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）
[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： [python] view plain copy 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 %准备做点实验，这里介绍一下需要用到的数据集。
mnist.pkl.gz or git clone git://github.com/lisa-lab/DeepLearningTutorials.git
MNISTS数据集由手写数字图像组成。划分60，000样例作为训练数据集10，000样例作为测试集。在许多文章同时也在这个tutorial里面将60，000实际划分成50，000个测试集和10，000个验证集。所有的数字图像都长度正则化并且居中到28x28的像素里。在原始的数据集里每一个像素表示的值在0～255之间，0代表black，255代表white，以及在这之间的任何的不同灰度.
