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

 # Plot mnist dataset

 from keras.datasets import mnist

 import matplotlib.pyplot as plt

 # load the MNIST dataset

 (X_train, y_train), (X_test, y_test) = mnist.load_data()

 # plot 4 images as gray scale

 plt.subplot(221)

 plt.imshow(X_train[0], cmap=plt.get_cmap('PuBuGn_r'))

 plt.subplot(222)

 plt.imshow(X_train[1], cmap=plt.get_cmap('PuBuGn_r'))

 plt.subplot(223)

 plt.imshow(X_train[2], cmap=plt.get_cmap('PuBuGn_r'))

 plt.subplot(224)

 plt.imshow(X_train[3], cmap=plt.get_cmap('PuBuGn_r'))

 # show the plot

 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

 # Baseline MLP for MNIST dataset

 import numpy

 from keras.datasets import mnist

 from keras.models import Sequential

 from keras.layers import Dense

 from keras.layers import Dropout

 from keras.utils import np_utils

 seed = 7

 numpy.random.seed(seed)

 #加载数据

 (X_train, y_train), (X_test, y_test) = mnist.load_data()

 num_pixels = X_train.shape[1] * X_train.shape[2]

 X_train = X_train.reshape(X_train.shape[0], num_pixels).astype('float32')

 X_test = X_test.reshape(X_test.shape[0], num_pixels).astype('float32')

 X_train = X_train / 255

 X_test = X_test / 255

 # 对输出进行one hot编码

 y_train = np_utils.to_categorical(y_train)

 y_test = np_utils.to_categorical(y_test)

 num_classes = y_test.shape[1]

 # MLP模型

 def baseline_model():

     model = Sequential()

     model.add(Dense(num_pixels, input_dim=num_pixels, init='normal', activation='relu'))

     model.add(Dense(num_classes, init='normal', activation='softmax'))

     model.summary()

     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

     return model

 # 建立模型

 model = baseline_model()

 # Fit

 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=10, batch_size=200, verbose=2)

 #Evaluation

 scores = model.evaluate(X_test, y_test, verbose=0)

 print("Baseline Error: %.2f%%" % (100-scores[1]*100))#输出错误率

　　结果：

 Layer (type)                     Output Shape          Param #     Connected to

 ====================================================================================================

 dense_1 (Dense)                  (None, 784)           615440      dense_input_1[0][0]

 ____________________________________________________________________________________________________

 dense_2 (Dense)                  (None, 10)            7850        dense_1[0][0]

 ====================================================================================================

 Total params: 623290

 ____________________________________________________________________________________________________

 Train on 60000 samples, validate on 10000 samples

 Epoch 1/10

 3s - loss: 0.2791 - acc: 0.9203 - val_loss: 0.1420 - val_acc: 0.9579

 Epoch 2/10

 3s - loss: 0.1122 - acc: 0.9679 - val_loss: 0.0992 - val_acc: 0.9699

 Epoch 3/10

 3s - loss: 0.0724 - acc: 0.9790 - val_loss: 0.0784 - val_acc: 0.9745

 Epoch 4/10

 3s - loss: 0.0509 - acc: 0.9853 - val_loss: 0.0774 - val_acc: 0.9773

 Epoch 5/10

 3s - loss: 0.0366 - acc: 0.9898 - val_loss: 0.0626 - val_acc: 0.9794

 Epoch 6/10

 3s - loss: 0.0265 - acc: 0.9930 - val_loss: 0.0639 - val_acc: 0.9797

 Epoch 7/10

 3s - loss: 0.0185 - acc: 0.9956 - val_loss: 0.0611 - val_acc: 0.9811

 Epoch 8/10

 3s - loss: 0.0150 - acc: 0.9967 - val_loss: 0.0616 - val_acc: 0.9816

 Epoch 9/10

 4s - loss: 0.0107 - acc: 0.9980 - val_loss: 0.0604 - val_acc: 0.9821

 Epoch 10/10

 4s - loss: 0.0073 - acc: 0.9988 - val_loss: 0.0611 - val_acc: 0.9819

 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

 #Simple CNN

 import numpy

 from keras.datasets import mnist

 from keras.models import Sequential

 from keras.layers import Dense

 from keras.layers import Dropout

 from keras.layers import Flatten

 from keras.layers.convolutional import Convolution2D

 from keras.layers.convolutional import MaxPooling2D

 from keras.utils import np_utils

 seed = 7

 numpy.random.seed(seed)

