Convolution Neural Network (CNN) 原理与实现

转载自：http://blog.csdn.net/abcjennifer/article/details/25912675

本文结合Deep learning的一个应用，Convolution Neural Network 进行一些基本应用，参考Lecun的Document 0.1进行部分拓展，与结果展示（inPython）。

分为以下几部分：

1. Convolution（卷积）

2. Pooling（降采样过程）

3. CNN结构

4.  跑实验

下面分别介绍。

PS：本篇blog为ese机器学习短期班参考资料（20140516课程），本文只是简要讲最naive最simple的思想，重在实践部分，原理课上详述。

1. Convolution（卷积）

类似于高斯卷积，对imagebatch中的所有image进行卷积。对于一张图，其所有feature map用一个filter卷成一张feature map。 如下面的代码，对一个imagebatch（含两张图）进行操作，每个图初始有3张feature map(R,G,B), 用两个9*9的filter进行卷积，结果是，每张图得到两个feature map。

卷积操作由theano的conv.conv2d实现，这里我们用随机参数W，b。结果有点像edge detector是不是？

Code: （详见注释）

[python] view plain copy

    # -*- coding: utf-8 -*-      """     Created on Sat May 10 18:55:26 2014          @author: rachel          Function: convolution option of two pictures with same size (width,height)     input: 3 feature maps (3 channels <RGB> of a picture)     convolution: two 9*9 convolutional filters     """            from theano.tensor.nnet import conv      import theano.tensor as T      import numpy, theano                  rng = numpy.random.RandomState(23455)            # symbol variable      input = T.tensor4(name = 'input')            # initial weights      w_shape = (2,3,9,9) #2 convolutional filters, 3 channels, filter shape: 9*9      w_bound = numpy.sqrt(3*9*9)      W = theano.shared(numpy.asarray(rng.uniform(low = -1.0/w_bound, high = 1.0/w_bound,size = w_shape),                                      dtype = input.dtype),name = 'W')            b_shape = (2,)      b = theano.shared(numpy.asarray(rng.uniform(low = -.5, high = .5, size = b_shape),                                      dtype = input.dtype),name = 'b')                                            conv_out = conv.conv2d(input,W)            #T.TensorVariable.dimshuffle() can reshape or broadcast (add dimension)      #dimshuffle(self,*pattern)      # >>>b1 = b.dimshuffle('x',0,'x','x')      # >>>b1.shape.eval()      # array([1,2,1,1])      output = T.nnet.sigmoid(conv_out + b.dimshuffle('x',0,'x','x'))      f = theano.function([input],output)                                    # demo      import pylab      from PIL import Image      #minibatch_img = T.tensor4(name = 'minibatch_img')            #-------------img1---------------      img1 = Image.open(open('//home//rachel//Documents//ZJU_Projects//DL//Dataset//rachel.jpg'))      width1,height1 = img1.size      img1 = numpy.asarray(img1, dtype = 'float32')/256. # (height, width, 3)            # put image in 4D tensor of shape (1,3,height,width)      img1_rgb = img1.swapaxes(0,2).swapaxes(1,2).reshape(1,3,height1,width1) #(3,height,width)                  #-------------img2---------------      img2 = Image.open(open('//home//rachel//Documents//ZJU_Projects//DL//Dataset//rachel1.jpg'))      width2,height2 = img2.size      img2 = numpy.asarray(img2,dtype = 'float32')/256.      img2_rgb = img2.swapaxes(0,2).swapaxes(1,2).reshape(1,3,height2,width2) #(3,height,width)                        #minibatch_img = T.join(0,img1_rgb,img2_rgb)      minibatch_img = numpy.concatenate((img1_rgb,img2_rgb),axis = 0)      filtered_img = f(minibatch_img)                  # plot original image and two convoluted results      pylab.subplot(2,3,1);pylab.axis('off');      pylab.imshow(img1)            pylab.subplot(2,3,4);pylab.axis('off');      pylab.imshow(img2)            pylab.gray()      pylab.subplot(2,3,2); pylab.axis("off")      pylab.imshow(filtered_img[0,0,:,:]) #0:minibatch_index; 0:1-st filter            pylab.subplot(2,3,3); pylab.axis("off")      pylab.imshow(filtered_img[0,1,:,:]) #0:minibatch_index; 1:1-st filter            pylab.subplot(2,3,5); pylab.axis("off")      pylab.imshow(filtered_img[1,0,:,:]) #0:minibatch_index; 0:1-st filter            pylab.subplot(2,3,6); pylab.axis("off")      pylab.imshow(filtered_img[1,1,:,:]) #0:minibatch_index; 1:1-st filter      pylab.show()  

