CNN卷积神经网络

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CNN卷积神经网络

分类： 卷积神经网络CNN2015-04-23
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cnn

目录(?)[+]

CNN是一种多层神经网络，基于人工神经网络，在人工神经网络前，用滤波器进行特征抽取，使用卷积核作为特征抽取器，自动训练特征抽取器，就是说卷积核以及阈值参数这些都需要由网络去学习。

图像可以直接作为网络的输入，避免了传统识别算法中复杂的特征提取和数据重建过程。

一般卷积神经网络的结构：



前面feature extraction部分体现了CNN的特点，feature extraction部分最后的输出可以作为分类器的输入。这个分类器你可以用softmax或RBF等等。

局部感受野与权值共享

权值共享指每一个map都由一个卷积核去做卷积得到。
权值共享减少了权值数量，降低了网络复杂度。

Conv layer

第一个卷积层对原输入图像进行卷积，后面的是对前一个卷积-采样层的S层的输出map进行卷积。

假设层为s层特征图像Xil-1（pooling层），l层为卷积C层，卷积结果为Xjl



参数kij为两层间卷积核（滤波器，kernals），由于s层有m个特征，c层有n个特征，所以一共有m*n个卷积核。bj为卷基层每个结果特征对应的一个偏置项bias，f为非线性变换函数sigmoid函数；Mj为选择s层特征输入的个数，即选择多少个s层的图像特征作为输入；由于选择s层的特征个数方法不同，主要分为三种卷积选择方式
1、全部选择：
s层的全部特征都作为输入， Mj=m。如上图所示。
2、自动稀疏选择：
在卷积计算前加入稀疏稀疏aij，通过稀疏规则限制（论文后面），使算法自动选取部分s层特征作为输入，具体个数不确定。



3、部分选择：
按照一定的规则，固定的选取2个或者3个作为输入。

Subsampling layer

下采样降低feature map的空间分辨率，从而实现一定程度的shift 和 distortion invariance。利用图像局部相关性的原理，对图像进行子抽样，可以减少数据处理量同时保留有用信息。这个过程也被称为pooling，常用pooling 有两种：

mean-pooling、max-pooling。



down(Xjl-1)表示下采样操作，就是对一个小区域进行pooling操作，使数据降维。

有的算法还会对mean-pooling、max-pooling后的输出进行非线性映射



f可以是sigmoid函数。

输出层

最后一个卷积-采样层的输出可作为输出层的输入，输出层是全连接层，可采用svm、bp算法、softmax等分类算法。

以LeNet5为例，其结构如下：

C1,C3,C5 : Convolutional layer.

5 × 5 Convolution matrix.

S2 , S4 : Subsampling layer.

Subsampling by factor 2.

F6 : Fully connected layer

OUTPUT : RBF

C层和S层成对出现，C承担特征抽取，S承担抗变形。C元中涉及两个重要参数，即感受野与阈值参数，前者确定输入连接的数目，后者则控制对特征子模式的反应程度。



C1层是一个卷积层（通过卷积运算，可以增强图像的某种特征，并且降低噪音），由6个特征图Feature Map构成。Feature Map中每个神经元与输入中5*5的邻域相连。特征图的大小为28*28。C1有156个可训练参数（每个滤波器5*5=25个unit参数和一个bias参数，一共6个滤波器，共(5*5+1)*6=156个参数），共156*(28*28)=122,304个连接。

S2层是一个下采样层，有6个14*14的特征图。特征图中的每个单元与C1中相对应特征图的2*2邻域相连接。S2层每个单元的4个输入相加，乘以一个可训练参数，再加上一个可训练偏置。结果通过sigmoid函数计算。可训练系数和偏置控制着sigmoid函数的非线性程度。如果系数比较小，那么运算近似于线性运算，亚采样相当于模糊图像。如果系数比较大，根据偏置的大小亚采样可以被看成是有噪声的“或”运算或者有噪声的“与”运算。每个单元的2*2感受野并不重叠，因此S2中每个特征图的大小是C1中特征图大小的1/4（行和列各1/2）。S2层有12个可训练参数和5880个连接。

C3层也是一个卷积层，它同样通过5x5的卷积核去卷积层S2，然后得到的特征map就只有10x10个神经元，但是它有16种不同的卷积核，所以就存在16个特征map了。这里需要注意的一点是：C3中的每个特征map是连接到S2中的所有6个或者几个特征map的，表示本层的特征map是上一层提取到的特征map的不同组合。



