UFLDL是吳恩達團隊編寫的較早的一門深度學習入門，里面理論加上練習的節奏非常好，每次都想快點看完理論去動手編寫練習，因為他幫你打好了整個代碼框架，也有詳細的注釋，所以我們只要實現一點核心的代碼編寫工作就行了，上手快！

我這里找不到新版對應這塊的中文翻譯了，-_-，趁早寫一下，否則又沒感覺了！

第七節是：Convolution and Pooling(卷積和池化)

卷積(Convolution)

之前的多層卷積網絡是Fully Connected Networks，而卷積神經網絡是Locally Connected Networks，現在CNN這么火，想必提到卷積大家都會想到類似這種的圖吧：

[圖片上傳失敗...(image-cb3ff4-1565444895291)]

實際上，數學中離散變量的二維卷積是這樣的;

而我們可以利用matlab里面的conv2函數快捷地實現二維卷積操作(注意要先翻轉W 180°)，通過卷積我們就可以讓一張

大圖片

，用小的

卷積核

滑過，就可以得到大小為

的特征圖了，下面就是我的cnnConvolve.m代碼，其中還有一段利用GPU運算的，被我注釋掉了

function convolvedFeatures = cnnConvolve(filterDim, numFilters, images, W, b)

% convolvedFeatures = cnnConvolve(filterDim, numFilters, convImages, W, b);

% in cnnExercise.m 8 100 28*28*8 8*8*100 100*100

%cnnConvolve Returns the convolution of the features given by W and b with

%the given images

%

% Parameters:

% filterDim - filter (feature) dimension

% numFilters - number of feature maps

% images - large images to convolve with, matrix in the form

% images(r, c, image number)

% W, b - W, b for features from the sparse autoencoder

% W is of shape (filterDim,filterDim,numFilters)

% b is of shape (numFilters,1)

%

% Returns:

% convolvedFeatures - matrix of convolved features in the form

% convolvedFeatures(imageRow, imageCol, featureNum, imageNum)

numImages = size(images, 3);

imageDim = size(images, 1); % 方陣

convDim = imageDim - filterDim + 1; % 28 - 8 + 1 = 21

convolvedFeatures = zeros(convDim, convDim, numFilters, numImages);

% Instructions:

% Convolve every filter with every image here to produce the

% (imageDim - filterDim + 1) x (imageDim - filterDim + 1) x numFeatures x numImages

% matrix convolvedFeatures, such that

% convolvedFeatures(imageRow, imageCol, featureNum, imageNum) is the

% value of the convolved featureNum feature for the imageNum image over

% the region (imageRow, imageCol) to (imageRow + filterDim - 1, imageCol + filterDim - 1)

%

% Expected running times:

% Convolving with 100 images should take less than 30 seconds

% Convolving with 5000 images should take around 2 minutes

% (So to save time when testing, you should convolve with less images, as

% described earlier)

for imageNum = 1:numImages

for filterNum = 1:numFilters

% convolution of image with feature matrix

convolvedImage = zeros(convDim, convDim);

% Obtain the feature (filterDim x filterDim) needed during the convolution

%%% YOUR CODE HERE %%%

filter = squeeze(W(:,:,filterNum));

% Flip the feature matrix because of the definition of convolution, as explained later

filter = rot90(squeeze(filter),2); % squeeze 刪除單一維度 二維數組不受 squeeze 的影響

% Obtain the image

im = squeeze(images(:, :, imageNum));

% Convolve "filter" with "im", adding the result to convolvedImage

% be sure to do a 'valid' convolution

%%% YOUR CODE HERE %%%

convolvedImage = conv2(im,filter,'valid'); % 21*21

% Add the bias unit

% Then, apply the sigmoid function to get the hidden activation

%%% YOUR CODE HERE %%%

convolvedImage = convolvedImage + b(filterNum);

convolvedImage = sigmoid(convolvedImage);

convolvedFeatures(:, :, filterNum, imageNum) = convolvedImage;

end

end

%%%%%%%%%%%%%%%%%%% use gpu(can comment) %%%%%%%%%%%%%

% for imageNum = 1:numImages

% for filterNum = 1:numFilters

%

% % convolution of image with feature matrix

% convolvedImage = zeros(convDim, convDim);

% gpu_convolvedImage = gpuArray(convolvedImage);

