ufldl学习笔记与编程作业：Convolutional Neural Network(卷积神经网络)

ufldl学习笔记与编程作业：Convolutional Neural Network(卷积神经网络)

ufldl出了新教程，感觉比之前的好，从基础讲起，系统清晰，又有编程实践。

在deep learning高质量群里面听一些前辈说，不必深究其他机器学习的算法，可以直接来学dl。

于是最近就开始搞这个了，教程加上matlab编程，就是完美啊。

新教程的地址是：http://ufldl.stanford.edu/tutorial/

本节学习地址：http://ufldl.stanford.edu/tutorial/supervised/ConvolutionalNeuralNetwork/

一直没更新UFLDL的学习笔记，因为之前用octave跑这份代码失败了，检查了代码觉得没错误，后来想着用matlab跑，

不过一直耽搁着，今天装了matlab，果然，成功了。

其实卷积神经网络没什么特别，卷积层的连接可以看成是local connection就可以了。

下面是主要代码：

cnnCost.m

function [cost, grad, preds] = cnnCost(theta,images,labels,numClasses,...                                filterDim,numFilters,poolDim,pred)% Calcualte cost and gradient for a single layer convolutional% neural network followed by a softmax layer with cross entropy% objective.%                            % Parameters:%  theta      -  unrolled parameter vector%  images     -  stores images in imageDim x imageDim x numImges%                array%  numClasses -  number of classes to predict%  filterDim  -  dimension of convolutional filter                            %  numFilters -  number of convolutional filters%  poolDim    -  dimension of pooling area%  pred       -  boolean only forward propagate and return%                predictions%%% Returns:%  cost       -  cross entropy cost%  grad       -  gradient with respect to theta (if pred==False)%  preds      -  list of predictions for each example (if pred==True)if ~exist('pred','var')    pred = false;end;weightDecay = 0.0001;imageDim = size(images,1); % height/width of imagenumImages = size(images,3); % number of images%% Reshape parameters and setup gradient matrices% Wc is filterDim x filterDim x numFilters parameter matrix %convolution参数% bc is the corresponding bias% Wd is numClasses x hiddenSize parameter matrix where hiddenSize% is the number of output units from the convolutional layer %这个convolutional layer应该是包含了卷积层和pool层% bd is corresponding bias[Wc, Wd, bc, bd] = cnnParamsToStack(theta,imageDim,filterDim,numFilters,...                        poolDim,numClasses);% Same sizes as Wc,Wd,bc,bd. Used to hold gradient w.r.t above params.Wc_grad = zeros(size(Wc));Wd_grad = zeros(size(Wd));bc_grad = zeros(size(bc));bd_grad = zeros(size(bd));%%======================================================================%% STEP 1a: Forward Propagation%  In this step you will forward propagate the input through the%  convolutional and subsampling (mean pooling) layers.  You will then use%  the responses from the convolution and pooling layer as the input to a%  standard softmax layer.%% Convolutional Layer%  For each image and each filter, convolve the image with the filter, add%  the bias and apply the sigmoid nonlinearity.  Then subsample the %  convolved activations with mean pooling.  Store the results of the%  convolution in activations and the results of the pooling in%  activationsPooled.  You will need to save the convolved activations for%  backpropagation.convDim = imageDim-filterDim+1; % dimension of convolved outputoutputDim = (convDim)/poolDim; % dimension of subsampled output% convDim x convDim x numFilters x numImages tensor for storing activationsactivations = zeros(convDim,convDim,numFilters,numImages);% outputDim x outputDim x numFilters x numImages tensor for storing% subsampled activationsactivationsPooled = zeros(outputDim,outputDim,numFilters,numImages);%%% YOUR CODE HERE %%%   %调用之前写的两个函数activations = cnnConvolve(filterDim, numFilters, images, Wc, bc);activationsPooled = cnnPool(poolDim, activations); % Reshape activations into 2-d matrix, hiddenSize x numImages,% for Softmax layeractivationsPooled = reshape(activationsPooled,[],numImages);%就变成了传统的softmax模式%% Softmax Layer%  Forward propagate the pooled activations calculated above into a%  standard softmax layer. For your convenience we have reshaped%  activationPooled into a hiddenSize x numImages matrix.  