Exercise:Convolution and Pooling 代码示例

练习参考Convolution and Pooling

       这个练习用于处理大型图像，需要编写代码实现卷积特征提取和池化（采样）两个过程。在上一个练习中，通过小尺寸图像样本训练线性编码器得到的权重矩阵W、偏差向量b以及预处理的ZCA白化矩阵ZCAWhite、均值向量meanPatch存为文件STL10Features.mat。此练习利用STL10Features.mat中的特征与大图作卷积生成卷积特征矩阵。

       卷积计算在cnnConvolve.m中实现。对每张图像的每个特征（隐藏单元）的每个RGB分量（三层循环），从W中提取对应的卷积核，将其与大图做卷积。这里计算大图与卷积核的卷积与数学中的矩阵卷积不同，是两矩阵的对应项直接相乘再求和，具体过程如下图：

       每个RGB分量计算的卷积累加起来，其结果加上特征的偏置后取sigmoid就得到了一张图像的一个特征的卷积矩阵。三层循环结束后就得到了全部图像的卷积特征矩阵族。

cnnConvolve.m

function convolvedFeatures = cnnConvolve(patchDim, numFeatures, images, W, b, ZCAWhite, meanPatch)%cnnConvolve Returns the convolution of the features given by W and b with%the given images%% Parameters:%  patchDim - patch (feature) dimension%  numFeatures - number of features%  images - large images to convolve with, matrix in the form%           images(r, c, channel, image number)%  W, b - W, b for features from the sparse autoencoder%  ZCAWhite, meanPatch - ZCAWhitening and meanPatch matrices used for%                        preprocessing%% Returns:%  convolvedFeatures - matrix of convolved features in the form%                      convolvedFeatures(featureNum, imageNum, imageRow, imageCol)numImages = size(images, 4);imageDim = size(images, 1);imageChannels = size(images, 3);% Instructions:%   Convolve every feature with every large image here to produce the %   numFeatures x numImages x (imageDim - patchDim + 1) x (imageDim - patchDim + 1) %   matrix convolvedFeatures, such that %   convolvedFeatures(featureNum, imageNum, imageRow, imageCol) is the%   value of the convolved featureNum feature for the imageNum image over%   the region (imageRow, imageCol) to (imageRow + patchDim - 1, imageCol + patchDim - 1)%% Expected running times: %   Convolving with 100 images should take less than 3 minutes %   Convolving with 5000 images should take around an hour%   (So to save time when testing, you should convolve with less images, as%   described earlier)% -------------------- YOUR CODE HERE --------------------% Precompute the matrices that will be used during the convolution. Recall% that you need to take into account the whitening and mean subtraction% steps% patchDim    8% numFeatures 400; is hiddenSize% images      images(r, c, channel, image number)% W           hiddenSize X visibleSize% b           hiddenSize X 1% ZCAWhite    visibleSize X visibleSize% meanPatch   visibleSize X 1WT = W * ZCAWhite;bias = b - WT * meanPatch;patchSize = patchDim * patchDim;% --------------------------------------------------------convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1);for imageNum = 1:numImages  for featureNum = 1:numFeatures    % convolution of image with feature matrix for each channel    convolvedImage = zeros(imageDim - patchDim + 1, imageDim - patchDim + 1);    for channel = 1:imageChannels      % Obtain the feature (patchDim x patchDim) needed during the convolution      % ---- YOUR CODE HERE ----      feature = reshape(WT(featureNum,(channel-1)*patchSize+1:channel*patchSize), patchDim, patchDim);           % ------------------------      % Flip the feature matrix because of the definition of convolution, as explained later      feature = rot90(squeeze(feature),2);            % Obtain the image      im = squeeze(images(:, :, channel, imageNum));      % Convolve "feature" with "im", adding the result to convolvedImage      % be sure to do a 'valid' convolution      % ---- YOUR CODE HERE ----      convolvedImage = convolvedImage + conv2(im, feature, 'valid');       % ------------------------    end        % Subtract the bias unit (correcting for the mean subtraction as well)    % Then, apply the sigmoid function to get the hidden activation    % ---- YOUR CODE HERE ----    convolvedImage = sigmoid(convolvedImage + bias(featureNum));    % ------------------------        % The convolved feature is the sum of the convolved values for all channels    convolvedFeatures(featureNum, imageNum, :, :) = convolvedImage;  endendendfunction sigm = sigmoid(x)      sigm = 1 ./ (1 + exp(-x));end

       池化采用平均采样。对每个卷积特征矩阵划分为若干个池化区域，每个区域取特征均值作为一个采样特征。在采样特征上做Softmax分类及测试。

cnnPool.m

for imageNum = 1:numImages  for featureNum = 1:numFeatures      temp = conv2(squeeze(convolvedFeatures(featureNum,imageNum,:,:)),ones(poolDim)/poolDim/poolDim,'valid');      pooledFeatures(featureNum,imageNum,:,:) = temp(1:poolDim:end,1:poolDim:end);  endend