如何用卷积神经网络CNN识别手写数字集？

　　前几天用CNN识别手写数字集，后来看到kaggle上有一个比赛是识别手写数字集的，已经进行了一年多了，目前有1179个有效提交，最高的是100%，我做了一下，用keras做的，一开始用最简单的MLP，准确率只有98.19%，然后不断改进，现在是99.78%，然而我看到排名第一是100%，心碎 = =，于是又改进了一版，现在把最好的结果记录一下，如果提升了再来更新。

　　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：

# 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 plot17 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：

# 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 = 711 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 / 25520 X_test = X_test / 25521 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 model35 36 # 建立模型37 model = baseline_model()38 39 # Fit40 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=10, batch_size=200, verbose=2)41 42 #Evaluation43 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：

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 samples10 Epoch 1/1011 3s - loss: 0.2791 - acc: 0.9203 - val_loss: 0.1420 - val_acc: 0.957912 Epoch 2/1013 3s - loss: 0.1122 - acc: 0.9679 - val_loss: 0.0992 - val_acc: 0.969914 Epoch 3/1015 3s - loss: 0.0724 - acc: 0.9790 - val_loss: 0.0784 - val_acc: 0.974516 Epoch 4/1017 3s - loss: 0.0509 - acc: 0.9853 - val_loss: 0.0774 - val_acc: 0.977318 Epoch 5/1019 3s - loss: 0.0366 - acc: 0.9898 - val_loss: 0.0626 - val_acc: 0.979420 Epoch 6/1021 3s - loss: 0.0265 - acc: 0.9930 - val_loss: 0.0639 - val_acc: 0.979722 Epoch 7/1023 3s - loss: 0.0185 - acc: 0.9956 - val_loss: 0.0611 - val_acc: 0.981124 Epoch 8/1025 3s - loss: 0.0150 - acc: 0.9967 - val_loss: 0.0616 - val_acc: 0.981626 Epoch 9/1027 4s - loss: 0.0107 - acc: 0.9980 - val_loss: 0.0604 - val_acc: 0.982128 Epoch 10/1029 4s - loss: 0.0073 - acc: 0.9988 - val_loss: 0.0611 - val_acc: 0.981930 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：

#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 Convolution2D10 from keras.layers.convolutional import MaxPooling2D11 from keras.utils import np_utils12 13 seed = 714 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 0-123 X_train = X_train / 25524 X_test = X_test / 25525 26 # one hot encode outputs27 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 model32 def baseline_model():33     # create model34     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 model42     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])43     return model44 45 # build the model46 model = baseline_model()47 48 # Fit the model49 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 model52 scores = model.evaluate(X_test, y_test, verbose=0)53 print("CNN Error: %.2f%%" % (100-scores[1]*100))

　　结果：

____________________________________________________________________________________________________ 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: 59207417 ____________________________________________________________________________________________________18 Train on 60000 samples, validate on 10000 samples19 Epoch 1/1020 32s - loss: 0.2412 - acc: 0.9318 - val_loss: 0.0754 - val_acc: 0.976621 Epoch 2/1022 32s - loss: 0.0726 - acc: 0.9781 - val_loss: 0.0534 - val_acc: 0.982923 Epoch 3/1024 32s - loss: 0.0497 - acc: 0.9852 - val_loss: 0.0391 - val_acc: 0.985825 Epoch 4/1026 32s - loss: 0.0413 - acc: 0.9870 - val_loss: 0.0432 - val_acc: 0.985427 Epoch 5/1028 34s - loss: 0.0323 - acc: 0.9897 - val_loss: 0.0375 - val_acc: 0.986929 Epoch 6/1030 36s - loss: 0.0281 - acc: 0.9909 - val_loss: 0.0424 - val_acc: 0.986431 Epoch 7/1032 36s - loss: 0.0223 - acc: 0.9930 - val_loss: 0.0328 - val_acc: 0.989333 Epoch 8/1034 36s - loss: 0.0198 - acc: 0.9939 - val_loss: 0.0381 - val_acc: 0.988035 Epoch 9/1036 36s - loss: 0.0156 - acc: 0.9954 - val_loss: 0.0347 - val_acc: 0.988437 Epoch 10/1038 36s - loss: 0.0141 - acc: 0.9955 - val_loss: 0.0318 - val_acc: 0.989339 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：

