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： 复制代码
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() 复制代码 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： 复制代码
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(\输出错误率 复制代码
结果： 复制代码
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% 复制代码
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： 复制代码 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()