S4层是一个下采样层，由16个5*5大小的特征图构成。特征图中的每个单元与C3中相应特征图的2*2邻域相连接，跟C1和S2之间的连接一样。S4层有32个可训练参数（每个特征图1个因子和一个偏置）和2000个连接。

C5层是一个卷积层，有120个特征图。每个单元与S4层的全部16个单元的5*5邻域相连。由于S4层特征图的大小也为5*5（同滤波器一样），故C5特征图的大小为1*1：这构成了S4和C5之间的全连接。之所以仍将C5标示为卷积层而非全相联层，是因为如果LeNet-5的输入变大，而其他的保持不变，那么此时特征图的维数就会比1*1大。C5层有48120个可训练连接。

F6层有84个单元（之所以选这个数字的原因来自于输出层的设计），与C5层全相连。有10164个可训练参数。如同经典神经网络，F6层计算输入向量和权重向量之间的点积，再加上一个偏置。然后将其传递给sigmoid函数产生单元i的一个状态。

最后，输出层由欧式径向基函数（Euclidean Radial Basis Function）单元组成，每类一个单元，每个有84个输入。换句话说，每个输出RBF单元计算输入向量和参数向量之间的欧式距离。输入离参数向量越远，RBF输出的越大。一个RBF输出可以被理解为衡量输入模式和与RBF相关联类的一个模型的匹配程度的惩罚项。用概率术语来说，RBF输出可以被理解为F6层配置空间的高斯分布的负log-likelihood。给定一个输入模式，损失函数应能使得F6的配置与RBF参数向量（即模式的期望分类）足够接近。这些单元的参数是人工选取并保持固定的（至少初始时候如此）。这些参数向量的成分被设为-1或1。虽然这些参数可以以-1和1等概率的方式任选，或者构成一个纠错码，但是被设计成一个相应字符类的7*12大小（即84）的格式化图片。

卷积核和偏置的初始化

卷积核和偏置在开始时要随机初始化，这些参数是要在训练过程中学习的。

CNN涉及的算法

这张图来自博客http://blog.csdn.net/wds555/article/details/44100581，总结得很好

CNN网络算法流程

/***********训练阶段************/
/*********************************/
for t = 0; t < repeat; t++)
{

epochsNum = trainset.size() / batchSize;

for i = 0; i < epochsNum; i++
{
随机抽取batchSize个[0,size)的数batch[batchSize]作为本次批量训练的训练集 //size为总体trainSet的大小
for j=0;j<batchSize;j++
{
train(trainset.getRecord(batch[j]))
}
跑完一个batch后更新权重updateParas();

}
动态调整准学习速率
}

训练单个样本
train(Record record) {

forward(record);

boolean result = backPropagation(record);

return result;

}

反向传输

*/

private boolean backPropagation(Record record) {

boolean result = setOutLayerErrors(record);

setHiddenLayerErrors();

return result;

}

[python] view
plaincopy

"""This tutorial introduces the LeNet5 neural network architecture

using Theano. LeNet5 is a convolutional neural network, good for

classifying images. This tutorial shows how to build the architecture,

and comes with all the hyper-parameters you need to reproduce the

paper's MNIST results.

This implementation simplifies the model in the following ways:

- LeNetConvPool doesn't implement location-specific gain and bias parameters

- LeNetConvPool doesn't implement pooling by average, it implements pooling

by max.

- Digit classification is implemented with a logistic regression rather than

an RBF network

- LeNet5 was not fully-connected convolutions at second layer

References:

- Y. LeCun, L. Bottou, Y. Bengio and P. Haffner:

Gradient-Based Learning Applied to Document

Recognition, Proceedings of the IEEE, 86(11):2278-2324, November 1998.

http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf

"""

import os

import sys

import time



import numpy



import theano

import theano.tensor as T

from theano.tensor.signal import downsample

from theano.tensor.nnet import conv



from logistic_sgd import LogisticRegression, load_data

from mlp import HiddenLayer





class LeNetConvPoolLayer(object):

"""Pool Layer of a convolutional network """



def __init__(self, rng, input, filter_shape, image_shape, poolsize=(2, 2)):

"""

Allocate a LeNetConvPoolLayer with shared variable internal parameters.

