9、Convolution and Pooling
- 总结：
1）就是用前一个线性解码器的实验学习到的权值作为卷积核，然后卷积、池化，最后送入softmax分类器。
2）这种方法有个特殊就地方，就是由于原始数据用了0均值和ZCAWhite，所以对于线性解码器的参数进行了相应的处理，这里没有学过的。
3）MATLAB没办法搞DL，就这相当费时，费内存。在这上面跑就是浪费时间。
4）这里面没有CNN的BP，后面马上看。
5）对于图像的3个通道，这里用了累加，然后sigmoid函数处理的方法，感觉还是有道理的。也是对于3通道的图像处理，了解了一个CNN处理的方法。
6）这里就是用的没有重叠的平均池化
- 问题：
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- 想法：
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实验需要下载代码：cnn_exercise.zip 数据集stlSubset.zip
cnnExercise.m
clear;close all;clc;
disp('当前正在执行的程序是：');
disp([mfilename('fullpath'),'.m']);
%% CS294A/CS294W Convolutional Neural Networks Exercise
% Instructions
% ------------
%
% This file contains code that helps you get started on the
% convolutional neural networks exercise. In this exercise, you will only
% need to modify cnnConvolve.m and cnnPool.m. You will not need to modify
% this file.
%%======================================================================
%% STEP 0: Initialization
% Here we initialize some parameters used for the exercise.
imageDim = 64; % image dimension
imageChannels = 3; % number of channels (rgb, so 3)
patchDim = 8; % patch dimension
numPatches = 50000; % number of patches
visibleSize = patchDim * patchDim * imageChannels; % number of input units 192
outputSize = visibleSize; % number of output units
hiddenSize = 400; % number of hidden units
epsilon = 0.1; % epsilon for ZCA whitening
poolDim = 19; % dimension of pooling region
%%======================================================================
%% STEP 1: Train a sparse autoencoder (with a linear decoder) to learn
% features from color patches. If you have completed the linear decoder
% execise, use the features that you have obtained from that exercise,
% loading them into optTheta. Recall that we have to keep around the
% parameters used in whitening (i.e., the ZCA whitening matrix and the
% meanPatch)
% --------------------------- YOUR CODE HERE --------------------------
% Train the sparse autoencoder and fill the following variables with
% the optimal parameters:
optTheta = zeros(2*hiddenSize*visibleSize+hiddenSize+visibleSize, 1);
ZCAWhite = zeros(visibleSize, visibleSize);
meanPatch = zeros(visibleSize, 1);
%导入上一个实验学习到的上面三个参数
load STL10Features.mat
% --------------------------------------------------------------------
% Display and check to see that the features look good
%取出了第一层的权系数
W = reshape(optTheta(1:visibleSize * hiddenSize), hiddenSize, visibleSize);
%隐层的偏差
b = optTheta(2*hiddenSize*visibleSize+1:2*hiddenSize*visibleSize+hiddenSize);
figure;
displayColorNetwork( (W*ZCAWhite)');
set(gcf,'NumberTitle','off');
set(gcf,'Name','自编码线性解码器学习到的特征');
%%======================================================================
%{
%% STEP 2: Implement and test convolution and pooling
% In this step, you will implement convolution and pooling, and test them
% on a small part of the data set to ensure that you have implemented
% these two functions correctly. In the next step, you will actually
% convolve and pool the features with the STL10 images.
%% STEP 2a: Implement convolution
% Implement convolution in the function cnnConvolve in cnnConvolve.m
% Note that we have to preprocess the images in the exact same way
% we preprocessed the patches before we can obtain the feature activations.
load stlTrainSubset.mat % loads numTrainImages, trainImages, trainLabels
%% Use only the first 8 images for testing
%trainImages尺寸为[64,64,3,2000]
convImages = trainImages(:, :, :, 1:8);
% NOTE: Implement cnnConvolve in cnnConvolve.m first!
