这篇文章介绍如何使用Michael Nielsen 用python写的卷积神经网络代码，以及比较卷积神经网络和普通神经网络预测的效果。
这个例子是经典的识别MNIST手写体的AI程序。如下面这些手写数字，分别代表504192。这个程序会对这样的样本进行训练，并在测试集上验证正确率。
至于卷积神经网络的原理，我以后会单独写一篇文章介绍。
准备：
- 安装 virtualenv
pip install virtualenv- 创建env
virtualenv neural
cd neural
source bin/activate- 安装 Theano库
pip install Theano- 下载 代码
git clone https://github.com/mnielsen/neural-networks-and-deep-learning.git卷积神经网络在src/network3.py里。因为在作者写完代码后，Theano库又有更新, 且downsample被废弃，所以network3.py需要做如2处修改：'＃'后面的为原来的代码，不带'#'的是修改后的代码。
代码语言：javascript复制#from theano.tensor.signal import downsample
from theano.tensor.signal.pool import pool_2d
...
#pooled_out = downsample.max_pool_2d(input=conv_out, ds=self.poolsize, ignore_border=True)
pooled_out = pool_2d(input=conv_out, ws=self.poolsize, ignore_border=True)- 进入python
cd neural-networks-and-deep-learning/src
phtyon普通神经网络
- 使用普通的full-connected layer模型训练 各种参数如下。每个参数的含义，我以后会专门写文章介绍，也可参考作者的书。
single hidden layer
100 hidden neurons
60 epochs
learning rate : η=0.1
mini-batch size : 10
no regularization- 先用普通神经网络训练，执行命令:
>>> import network3
>>> from network3 import Network
>>> from network3 import ConvPoolLayer, FullyConnectedLayer, SoftmaxLayer
>>> training_data, validation_data, test_data = network3.load_data_shared()
>>> mini_batch_size = 10
>>> net = Network([
FullyConnectedLayer(n_in=784, n_out=100),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(training_data, 60, mini_batch_size, 0.1,
validation_data, test_data)- 执行结果
Training mini-batch number 0
Training mini-batch number 1000
Training mini-batch number 2000
Training mini-batch number 3000
Training mini-batch number 4000
Epoch 0: validation accuracy 92.62%
This is the best validation accuracy to date.
The corresponding test accuracy is 92.00%
Training mini-batch number 5000
Training mini-batch number 6000
Training mini-batch number 7000
Training mini-batch number 8000
Training mini-batch number 9000
Epoch 1: validation accuracy 94.64%
This is the best validation accuracy to date.
The corresponding test accuracy is 94.10%
...
Training mini-batch number 295000
Training mini-batch number 296000
Training mini-batch number 297000
Training mini-batch number 298000
Training mini-batch number 299000
Epoch 59: validation accuracy 97.76%
This is the best validation accuracy to date.
The corresponding test accuracy is 97.79%
Finished training network.
Best validation accuracy of 97.76% obtained at iteration 299999
Corresponding test accuracy of 97.79%准确率为97.79%，或者说错误率2.21%
卷积神经网络
- 使用卷积模型训练 各种参数如下：
local receptive fields: 5x5
stride length : 1
feature maps : 20
max-pooling layer
pooling windows: 2x2- 执行命令
>>> net = Network([
ConvPoolLayer(image_shape=(mini_batch_size, 1, 28, 28),
filter_shape=(20, 1, 5, 5),
poolsize=(2, 2)),
FullyConnectedLayer(n_in=20*12*12, n_out=100),
SoftmaxLayer(n_in=100, n_out=10)], mini_batch_size)
>>> net.SGD(training_data, 60, mini_batch_size, 0.1,
validation_data, test_data)- 输出
Training mini-batch number 0
Training mini-batch number 1000
Training mini-batch number 2000
Training mini-batch number 3000
Training mini-batch number 4000
Epoch 0: validation accuracy 94.18%
This is the best validation accuracy to date.
The corresponding test accuracy is 93.43%
Training mini-batch number 5000
Training mini-batch number 6000
Training mini-batch number 7000
Training mini-batch number 8000
Training mini-batch number 9000
Epoch 1: validation accuracy 96.12%
This is the best validation accuracy to date.
The corresponding test accuracy is 95.85%
...
Training mini-batch number 295000
Training mini-batch number 296000
Training mini-batch number 297000
Training mini-batch number 298000
Training mini-batch number 299000
Epoch 59: validation accuracy 98.74%
Finished training network.
Best validation accuracy of 98.74% obtained at iteration 214999
Corresponding test accuracy of 98.84%准确率为98.84%，或者说错误率1.16%. 错误率几乎降低了一半！
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卷积神经网络的原理