%

% % Obtain the feature (filterDim x filterDim) needed during the convolution

%

% %%% YOUR CODE HERE %%%

% filter = squeeze(W(:,:,filterNum));

% % Flip the feature matrix because of the definition of convolution, as explained later

% filter = rot90(squeeze(filter),2); % squeeze 刪除單一維度 二維數組不受 squeeze 的影響

%

% % Obtain the image

% im = squeeze(images(:, :, imageNum));

%

% % Convolve "filter" with "im", adding the result to convolvedImage

% % be sure to do a 'valid' convolution

%

% %%% YOUR CODE HERE %%%

% gpu_filter = gpuArray(filter);

% gpu_im = gpuArray(im);

% gpu_convolvedImage = conv2(gpu_im,gpu_filter,'valid');

% % Add the bias unit

% % Then, apply the sigmoid function to get the hidden activation

%

% %%% YOUR CODE HERE %%%

% convolvedImage = gpu_convolvedImage + b(filterNum);

% convolvedImage = sigmoid(convolvedImage);

%

% convolvedFeatures(:, :, filterNum, imageNum) = gather(convolvedImage);

% end

% end

end

池化(Pooling)

下面這張動圖很好解釋了池化操作：

[圖片上傳失敗...(image-359be6-1565444895291)]

池化可以降低特征維數，降低計算量吧！下面是我的cnnPool.m代碼，用了mean函數和conv2函數都可以實現池化，我把其中一種注釋了：

function pooledFeatures = cnnPool(poolDim, convolvedFeatures)

% 3 21*21*100*8

%cnnPool Pools the given convolved features

%

% Parameters:

% poolDim - dimension of pooling region

% convolvedFeatures - convolved features to pool (as given by cnnConvolve)

% convolvedFeatures(imageRow, imageCol, featureNum, imageNum)

%

% Returns:

% pooledFeatures - matrix of pooled features in the form

% pooledFeatures(poolRow, poolCol, featureNum, imageNum)

%

numImages = size(convolvedFeatures, 4);

numFilters = size(convolvedFeatures, 3);

convolvedDim = size(convolvedFeatures, 1);

pooledFeatures = zeros(convolvedDim / poolDim, ...

convolvedDim / poolDim, numFilters, numImages); % 7*7*100*8

% Instructions:

% Now pool the convolved features in regions of poolDim x poolDim,

% to obtain the

% (convolvedDim/poolDim) x (convolvedDim/poolDim) x numFeatures x numImages

% matrix pooledFeatures, such that

% pooledFeatures(poolRow, poolCol, featureNum, imageNum) is the

% value of the featureNum feature for the imageNum image pooled over the

% corresponding (poolRow, poolCol) pooling region.

%

% Use mean pooling here.

%%% YOUR CODE HERE %%%

%% METHOD1:Using mean to pool

% for imageNum = 1:numImages

% for filterNum = 1:numFilters

% pooledImage = zeros(convolvedDim / poolDim, convolvedDim / poolDim);

% im = convolvedFeatures(:,:,filterNum, imageNum);

% for i=1:(convolvedDim / poolDim)

% for j=1:(convolvedDim / poolDim)

% pooledImage(i,j) = mean(mean(im((i-1)*poolDim+1:i*poolDim,(j-1)*poolDim+1:j*poolDim)));

% end

% end

%

% pooledFeatures(:,:,filterNum, imageNum) = pooledImage;

% end

% end

%%======================================================================

%% METHOD2:Using conv2 as well to pool

% (if numImages is large,this method may be better,can use "gpuArray.conv2"to speed up!)

pool_filter = 1/(poolDim*poolDim) * ones(poolDim,poolDim);

for imageNum = 1:numImages

for filterNum = 1:numFilters

pooledImage = zeros(convolvedDim / poolDim, convolvedDim / poolDim);

im = convolvedFeatures(:,:,filterNum, imageNum);

for i=1:(convolvedDim / poolDim)

for j=1:(convolvedDim / poolDim)

temp = conv2(im,pool_filter,'valid');

pooledImage(i,j) = temp(poolDim*(i-1)+1,poolDim*(j-1)+1);

end

end

pooledFeatures(:,:,filterNum, imageNum) = pooledImage;

end

end

end

運行結果(這個練習偏簡單，只是測試一下，為之后卷積神經網絡打鋪墊的)：

卷積池化結果

有理解不到位之處，還請指出，有更好的想法，可以在下方評論交流！

總結

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