convolvedFeatures = cnnConvolve(patchDim, hiddenSize, convImages, W, b, ZCAWhite, meanPatch);
%% STEP 2b: Checking your convolution
% To ensure that you have convolved the features correctly, we have
% provided some code to compare the results of your convolution with
% activations from the sparse autoencoder
% For 1000 random points
for i = 1:1000
featureNum = randi([1, hiddenSize]);
imageNum = randi([1, 8]);
imageRow = randi([1, imageDim - patchDim + 1]);
imageCol = randi([1, imageDim - patchDim + 1]);
patch = convImages(imageRow:imageRow + patchDim - 1, imageCol:imageCol + patchDim - 1, :, imageNum);
patch = patch(:);
patch = patch - meanPatch;
patch = ZCAWhite * patch;
features = feedForwardAutoencoder(optTheta, hiddenSize, visibleSize, patch);
if abs(features(featureNum, 1) - convolvedFeatures(featureNum, imageNum, imageRow, imageCol)) > 1e-9
fprintf('Convolved feature does not match activation from autoencoder\n');
fprintf('Feature Number : %d\n', featureNum);
fprintf('Image Number : %d\n', imageNum);
fprintf('Image Row : %d\n', imageRow);
fprintf('Image Column : %d\n', imageCol);
fprintf('Convolved feature : %0.5f\n', convolvedFeatures(featureNum, imageNum, imageRow, imageCol));
fprintf('Sparse AE feature : %0.5f\n', features(featureNum, 1));
error('Convolved feature does not match activation from autoencoder');
end
end
disp('Congratulations! Your convolution code passed the test.');
%% STEP 2c: Implement pooling
% Implement pooling in the function cnnPool in cnnPool.m
% NOTE: Implement cnnPool in cnnPool.m first!
pooledFeatures = cnnPool(poolDim, convolvedFeatures);
%% STEP 2d: Checking your pooling
% To ensure that you have implemented pooling, we will use your pooling
% function to pool over a test matrix and check the results.
testMatrix = reshape(1:64, 8, 8);
expectedMatrix = [mean(mean(testMatrix(1:4, 1:4))) mean(mean(testMatrix(1:4, 5:8))); ...
mean(mean(testMatrix(5:8, 1:4))) mean(mean(testMatrix(5:8, 5:8))); ];
testMatrix = reshape(testMatrix, 1, 1, 8, 8);
pooledFeatures = squeeze(cnnPool(4, testMatrix));
if ~isequal(pooledFeatures, expectedMatrix)
disp('Pooling incorrect');
disp('Expected');
disp(expectedMatrix);
disp('Got');
disp(pooledFeatures);
else
disp('Congratulations! Your pooling code passed the test.');
end
%}
%%======================================================================
%% STEP 3: Convolve and pool with the dataset
% In this step, you will convolve each of the features you learned with
% the full large images to obtain the convolved features. You will then
% pool the convolved features to obtain the pooled features for
% classification.
%
% Because the convolved features matrix is very large, we will do the
% convolution and pooling 50 features at a time to avoid running out of
% memory. Reduce this number if necessary
stepSize = 50;
assert(mod(hiddenSize, stepSize) == 0, 'stepSize should divide hiddenSize');
load stlTrainSubset.mat % loads numTrainImages, trainImages, trainLabels
load stlTestSubset.mat % loads numTestImages, testImages, testLabels
pooledFeaturesTrain = zeros(hiddenSize, numTrainImages, ...
floor((imageDim - patchDim + 1) / poolDim), ...
floor((imageDim - patchDim + 1) / poolDim) );
pooledFeaturesTest = zeros(hiddenSize, numTestImages, ...
floor((imageDim - patchDim + 1) / poolDim), ...
floor((imageDim - patchDim + 1) / poolDim) );
tic();
%{
for convPart = 1:(hiddenSize / stepSize)
featureStart = (convPart - 1) * stepSize + 1;
featureEnd = convPart * stepSize;
fprintf('Step %d: features %d to %d\n', convPart, featureStart, featureEnd);
Wt = W(featureStart:featureEnd, :);
bt = b(featureStart:featureEnd);
fprintf('Convolving and pooling train images\n');
convolvedFeaturesThis = cnnConvolve(patchDim, stepSize, ...
trainImages, Wt, bt, ZCAWhite, meanPatch);
pooledFeaturesThis = cnnPool(poolDim, convolvedFeaturesThis);
pooledFeaturesTrain(featureStart:featureEnd, :, :, :) = pooledFeaturesThis;
toc();
clear convolvedFeaturesThis pooledFeaturesThis;
fprintf('Convolving and pooling test images\n');
convolvedFeaturesThis = cnnConvolve(patchDim, stepSize, ...