:type rng: numpy.random.RandomState

:param rng: a random number generator used to initialize weights

:type input: theano.tensor.dtensor4

:param input: symbolic image tensor, of shape image_shape

:type filter_shape: tuple or list of length 4

:param filter_shape: (number of filters, num input feature maps,

filter height, filter width)

:type image_shape: tuple or list of length 4

:param image_shape: (batch size, num input feature maps,

image height, image width)

:type poolsize: tuple or list of length 2

:param poolsize: the downsampling (pooling) factor (#rows, #cols)

"""



assert image_shape[1] == filter_shape[1]

self.input = input



# there are "num input feature maps * filter height * filter width"

# inputs to each hidden unit

fan_in = numpy.prod(filter_shape[1:])

# each unit in the lower layer receives a gradient from:

# "num output feature maps * filter height * filter width" /

# pooling size

fan_out = (filter_shape[0] * numpy.prod(filter_shape[2:]) /

numpy.prod(poolsize))

# initialize weights with random weights

W_bound = numpy.sqrt(6. / (fan_in + fan_out))

self.W = theano.shared(

numpy.asarray(

rng.uniform(low=-W_bound, high=W_bound, size=filter_shape),

dtype=theano.config.floatX

),

borrow=True

)



# the bias is a 1D tensor -- one bias per output feature map

b_values = numpy.zeros((filter_shape[0],), dtype=theano.config.floatX)

self.b = theano.shared(value=b_values, borrow=True)



# convolve input feature maps with filters

conv_out = conv.conv2d(

input=input,

filters=self.W,

filter_shape=filter_shape,

image_shape=image_shape

)



# downsample each feature map individually, using maxpooling

pooled_out = downsample.max_pool_2d(

input=conv_out,

ds=poolsize,

ignore_border=True

)



# add the bias term. Since the bias is a vector (1D array), we first

# reshape it to a tensor of shape (1, n_filters, 1, 1). Each bias will

# thus be broadcasted across mini-batches and feature map

# width & height

self.output = T.tanh(pooled_out + self.b.dimshuffle('x', 0, 'x', 'x'))



# store parameters of this layer

self.params = [self.W, self.b]





def evaluate_lenet5(learning_rate=0.1, n_epochs=200,

dataset='mnist.pkl.gz',

nkerns=[20, 50], batch_size=500):

""" Demonstrates lenet on MNIST dataset

:type learning_rate: float

:param learning_rate: learning rate used (factor for the stochastic

gradient)

:type n_epochs: int

:param n_epochs: maximal number of epochs to run the optimizer

:type dataset: string

:param dataset: path to the dataset used for training /testing (MNIST here)

:type nkerns: list of ints

:param nkerns: number of kernels on each layer

"""



rng = numpy.random.RandomState(23455)



datasets = load_data(dataset)



train_set_x, train_set_y = datasets[0]

valid_set_x, valid_set_y = datasets[1]

test_set_x, test_set_y = datasets[2]



# compute number of minibatches for training, validation and testing

n_train_batches = train_set_x.get_value(borrow=True).shape[0]

n_valid_batches = valid_set_x.get_value(borrow=True).shape[0]

n_test_batches = test_set_x.get_value(borrow=True).shape[0]

n_train_batches /= batch_size

n_valid_batches /= batch_size

n_test_batches /= batch_size



# allocate symbolic variables for the data

index = T.lscalar() # index to a [mini]batch



# start-snippet-1

x = T.matrix('x') # the data is presented as rasterized images

y = T.ivector('y') # the labels are presented as 1D vector of

# [int] labels



######################

# BUILD ACTUAL MODEL #

######################

print '... building the model'



# Reshape matrix of rasterized images of shape (batch_size, 28 * 28)

# to a 4D tensor, compatible with our LeNetConvPoolLayer

# (28, 28) is the size of MNIST images.

layer0_input = x.reshape((batch_size, 1, 28, 28))



# Construct the first convolutional pooling layer:

# filtering reduces the image size to (28-5+1 , 28-5+1) = (24, 24)

# maxpooling reduces this further to (24/2, 24/2) = (12, 12)

# 4D output tensor is thus of shape (batch_size, nkerns[0], 12, 12)

layer0 = LeNetConvPoolLayer(

rng,

input=layer0_input,

image_shape=(batch_size, 1, 28, 28),

filter_shape=(nkerns[0], 1, 5, 5),

poolsize=(2, 2)

)



# Construct the second convolutional pooling layer

# filtering reduces the image size to (12-5+1, 12-5+1) = (8, 8)

# maxpooling reduces this further to (8/2, 8/2) = (4, 4)

# 4D output tensor is thus of shape (batch_size, nkerns[1], 4, 4)

layer1 = LeNetConvPoolLayer(

rng,

input=layer0.output,

image_shape=(batch_size, nkerns[0], 12, 12),

filter_shape=(nkerns[1], nkerns[0], 5, 5),

poolsize=(2, 2)

