Convolution Neural Network CNN 原理与实现

               

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(in python)。

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)


# -*- coding: utf-8 -*-"""Created on Sat May 10 18:55:26 2014@author: rachelFunction: convolution option of two pictures with same size (width,height)input: 3 feature maps (3 channels  of a picture)convolution: two 9*9 convolutional filters"""from theano.tensor.nnet import convimport theano.tensor as Timport numpy, theanorng = numpy.random.RandomState(23455)# symbol variableinput = T.tensor4(name = 'input')# initial weightsw_shape = (2,3,9,9) #2 convolutional filters, 3 channels, filter shape: 9*9w_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)# demoimport pylabfrom 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.sizeimg1 = 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.sizeimg2 = 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 resultspylab.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 filterpylab.subplot(2,3,3); pylab.axis("off")pylab.imshow(filtered_img[0,1,:,:]) #0:minibatch_index; 1:1-st filterpylab.subplot(2,3,5); pylab.axis("off")pylab.imshow(filtered_img[1,0,:,:]) #0:minibatch_index; 0:1-st filterpylab.subplot(2,3,6); pylab.axis("off")pylab.imshow(filtered_img[1,1,:,:]) #0:minibatch_index; 1:1-st filterpylab.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)


# -*- coding: utf-8 -*-"""Created on Sat May 10 18:55:26 2014@author: rachelFunction: convolution option input: 3 feature maps (3 channels  of a picture)convolution: two 9*9 convolutional filters"""from theano.tensor.nnet import convimport theano.tensor as Timport numpy, theanorng = numpy.random.RandomState(23455)# symbol variableinput = T.tensor4(name = 'input')# initial weightsw_shape = (2,3,9,9) #2 convolutional filters, 3 channels, filter shape: 9*9w_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)# demoimport pylabfrom PIL import Imagefrom matplotlib.pyplot import *#open random imageimg = Image.open(open('//home//rachel//Documents//ZJU_Projects//DL//Dataset//rachel.jpg'))width,height = img.sizeimg = 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 resultspylab.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 filtertitle('convolution 1')pylab.subplot(2,3,3); pylab.axis("off")pylab.imshow(filtered_img[0,1,:,:]) #0:minibatch_index; 1:1-st filtertitle('convolution 2')#pylab.show()# maxpoolingfrom theano.tensor.signal import downsampleinput = 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(

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:

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:

    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






final result:
Optimization complete. Best validation score of 0.990000 % obtained at iteration 122500, with test performance 0.950000 %






欢迎参与讨论并关注本博客和微博Rachel____Zhang, 后续内容继续更新哦~








           

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