testImages, Wt, bt, ZCAWhite, meanPatch);
pooledFeaturesThis = cnnPool(poolDim, convolvedFeaturesThis);
pooledFeaturesTest(featureStart:featureEnd, :, :, :) = pooledFeaturesThis;
toc();
clear convolvedFeaturesThis pooledFeaturesThis;
end
% You might want to save the pooled features since convolution and pooling takes a long time
save('cnnPooledFeatures.mat', 'pooledFeaturesTrain', 'pooledFeaturesTest');
toc();
%}
load cnnPooledFeatures.mat
%%======================================================================
%% STEP 4: Use pooled features for classification
% Now, you will use your pooled features to train a softmax classifier,
% using softmaxTrain from the softmax exercise.
% Training the softmax classifer for 1000 iterations should take less than
% 10 minutes.
% Add the path to your softmax solution, if necessary
% addpath /path/to/solution/
% Setup parameters for softmax
softmaxLambda = 1e-4;
numClasses = 4;
% Reshape the pooledFeatures to form an input vector for softmax
softmaxX = permute(pooledFeaturesTrain, [1 3 4 2]);
softmaxX = reshape(softmaxX, numel(pooledFeaturesTrain) / numTrainImages,...
numTrainImages);
softmaxY = trainLabels;
options = struct;
options.maxIter = 200;
softmaxModel = softmaxTrain(numel(pooledFeaturesTrain) / numTrainImages,...
numClasses, softmaxLambda, softmaxX, softmaxY, options);
%%======================================================================
%% STEP 5: Test classifer
% Now you will test your trained classifer against the test images
softmaxX = permute(pooledFeaturesTest, [1 3 4 2]);
softmaxX = reshape(softmaxX, numel(pooledFeaturesTest) / numTestImages, numTestImages);
softmaxY = testLabels;
[pred] = softmaxPredict(softmaxModel, softmaxX);
acc = (pred(:) == softmaxY(:));
acc = sum(acc) / size(acc, 1);
fprintf('Accuracy: %2.3f%%\n', acc * 100);
% You should expect to get an accuracy of around 80% on the test images.
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)
% 分别取出图像的数量，图像的维度，图像的通道数量
numImages = size(images, 4);
imageDim = size(images, 1);
%imageChannels = size(images, 3);
%预先定义卷积后的特征
%numFeatures特征的数量，也就是特征的层数，这里就是隐神经元的数量，就是对于每一幅图像都要经过那么多的卷积核
%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
% steps
%下面两项就是把0均值和ZCAWhite都放进参数中，使得可以输入原始数据。
%W尺寸为[hiddenSize,visibleSize]
WT=W*ZCAWhite;%等效的网络参数
%ZCAWhite尺寸为[visibleSize, visibleSize]
%下面这项就是b=b-W*ZCAWhite*meanPath，等于把对于x的0均值处理，搬到了偏差b中
b=b-WT*meanPatch;%等效的b
patchSize=patchDim*patchDim;
% --------------------------------------------------------
%trainImages尺寸为[64,64,3,2000]
% 分别取出图像的数量，图像的维度，图像的通道数量
% numImages = size(images, 4);
% imageDim = size(images, 1);
% imageChannels = size(images, 3);
convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1);
for imageNum = 1:numImages%先图像的数量
%再卷积核的数量，也就是隐单元数量
for featureNum = 1:numFeatures%numFeatures=hiddenSize
% convolution of image with feature matrix for each channel
convolvedImage = zeros(imageDim - patchDim + 1, imageDim - patchDim + 1);
%然后层的数量，不同的层对应着不同的卷积核
for channel = 1:3
% Obtain the feature (patchDim x patchDim) needed during the convolution
% ---- YOUR CODE HERE ----
%获取卷积核
%feature = zeros(8,8); % You should replace this
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
%squeeze为移除单一维度的意思
%flipud为上下翻转，fliplr为左右翻转,flipud和fliplr结合就是翻转180度的意思。