)



# the HiddenLayer being fully-connected, it operates on 2D matrices of

# shape (batch_size, num_pixels) (i.e matrix of rasterized images).

# This will generate a matrix of shape (batch_size, nkerns[1] * 4 * 4),

# or (500, 50 * 4 * 4) = (500, 800) with the default values.

layer2_input = layer1.output.flatten(2)



# construct a fully-connected sigmoidal layer

layer2 = HiddenLayer(

rng,

input=layer2_input,

n_in=nkerns[1] * 4 * 4,

n_out=500,

activation=T.tanh

)



# classify the values of the fully-connected sigmoidal layer

layer3 = LogisticRegression(input=layer2.output, n_in=500, n_out=10)



# the cost we minimize during training is the NLL of the model

cost = layer3.negative_log_likelihood(y)



# create a function to compute the mistakes that are made by the model

test_model = theano.function(

[index],

layer3.errors(y),

givens={

x: test_set_x[index * batch_size: (index + 1) * batch_size],

y: test_set_y[index * batch_size: (index + 1) * batch_size]

}

)



validate_model = theano.function(

[index],

layer3.errors(y),

givens={

x: valid_set_x[index * batch_size: (index + 1) * batch_size],

y: valid_set_y[index * batch_size: (index + 1) * batch_size]

}

)



# create a list of all model parameters to be fit by gradient descent

params = layer3.params + layer2.params + layer1.params + layer0.params



# create a list of gradients for all model parameters

grads = T.grad(cost, params)



# train_model is a function that updates the model parameters by

# SGD Since this model has many parameters, it would be tedious to

# manually create an update rule for each model parameter. We thus

# create the updates list by automatically looping over all

# (params[i], grads[i]) pairs.

updates = [

(param_i, param_i - learning_rate * grad_i)

for param_i, grad_i in zip(params, grads)

]



train_model = theano.function(

[index],

cost,

updates=updates,

givens={

x: train_set_x[index * batch_size: (index + 1) * batch_size],

y: train_set_y[index * batch_size: (index + 1) * batch_size]

}

)

# end-snippet-1



###############

# TRAIN MODEL #

###############

print '... training'

# early-stopping parameters

patience = 10000 # look as this many examples regardless

patience_increase = 2 # wait this much longer when a new best is

# found

improvement_threshold = 0.995 # a relative improvement of this much is

# considered significant

validation_frequency = min(n_train_batches, patience / 2)

# go through this many

# minibatche before checking the network

# on the validation set; in this case we

# check every epoch



best_validation_loss = numpy.inf

best_iter = 0

test_score = 0.

start_time = time.clock()



epoch = 0

done_looping = False



while (epoch < n_epochs) and (not done_looping):

epoch = epoch + 1

for minibatch_index in xrange(n_train_batches):



iter = (epoch - 1) * n_train_batches + minibatch_index



if iter % 100 == 0:

print 'training @ iter = ', iter

cost_ij = train_model(minibatch_index)



if (iter + 1) % validation_frequency == 0:



# compute zero-one loss on validation set

validation_losses = [validate_model(i) for i

in xrange(n_valid_batches)]

this_validation_loss = numpy.mean(validation_losses)

print('epoch %i, minibatch %i/%i, validation error %f %%' %

(epoch, minibatch_index + 1, n_train_batches,

this_validation_loss * 100.))



# if we got the best validation score until now

if this_validation_loss < best_validation_loss:



#improve patience if loss improvement is good enough

if this_validation_loss < best_validation_loss * \

improvement_threshold:

patience = max(patience, iter * patience_increase)



# save best validation score and iteration number

best_validation_loss = this_validation_loss

best_iter = iter



# test it on the test set

test_losses = [

test_model(i)

for i in xrange(n_test_batches)

]

test_score = numpy.mean(test_losses)

print((' epoch %i, minibatch %i/%i, test error of '

'best model %f %%') %

(epoch, minibatch_index + 1, n_train_batches,

test_score * 100.))



if patience <= iter:

done_looping = True

break



end_time = time.clock()

print('Optimization complete.')

print('Best validation score of %f %% obtained at iteration %i, '

'with test performance %f %%' %

(best_validation_loss * 100., best_iter + 1, test_score * 100.))

print >> sys.stderr, ('The code for file ' +

os.path.split(__file__)[1] +

' ran for %.2fm' % ((end_time - start_time) / 60.))



if __name__ == '__main__':

evaluate_lenet5()





def experiment(state, channel):

evaluate_lenet5(state.learning_rate, dataset=state.dataset)