# 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 MaxPooling2D10 from keras.utils import np_utils1112 seed = 713 numpy.random.seed(seed)14 # load data15 (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 0-120 X_train = X_train / 25521 X_test = X_test / 25522 # one hot encode outputs23 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 model27 def larger_model():28     # create model29     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 model40     model.summary()41     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])42     return model43 # build the model44 model = larger_model()45 # Fit the model46 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 model48 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 samplesEpoch 1/1034s - loss: 0.3789 - acc: 0.8796 - val_loss: 0.0811 - val_acc: 0.9742Epoch 2/1034s - loss: 0.0929 - acc: 0.9710 - val_loss: 0.0462 - val_acc: 0.9854Epoch 3/1035s - loss: 0.0684 - acc: 0.9786 - val_loss: 0.0376 - val_acc: 0.9869Epoch 4/1035s - loss: 0.0546 - acc: 0.9826 - val_loss: 0.0332 - val_acc: 0.9890Epoch 5/1035s - loss: 0.0467 - acc: 0.9856 - val_loss: 0.0289 - val_acc: 0.9897Epoch 6/1035s - loss: 0.0402 - acc: 0.9873 - val_loss: 0.0291 - val_acc: 0.9902Epoch 7/1034s - loss: 0.0369 - acc: 0.9880 - val_loss: 0.0233 - val_acc: 0.9924Epoch 8/1036s - loss: 0.0336 - acc: 0.9894 - val_loss: 0.0258 - val_acc: 0.9913Epoch 9/1039s - loss: 0.0317 - acc: 0.9899 - val_loss: 0.0219 - val_acc: 0.9926Epoch 10/1040s - loss: 0.0268 - acc: 0.9916 - val_loss: 0.0220 - val_acc: 0.9919Large 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。

# 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 MaxPooling2D10 from keras.utils import np_utils11 import matplotlib.pyplot as plt12 from keras.constraints import maxnorm13 from keras.optimizers import SGD14 # fix random seed for reproducibility15 seed = 716 numpy.random.seed(seed)17 # load data18 (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 0-123 X_train = X_train / 25524 X_test = X_test / 25525 # one hot encode outputs26 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 ###raw30 # define the larger model31 def larger_model():32     # create model33     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 model47     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])48     return model49 50 # build the model51 model = larger_model()52 # Fit the model53 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 model55 scores = model.evaluate(X_test, y_test, verbose=0)56 print("Large CNN Error: %.2f%%" % (100-scores[1]*100))

　结果：

____________________________________________________________________________________________________ 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: 5993323 ____________________________________________________________________________________________________24 Train on 60000 samples, validate on 10000 samples25 Epoch 1/6926 34s - loss: 0.4248 - acc: 0.8619 - val_loss: 0.0832 - val_acc: 0.974627 Epoch 2/6928 35s - loss: 0.1147 - acc: 0.9638 - val_loss: 0.0518 - val_acc: 0.983129 Epoch 3/6930 35s - loss: 0.0887 - acc: 0.9719 - val_loss: 0.0452 - val_acc: 0.985531 、、、32 Epoch 66/6933 38s - loss: 0.0134 - acc: 0.9955 - val_loss: 0.0211 - val_acc: 0.994334 Epoch 67/6935 38s - loss: 0.0114 - acc: 0.9960 - val_loss: 0.0171 - val_acc: 0.995036 Epoch 68/6937 38s - loss: 0.0116 - acc: 0.9959 - val_loss: 0.0192 - val_acc: 0.994238 Epoch 69/6939 38s - loss: 0.0132 - acc: 0.9958 - val_loss: 0.0188 - val_acc: 0.997840 Large CNN Error: 0.22%41 42 real    41m47.350s43 user    157m51.145s44 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。