2. Pooling（降采样过程）

最常用的Maxpooling. 解决了两个问题：

1. 减少计算量

2. 旋转不变性 （原因自己悟）

     PS：对于旋转不变性，回忆下SIFT，LBP：采用主方向；HOG：选择不同方向的模版

Maxpooling的降采样过程会将feature map的长宽各减半。（下面结果图中没有体现出来，python自动给拉到一样大了，但实际上像素数是减半的）

Code: （详见注释）

[python] view plain copy

    # -*- coding: utf-8 -*-      """     Created on Sat May 10 18:55:26 2014          @author: rachel          Function: convolution option      input: 3 feature maps (3 channels <RGB> of a picture)     convolution: two 9*9 convolutional filters     """            from theano.tensor.nnet import conv      import theano.tensor as T      import numpy, theano                  rng = numpy.random.RandomState(23455)            # symbol variable      input = T.tensor4(name = 'input')            # initial weights      w_shape = (2,3,9,9) #2 convolutional filters, 3 channels, filter shape: 9*9      w_bound = numpy.sqrt(3*9*9)      W = theano.shared(numpy.asarray(rng.uniform(low = -1.0/w_bound, high = 1.0/w_bound,size = w_shape),                                      dtype = input.dtype),name = 'W')            b_shape = (2,)      b = theano.shared(numpy.asarray(rng.uniform(low = -.5, high = .5, size = b_shape),                                      dtype = input.dtype),name = 'b')                                            conv_out = conv.conv2d(input,W)            #T.TensorVariable.dimshuffle() can reshape or broadcast (add dimension)      #dimshuffle(self,*pattern)      # >>>b1 = b.dimshuffle('x',0,'x','x')      # >>>b1.shape.eval()      # array([1,2,1,1])      output = T.nnet.sigmoid(conv_out + b.dimshuffle('x',0,'x','x'))      f = theano.function([input],output)                                    # demo      import pylab      from PIL import Image      from matplotlib.pyplot import *            #open random image      img = Image.open(open('//home//rachel//Documents//ZJU_Projects//DL//Dataset//rachel.jpg'))      width,height = img.size      img = numpy.asarray(img, dtype = 'float32')/256. # (height, width, 3)                  # put image in 4D tensor of shape (1,3,height,width)      img_rgb = img.swapaxes(0,2).swapaxes(1,2) #(3,height,width)      minibatch_img = img_rgb.reshape(1,3,height,width)      filtered_img = f(minibatch_img)                  # plot original image and two convoluted results      pylab.figure(1)      pylab.subplot(1,3,1);pylab.axis('off');      pylab.imshow(img)      title('origin image')            pylab.gray()      pylab.subplot(2,3,2); pylab.axis("off")      pylab.imshow(filtered_img[0,0,:,:]) #0:minibatch_index; 0:1-st filter      title('convolution 1')            pylab.subplot(2,3,3); pylab.axis("off")      pylab.imshow(filtered_img[0,1,:,:]) #0:minibatch_index; 1:1-st filter      title('convolution 2')            #pylab.show()                              # maxpooling      from theano.tensor.signal import downsample            input = T.tensor4('input')      maxpool_shape = (2,2)      pooled_img = downsample.max_pool_2d(input,maxpool_shape,ignore_border = False)            maxpool = theano.function(inputs = [input],                                outputs = [pooled_img])            pooled_res = numpy.squeeze(maxpool(filtered_img))                    #pylab.figure(2)      pylab.subplot(235);pylab.axis('off');      pylab.imshow(pooled_res[0,:,:])      title('down sampled 1')            pylab.subplot(236);pylab.axis('off');      pylab.imshow(pooled_res[1,:,:])      title('down sampled 2')            pylab.show()  

3. CNN结构

想必大家随便google下CNN的图都滥大街了，这里拖出来那时候学CNN的时候一张图，自认为陪上讲解的话画得还易懂（<!--囧-->）

废话不多说了，直接上Lenet结构图：（从下往上顺着箭头看，最下面为底层original input）

4. CNN代码

去资源里下载吧，我放上去了喔~（in python）

这里贴少部分代码，仅表示建模的NN：

[python] view plain copy

    rng = numpy.random.RandomState(23455)                # transfrom x from (batchsize, 28*28) to (batchsize,feature,28,28))          # I_shape = (28,28),F_shape = (5,5),          N_filters_0 = 20          D_features_0= 1          layer0_input = x.reshape((batch_size,D_features_0,28,28))          layer0 = LeNetConvPoolLayer(rng, input = layer0_input, filter_shape = (N_filters_0,D_features_0,5,5),                                      image_shape = (batch_size,1,28,28))          #layer0.output: (batch_size, N_filters_0, (28-5+1)/2, (28-5+1)/2) -> 20*20*12*12                    N_filters_1 = 50          D_features_1 = N_filters_0          layer1 = LeNetConvPoolLayer(rng,input = layer0.output, filter_shape = (N_filters_1,D_features_1,5,5),                                      image_shape = (batch_size,N_filters_0,12,12))          # layer1.output: (20,50,4,4)                    layer2_input = layer1.output.flatten(2) # (20,50,4,4)->(20,(50*4*4))          layer2 = HiddenLayer(rng,layer2_input,n_in = 50*4*4,n_out = 500, activation = T.tanh)                    layer3 = LogisticRegression(input = layer2.output, n_in = 500, n_out = 10)  

layer0, layer1 ：分别是卷积+降采样

layer2+layer3：组成一个MLP（ANN）

训练模型：

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    cost = layer3.negative_log_likelihood(y)      params = layer3.params + layer2.params + layer1.params + layer0.params      gparams = T.grad(cost,params)            updates = []      for par,gpar in zip(params,gparams):          updates.append((par, par - learning_rate * gpar))            train_model = theano.function(inputs = [minibatch_index],                                    outputs = [cost],                                    updates = updates,                                    givens = {x: train_set_x[minibatch_index * batch_size : (minibatch_index+1) * batch_size],                                              y: train_set_y[minibatch_index * batch_size : (minibatch_index+1) * batch_size]})  

根据cost（最上层MLP的输出NLL），对所有层的parameters进行训练

剩下的具体见代码和注释。

PS：数据为MNIST所有数据