動機

在用稀疏自編碼器對8*8 或28*28等小圖像提取特征時是可行的，但是若對大圖像學習整幅圖像的特征，將會非常耗時。因此需要把這種“全連接”的設計改為“部分聯通”的網絡。

卷積

自然圖像有其固有特性——圖像的一部分統計特征與其他部分是一樣的，這也意味著我們在這一部分上學習的特征也能用在另一部分上，所以對這個圖像上的所以位置，我們都能使用同樣的學習特征。
比如，可以8*8的樣本中學習到一些特征，并把這個特征應用到圖像的任意地方去。特別是，我們可以從8*8的樣本中學習的特征跟原來的大尺寸圖像做卷積。

池化

得到的卷積特征就可以去訓練分類器了，但是由于卷積特征的維數很高，除了計算慢之外，還容易出現過擬合。因此把每一個的卷積特征進行池化。如卷積特征是89^2*400，表示400個特征，每個特征有89^2維。池化就是對每一特征89^2，平均分成若干固定大小不相干的塊，可以用塊內的平均或最大值代表，這樣若分成了10塊，則89^2維就變成了10維。
池化具有平移性

練習

這個部分感覺做了練習才理解的清楚了。
step1：從大圖像中隨機提取8*8的小塊–> ZCA白化–>用SparseEncoder提取出特征。
step2:實現卷積

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);%convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1);% 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 % stepsWT=W*ZCAWhite; b_mean = b - WT*meanPatch;% --------------------------------------------------------convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1); for imageNum = 1:numImagesfor featureNum = 1:numFeatures% convolution of image with feature matrix for each channelconvolvedImage = 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 = zeros(8,8); % You should replace thisoffset=(channel-1)*patchDim*patchDim;fea=WT(featureNum,offset+1:offset+patchDim*patchDim);feature=reshape(fea,patchDim,patchDim);% ------------------------% Flip the feature matrix because of the definition of convolution, as explained laterfeature = flipud(fliplr(squeeze(feature)));% Obtain the imageim = 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+b_mean(featureNum));% ------------------------% The convolved feature is the sum of the convolved values for all channelsconvolvedFeatures(featureNum, imageNum, :, :) = convolvedImage;end endendfunction sigm=sigmoid(x)sigm=1./(1+exp(-x)); end

step3:池化

function pooledFeatures = cnnPool(poolDim, convolvedFeatures) %cnnPool Pools the given convolved features % % Parameters: % poolDim - dimension of pooling region % convolvedFeatures - convolved features to pool (as given by cnnConvolve) % convolvedFeatures(featureNum, imageNum, imageRow, imageCol) % % Returns: % pooledFeatures - matrix of pooled features in the form % pooledFeatures(featureNum, imageNum, poolRow, poolCol) % numImages = size(convolvedFeatures, 2); numFeatures = size(convolvedFeatures, 1); convolvedDim = size(convolvedFeatures, 3);pooledFeatures = zeros(numFeatures, numImages, floor(convolvedDim / poolDim), floor(convolvedDim / poolDim));numRegin=floor(convolvedDim / poolDim); for featureNum=1:numFeaturesfor imageNum=1:numImagesfor row=1:numReginfor col=1:numReginregin=convolvedFeatures(featureNum, imageNum,(row-1)*poolDim+1:row*poolDim,(col-1)*poolDim+1:col*poolDim);pooledFeatures(featureNum,imageNum,row,col)=mean(regin(:));endendend end end

總結

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