 32s - loss: 0.0726 - acc: 0.9781 - val_loss: 0.0534 - val_acc: 0.9829 23 Epoch 3/10 24 32s - loss: 0.0497 - acc: 0.9852 - val_loss: 0.0391 - val_acc: 0.9858 25 Epoch 4/10 26 32s - loss: 0.0413 - acc: 0.9870 - val_loss: 0.0432 - val_acc: 0.9854 27 Epoch 5/10 28 34s - loss: 0.0323 - acc: 0.9897 - val_loss: 0.0375 - val_acc: 0.9869 29 Epoch 6/10 30 36s - loss: 0.0281 - acc: 0.9909 - val_loss: 0.0424 - val_acc: 0.9864 31 Epoch 7/10 32 36s - loss: 0.0223 - acc: 0.9930 - val_loss: 0.0328 - val_acc: 0.9893 33 Epoch 8/10 34 36s - loss: 0.0198 - acc: 0.9939 - val_loss: 0.0381 - val_acc: 0.9880 35 Epoch 9/10 36 36s - loss: 0.0156 - acc: 0.9954 - val_loss: 0.0347 - val_acc: 0.9884 37 Epoch 10/10 38 36s - loss: 0.0141 - acc: 0.9955 - val_loss: 0.0318 - val_acc: 0.9893 39 CNN Error: 1.07%
迭代的结果中，loss和acc为训练集的结果，val_loss和val_acc为验证机的结果。从结果上来看，效果不错，比100次迭代的MLP（1.46%）提升了0.39%，CNN的误差率为1.07%。这里的CNN的网络结构还是比较简单的，如果把CNN的结果再加几层，边复杂一代，结果是否还能提升？
3.Larger CNN
这一次我加了几层卷积层，代码：
1 # Larger CNN
2 import numpy
3 from keras.datasets import mnist
4 from keras.models import Sequential
5 from keras.layers import Dense
6 from keras.layers import Dropout
7 from keras.layers import Flatten
8 from keras.layers.convolutional import Convolution2D
9 from keras.layers.convolutional import MaxPooling2D
10 from keras.utils import np_utils
11
12 seed = 7
13 numpy.random.seed(seed)
14 # load data
15 (X_train, y_train), (X_test, y_test) = mnist.load_data()
16 # reshape to be [samples][pixels][width][height]
17 X_train = X_train.reshape(X_train.shape[0], 1, 28, 28).astype('float32')
18 X_test = X_test.reshape(X_test.shape[0], 1, 28, 28).astype('float32')
19 # normalize inputs from 0-255 to 0-1
20 X_train = X_train / 255
21 X_test = X_test / 255
22 # one hot encode outputs
23 y_train = np_utils.to_categorical(y_train)
24 y_test = np_utils.to_categorical(y_test)
25 num_classes = y_test.shape[1]
26 # define the larger model
27 def larger_model():
28 # create model
29 model = Sequential()
30 model.add(Convolution2D(30, 5, 5, border_mode='valid', input_shape=(1, 28, 28), activation='relu'))
31 model.add(MaxPooling2D(pool_size=(2, 2)))
32 model.add(Convolution2D(15, 3, 3, activation='relu'))
33 model.add(MaxPooling2D(pool_size=(2, 2)))
34 model.add(Dropout(0.2))
35 model.add(Flatten())
36 model.add(Dense(128, activation='relu'))
37 model.add(Dense(50, activation='relu'))
38 model.add(Dense(num_classes, activation='softmax'))
39 # Compile model
40 model.summary()
41 model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
42 return model
43 # build the model
44 model = larger_model()
45 # Fit the model
46 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=69, batch_size=200, verbose=2)
47 # Final evaluation of the model
48 scores = model.evaluate(X_test, y_test, verbose=0)
49 print("Large CNN Error: %.2f%%" % (100-scores[1]*100))
结果：
___________________________________________________________________________________________________ Layer (type) Output Shape Param # Connected to ==================================================================================================== convolution2d_1 (Convolution2D) (None, 30, 24, 24) 780 convolution2d_input_1[0][0] ____________________________________________________________________________________________________ maxpooling2d_1 (MaxPooling2D) (None, 30, 12, 12) 0 convolution2d_1[0][0] ____________________________________________________________________________________________________ convolution2d_2 (Convolution2D) (None, 15, 10, 10) 4065 maxpooling2d_1[0][0] ____________________________________________________________________________________________________ maxpooling2d_2 (MaxPooling2D) (None, 15, 5, 5) 0 convolution2d_2[0][0] ____________________________________________________________________________________________________ dropout_1 (Dropout) (None, 15, 5, 5) 0 maxpooling2d_2[0][0] ____________________________________________________________________________________________________ flatten_1 (Flatten) (None, 375) 0 dropout_1[0][0] ____________________________________________________________________________________________________ dense_1 (Dense) (None, 128) 48128 flatten_1[0][0] ____________________________________________________________________________________________________ dense_2 (Dense) (None, 50) 6450 dense_1[0][0] ____________________________________________________________________________________________________ dense_3 (Dense) (None, 10) 510 dense_2[0][0] ==================================================================================================== Total params: 59933 ____________________________________________________________________________________________________ Train on 60000 samples, validate on 10000 samples Epoch 1/10 34s - loss: 0.3789 - acc: 0.8796 - val_loss: 0.0811 - val_acc: 0.9742 Epoch 2/10 34s - loss: 0.0929 - acc: 0.9710 - val_loss: 0.0462 - val_acc: 0.9854 Epoch 3/10 35s - loss: 0.0684 - acc: 0.9786 - val_loss: 0.0376 - val_acc: 0.9869 Epoch 4/10 35s - loss: 0.0546 - acc: 0.9826 - val_loss: 0.0332 - val_acc: 0.9890 Epoch 5/10 35s - loss: 0.0467 - acc: 0.9856 - val_loss: 0.0289 - val_acc: 0.9897 Epoch 6/10 35s - loss: 0.0402 - acc: 0.9873 - val_loss: 0.0291 - val_acc: 0.9902 Epoch 7/10 34s - loss: 0.0369 - acc: 0.9880 - val_loss: 0.0233 - val_acc: 0.9924 Epoch 8/10 36s - loss: 0.0336 - acc: 0.9894 - val_loss: 0.0258 - val_acc: 0.9913 Epoch 9/10 39s - loss: 0.0317 - acc: 0.9899 - val_loss: 0.0219 - val_acc: 0.9926 Epoch 10/10 40s - loss: 0.0268 - acc: 0.9916 - val_loss: 0.0220 - val_acc: 0.9919 Large CNN Error: 0.81%
效果不错，现在的准确率是99.19%
4.最终版本
网络结构没变，只是在每一层后面加了dropout，结果居然有显著提升。一开始迭代500次，跑死我了，结果过拟合了，然后观察到69次的时候结果就已经很好了，就选择了迭代69次。
1 # Larger CNN for the MNIST Dataset
2 import numpy
3 from keras.datasets import mnist
4 from keras.models import Sequential
5 from keras.layers import Dense
6 from keras.layers import Dropout
7 from keras.layers import Flatten
8 from keras.layers.convolutional import Convolution2D
9 from keras.layers.convolutional import MaxPooling2D
10 from keras.utils import np_utils
11 import matplotlib.pyplot as plt
12 from keras.constraints import maxnorm
13 from keras.optimizers import SGD
14 # fix random seed for reproducibility
15 seed = 7
16 numpy.random.seed(seed)
17 # load data
18 (X_train, y_train), (X_test, y_test) = mnist.load_data()
19 # reshape to be [samples][pixels][width][height]
20 X_train = X_train.reshape(X_train.shape[0], 1, 28, 28).astype('float32')
21 X_test = X_test.reshape(X_test.shape[0], 1, 28, 28).astype('float32')
22 # normalize inputs from 0-255 to 0-1
23 X_train = X_train / 255
24 X_test = X_test / 255
25 # one hot encode outputs
26 y_train = np_utils.to_categorical(y_train)
27 y_test = np_utils.to_categorical(y_test)
28 num_classes = y_test.shape[1]
29 ###raw
30 # define the larger model
31 def larger_model():
32 # create model
33 model = Sequential()
34 model.add(Convolution2D(30, 5, 5, border_mode='valid', input_shape=(1, 28, 28), activation='relu'))
35 model.add(MaxPooling2D(pool_size=(2, 2)))
36 model.add(Dropout(0.4))
37 model.add(Convolution2D(15, 3, 3, activation='relu'))
38 model.add(MaxPooling2D(pool_size=(2, 2)))
39 model.add(Dropout(0.4))
40 model.add(Flatten())