 #加载数据

 (X_train, y_train), (X_test, y_test) = mnist.load_data()

 # reshape to be [samples][channels][width][height]

 X_train = X_train.reshape(X_train.shape[0], 1, 28, 28).astype('float32')

 X_test = X_test.reshape(X_test.shape[0], 1, 28, 28).astype('float32')

 # normalize inputs from 0-255 to 0-1

 X_train = X_train / 255

 X_test = X_test / 255

 # one hot encode outputs

 y_train = np_utils.to_categorical(y_train)

 y_test = np_utils.to_categorical(y_test)

 num_classes = y_test.shape[1]

 # define a simple CNN model

 def baseline_model():

     # create model

     model = Sequential()

     model.add(Convolution2D(32, 5, 5, border_mode='valid', input_shape=(1, 28, 28), activation='relu'))

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

     model.add(Dropout(0.2))

     model.add(Flatten())

     model.add(Dense(128, activation='relu'))

     model.add(Dense(num_classes, activation='softmax'))

     # Compile model

     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

     return model

 # build the model

 model = baseline_model()

 # Fit the model

 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=10, batch_size=128, verbose=2)

 # Final evaluation of the model

 scores = model.evaluate(X_test, y_test, verbose=0)

 print("CNN Error: %.2f%%" % (100-scores[1]*100))

　　结果：

 ____________________________________________________________________________________________________

 Layer (type)                     Output Shape          Param #     Connected to

 ====================================================================================================

 convolution2d_1 (Convolution2D)  (None, 32, 24, 24)    832         convolution2d_input_1[0][0]

 ____________________________________________________________________________________________________

 maxpooling2d_1 (MaxPooling2D)    (None, 32, 12, 12)    0           convolution2d_1[0][0]

 ____________________________________________________________________________________________________

 dropout_1 (Dropout)              (None, 32, 12, 12)    0           maxpooling2d_1[0][0]

 ____________________________________________________________________________________________________

 flatten_1 (Flatten)              (None, 4608)          0           dropout_1[0][0]

 ____________________________________________________________________________________________________

 dense_1 (Dense)                  (None, 128)           589952      flatten_1[0][0]

 ____________________________________________________________________________________________________

 dense_2 (Dense)                  (None, 10)            1290        dense_1[0][0]

 ====================================================================================================

 Total params: 592074

 ____________________________________________________________________________________________________

 Train on 60000 samples, validate on 10000 samples

 Epoch 1/10

 32s - loss: 0.2412 - acc: 0.9318 - val_loss: 0.0754 - val_acc: 0.9766

 Epoch 2/10

 32s - loss: 0.0726 - acc: 0.9781 - val_loss: 0.0534 - val_acc: 0.9829

 Epoch 3/10

 32s - loss: 0.0497 - acc: 0.9852 - val_loss: 0.0391 - val_acc: 0.9858

 Epoch 4/10

 32s - loss: 0.0413 - acc: 0.9870 - val_loss: 0.0432 - val_acc: 0.9854

 Epoch 5/10

 34s - loss: 0.0323 - acc: 0.9897 - val_loss: 0.0375 - val_acc: 0.9869

 Epoch 6/10

 36s - loss: 0.0281 - acc: 0.9909 - val_loss: 0.0424 - val_acc: 0.9864

 Epoch 7/10

 36s - loss: 0.0223 - acc: 0.9930 - val_loss: 0.0328 - val_acc: 0.9893

 Epoch 8/10

 36s - loss: 0.0198 - acc: 0.9939 - val_loss: 0.0381 - val_acc: 0.9880

 Epoch 9/10

 36s - loss: 0.0156 - acc: 0.9954 - val_loss: 0.0347 - val_acc: 0.9884

 Epoch 10/10

 36s - loss: 0.0141 - acc: 0.9955 - val_loss: 0.0318 - val_acc: 0.9893

 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

 import numpy

 from keras.datasets import mnist

 from keras.models import Sequential

 from keras.layers import Dense

 from keras.layers import Dropout

 from keras.layers import Flatten

 from keras.layers.convolutional import Convolution2D

 from keras.layers.convolutional import MaxPooling2D

 from keras.utils import np_utils

 seed = 7

 numpy.random.seed(seed)

 # load data

 (X_train, y_train), (X_test, y_test) = mnist.load_data()

 # reshape to be [samples][pixels][width][height]

 X_train = X_train.reshape(X_train.shape[0], 1, 28, 28).astype('float32')