%由于MATLAB提示，用rot90(x,2)替换更快，所以替换。
%feature = flipud(fliplr(squeeze(feature)));
%这里翻转是由于这个权值是实现训练好的，而在conv2中会把权值翻转180度，所以在前面先翻转180度
%这样，与conv2中的翻转抵消，权值就能够在正确的位置上滤波。
%但感觉其实，就这2D图像，更多是借助于这个函数，单从滤波器的角度，没有必要翻转也是可以的
%翻转权值都是学习来的。
feature =rot90(feature,2);
% Obtain the image
%获得对应图像在对应通道上的图像
im = squeeze(images(:, :, channel, imageNum));
% Convolve "feature" with "im", adding the result to convolvedImage
% be sure to do a 'valid' convolution
% ---- YOUR CODE HERE ----
%由于这里定义的卷积后的特征图谱的尺寸，分别为特征图谱的层数（隐层数量），图像数量，卷积后特征图谱的尺寸
%convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1);
%并没有考虑到彩色图像的3个通道，所以最简单的方法，就是把3个通道算出来的特征图谱累加
%不过感觉下面这个3个通道累加，可能出现超出图像值域的情形，虽然别人的代码都没考虑这种情况，但是自己还是做个平均。
%convolvedImage=convolvedImage+1/3.*conv2(im,feature,'valid');
%但是没想到，做了个平均，反而不能通过cnnExercise.m中
%111行error('Convolved feature does not match activation from autoencoder');
%多通道的特征，都是这样直接累加，然后也不做均值处理，应该是考虑后面反正都会进行sigmoid处理
%会自动进行输出值域的压缩，所以就自然不进行这个平均，会减慢速度
%从理论上这样分析是可以的。这样也在一定程度上，打破了对于颜色的依赖？
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 ----
%MATLAB一个矩阵和一个常数的加法，就是对于这个矩阵所有的元素的相同位置都加上这个数字
convolvedImage=sigmoid(convolvedImage+b(featureNum));
% ------------------------
% The convolved feature is the sum of the convolved values for all channels
convolvedFeatures(featureNum, imageNum, :, :) = convolvedImage;
end
end
end
function sigm = sigmoid(x)
sigm = 1 ./ (1 + exp(-x));
end
cnnPool.m
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)
%
%convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1);
numImages = size(convolvedFeatures, 2);
numFeatures = size(convolvedFeatures, 1);
convolvedDim = size(convolvedFeatures, 3);
%floor趋向于负无穷，就是针对于池化的步长，选定要池化的范围
pooledFeatures = zeros(numFeatures, numImages, floor(convolvedDim / poolDim), floor(convolvedDim / poolDim));
%定义一个池化尺寸方便后面程序的编写
pooledDim=floor(convolvedDim / poolDim);
% -------------------- YOUR CODE HERE --------------------
% Instructions:
% Now pool the convolved features in regions of poolDim x poolDim,
% to obtain the
% numFeatures x numImages x (convolvedDim/poolDim) x (convolvedDim/poolDim)
% matrix pooledFeatures, such that
% pooledFeatures(featureNum, imageNum, poolRow, poolCol) is the
% value of the featureNum feature for the imageNum image pooled over the
% corresponding (poolRow, poolCol) pooling region
% (see http://ufldl/wiki/index.php/Pooling )
%
% Use mean pooling here.
% -------------------- YOUR CODE HERE --------------------
%convolvedFeatures = zeros(numFeatures, numImages, imageDim - patchDim + 1, imageDim - patchDim + 1);
% numImages = size(convolvedFeatures, 2);
% numFeatures = size(convolvedFeatures, 1);
% convolvedDim = size(convolvedFeatures, 3);
%floor趋向于负无穷，就是池化后的尺寸，在缩小规整
% pooledFeatures = zeros(numFeatures, numImages, floor(convolvedDim / poolDim), floor(convolvedDim / poolDim));
%这其实模仿cnnConvolve.m就行
for imageNum = 1:numImages%先图像的数量
%再特征的数量
for featureNum = 1:numFeatures%numFeatures=hiddenSize
%再做池化循环遍历
for rowNum = 1:pooledDim
for colNum = 1:pooledDim
pooledFeatures(featureNum, imageNum, rowNum, colNum)= ...
mean(mean(convolvedFeatures(featureNum, imageNum, ...
(rowNum-1)*poolDim+1:rowNum*poolDim, (colNum-1)*poolDim+1:colNum*poolDim)));
end
end
end
end
end
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