41 model.add(Dense(128, activation='relu'))
42 model.add(Dropout(0.4))
43 model.add(Dense(50, activation='relu'))
44 model.add(Dropout(0.4))
45 model.add(Dense(num_classes, activation='softmax'))
46 # Compile model
47 model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
48 return model
49
50 # build the model
51 model = larger_model()
52 # Fit the model
53 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=200, batch_size=200, verbose=2)
54 # Final evaluation of the model
55 scores = model.evaluate(X_test, y_test, verbose=0)
56 print("Large CNN Error: %.2f%%" % (100-scores[1]*100))
结果：
1 ____________________________________________________________________________________________________ 2 Layer (type) Output Shape Param # Connected to 3 ==================================================================================================== 4 convolution2d_1 (Convolution2D) (None, 30, 24, 24) 780 convolution2d_input_1[0][0] 5 ____________________________________________________________________________________________________ 6 maxpooling2d_1 (MaxPooling2D) (None, 30, 12, 12) 0 convolution2d_1[0][0] 7 ____________________________________________________________________________________________________ 8 convolution2d_2 (Convolution2D) (None, 15, 10, 10) 4065 maxpooling2d_1[0][0] 9 ____________________________________________________________________________________________________ 10 maxpooling2d_2 (MaxPooling2D) (None, 15, 5, 5) 0 convolution2d_2[0][0] 11 ____________________________________________________________________________________________________ 12 dropout_1 (Dropout) (None, 15, 5, 5) 0 maxpooling2d_2[0][0] 13 ____________________________________________________________________________________________________ 14 flatten_1 (Flatten) (None, 375) 0 dropout_1[0][0] 15 ____________________________________________________________________________________________________ 16 dense_1 (Dense) (None, 128) 48128 flatten_1[0][0] 17 ____________________________________________________________________________________________________ 18 dense_2 (Dense) (None, 50) 6450 dense_1[0][0] 19 ____________________________________________________________________________________________________ 20 dense_3 (Dense) (None, 10) 510 dense_2[0][0] 21 ==================================================================================================== 22 Total params: 59933 23 ____________________________________________________________________________________________________ 24 Train on 60000 samples, validate on 10000 samples 25 Epoch 1/69 26 34s - loss: 0.4248 - acc: 0.8619 - val_loss: 0.0832 - val_acc: 0.9746 27 Epoch 2/69 28 35s - loss: 0.1147 - acc: 0.9638 - val_loss: 0.0518 - val_acc: 0.9831 29 Epoch 3/69 30 35s - loss: 0.0887 - acc: 0.9719 - val_loss: 0.0452 - val_acc: 0.9855 31 、、、 32 Epoch 66/69 33 38s - loss: 0.0134 - acc: 0.9955 - val_loss: 0.0211 - val_acc: 0.9943 34 Epoch 67/69 35 38s - loss: 0.0114 - acc: 0.9960 - val_loss: 0.0171 - val_acc: 0.9950 36 Epoch 68/69 37 38s - loss: 0.0116 - acc: 0.9959 - val_loss: 0.0192 - val_acc: 0.9956 38 Epoch 69/69 39 38s - loss: 0.0132 - acc: 0.9969 - val_loss: 0.0188 - val_acc: 0.9978 40 Large CNN Error: 0.22% 41 42 real 41m47.350s 43 user 157m51.145s 44 sys 6m5.829s
这是目前的最好结果，99.78%，然而还有很多地方可以提升，下次准确率提高了再来更 。
总结：
1.CNN在图像识别上确实比传统的MLP有优势，比传统的机器学习算法也有优势（不过也有通过随机森林取的很好效果的）
2.加深网络结构，即多加几层卷积层有助于提升准确率，但是也能大大降低运行速度
3.适当加Dropout可以提高准确率
4.激活函数最好，算了，直接说就选relu吧，没有为啥，就因为relu能避免梯度消散这一点应该选它，训练速度快等其他优点下次专门总结一篇文章再说吧。
5.迭代次数不是越多越好，很可能会过拟合，自己可以做一个收敛曲线，keras里可以用history函数plot一下，看算法是否收敛，还是发散。
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