 X_test = X_test.reshape(X_test.shape[0], 1, 28, 28).astype('float32')

 # normalize inputs from 0-255 to 0-1

 X_train = X_train / 255

 X_test = X_test / 255

 # one hot encode outputs

 y_train = np_utils.to_categorical(y_train)

 y_test = np_utils.to_categorical(y_test)

 num_classes = y_test.shape[1]

 # define the larger model

 def larger_model():

     # create model

     model = Sequential()

     model.add(Convolution2D(30, 5, 5, border_mode='valid', input_shape=(1, 28, 28), activation='relu'))

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

     model.add(Convolution2D(15, 3, 3, activation='relu'))

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

     model.add(Dropout(0.2))

     model.add(Flatten())

     model.add(Dense(128, activation='relu'))

     model.add(Dense(50, activation='relu'))

     model.add(Dense(num_classes, activation='softmax'))

     # Compile model

     model.summary()

     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

     return model

 # build the model

 model = larger_model()

 # Fit the model

 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=69, batch_size=200, verbose=2)

 # Final evaluation of the model

 scores = model.evaluate(X_test, y_test, verbose=0)

 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。

 # Larger CNN for the MNIST Dataset

 import numpy

 from keras.datasets import mnist

 from keras.models import Sequential

 from keras.layers import Dense

 from keras.layers import Dropout

 from keras.layers import Flatten

 from keras.layers.convolutional import Convolution2D

 from keras.layers.convolutional import MaxPooling2D

 from keras.utils import np_utils

 import matplotlib.pyplot as plt

 from keras.constraints import maxnorm

 from keras.optimizers import SGD

 # fix random seed for reproducibility

 seed = 7

 numpy.random.seed(seed)

 # load data

 (X_train, y_train), (X_test, y_test) = mnist.load_data()

 # reshape to be [samples][pixels][width][height]

 X_train = X_train.reshape(X_train.shape[0], 1, 28, 28).astype('float32')

 X_test = X_test.reshape(X_test.shape[0], 1, 28, 28).astype('float32')

 # normalize inputs from 0-255 to 0-1

 X_train = X_train / 255

 X_test = X_test / 255

 # one hot encode outputs

 y_train = np_utils.to_categorical(y_train)

 y_test = np_utils.to_categorical(y_test)

 num_classes = y_test.shape[1]

 ###raw

 # define the larger model

 def larger_model():

     # create model

     model = Sequential()

     model.add(Convolution2D(30, 5, 5, border_mode='valid', input_shape=(1, 28, 28), activation='relu'))

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

     model.add(Dropout(0.4))

     model.add(Convolution2D(15, 3, 3, activation='relu'))

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

     model.add(Dropout(0.4))

     model.add(Flatten())

     model.add(Dense(128, activation='relu'))

     model.add(Dropout(0.4))

     model.add(Dense(50, activation='relu'))

     model.add(Dropout(0.4))

     model.add(Dense(num_classes, activation='softmax'))

     # Compile model

     model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

     return model

 # build the model

 model = larger_model()

 # Fit the model

 model.fit(X_train, y_train, validation_data=(X_test, y_test), nb_epoch=200, batch_size=200, verbose=2)

 # Final evaluation of the model

 scores = model.evaluate(X_test, y_test, verbose=0)

 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 1/69

 34s - loss: 0.4248 - acc: 0.8619 - val_loss: 0.0832 - val_acc: 0.9746

 Epoch 2/69

 35s - loss: 0.1147 - acc: 0.9638 - val_loss: 0.0518 - val_acc: 0.9831

 Epoch 3/69

 35s - loss: 0.0887 - acc: 0.9719 - val_loss: 0.0452 - val_acc: 0.9855

 、、、

 Epoch 66/69

 38s - loss: 0.0134 - acc: 0.9955 - val_loss: 0.0211 - val_acc: 0.9943

 Epoch 67/69

 38s - loss: 0.0114 - acc: 0.9960 - val_loss: 0.0171 - val_acc: 0.9950

 Epoch 68/69

 38s - loss: 0.0116 - acc: 0.9959 - val_loss: 0.0192 - val_acc: 0.9956

 Epoch 69/69

 38s - loss: 0.0132 - acc: 0.9969 - val_loss: 0.0188 - val_acc: 0.9978

 Large CNN Error: 0.22%

 real    41m47.350s

 user    157m51.145s

 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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