Store the%  results in probs.% numClasses x numImages for storing probability that each image belongs to% each class.probs = zeros(numClasses,numImages);%%% YOUR CODE HERE %%%z = Wd*activationsPooled;z = bsxfun(@plus,z,bd);%z = Wd * activationsPooled+repmat(bd,[1,numImages]); z = bsxfun(@minus,z,max(z,[],1));%减去最大值，减少一个维度z = exp(z);probs = bsxfun(@rdivide,z,sum(z,1));preds = probs;%%======================================================================%% STEP 1b: Calculate Cost%  In this step you will use the labels given as input and the probs%  calculate above to evaluate the cross entropy objective.  Store your%  results in cost.cost = 0; % save objective into cost%%% YOUR CODE HERE %%%logProbs = log(probs);   labelIndex=sub2ind(size(logProbs), labels', 1:size(logProbs,2));%找出矩阵logProbs的线性索引，行由labels指定，列由1:size(logProbs,2)指定，生成线性索引返回给labelIndexvalues = logProbs(labelIndex);  cost = -sum(values);weightDecayCost = (weightDecay/2) * (sum(Wd(:) .^ 2) + sum(Wc(:) .^ 2));cost = cost / numImages+weightDecayCost; %Make sure to scale your gradients by the inverse size of the training set %if you included this scale in the cost calculation otherwise your code will not pass the numerical gradient check.% Makes predictions given probs and returns without backproagating errors.if pred    [~,preds] = max(probs,[],1);    preds = preds';    grad = 0;    return;end;%%======================================================================%% STEP 1c: Backpropagation%  Backpropagate errors through the softmax and convolutional/subsampling%  layers.  Store the errors for the next step to calculate the gradient.%  Backpropagating the error w.r.t the softmax layer is as usual.  To%  backpropagate through the pooling layer, you will need to upsample the%  error with respect to the pooling layer for each filter and each image.  %  Use the kron function and a matrix of ones to do this upsampling %  quickly.%%% YOUR CODE HERE %%%%softmax残差targetMatrix = zeros(size(probs));  targetMatrix(labelIndex) = 1;  softmaxError = probs-targetMatrix;%pool层残差poolError = Wd'*softmaxError;poolError = reshape(poolError, outputDim, outputDim, numFilters, numImages);unpoolError = zeros(convDim, convDim, numFilters, numImages);unpoolingFilter = ones(poolDim);poolArea = poolDim*poolDim;%展开poolError为unpoolErrorfor imageNum = 1:numImages    for filterNum = 1:numFilters        e = poolError(:, :, filterNum, imageNum);        unpoolError(:, :, filterNum, imageNum) = kron(e, unpoolingFilter)./poolArea;    endendconvError = unpoolError .* activations .* (1 - activations); %%======================================================================%% STEP 1d: Gradient Calculation%  After backpropagating the errors above, we can use them to calculate the%  gradient with respect to all the parameters.  The gradient w.r.t the%  softmax layer is calculated as usual.  To calculate the gradient w.r.t.%  a filter in the convolutional layer, convolve the backpropagated error%  for that filter with each image and aggregate over images.%%% YOUR CODE HERE %%%%softmax梯度Wd_grad = (1/numImages).*softmaxError * activationsPooled'+weightDecay * Wd; % l+1层残差 * l层激活值bd_grad = (1/numImages).*sum(softmaxError, 2);% Gradient of the convolutional layerbc_grad = zeros(size(bc));Wc_grad = zeros(size(Wc));%计算bc_gradfor filterNum = 1 : numFilters    e = convError(:, :, filterNum, :);    bc_grad(filterNum) = (1/numImages).*sum(e(:));end%翻转convErrorfor filterNum = 1 : numFilters    for imageNum = 1 : numImages        e = convError(:, :, filterNum, imageNum);        convError(:, :, filterNum, imageNum) = rot90(e, 2);    endendfor filterNum = 1 : numFilters    Wc_gradFilter = zeros(size(Wc_grad, 1), size(Wc_grad, 2));    for imageNum = 1 : numImages             Wc_gradFilter = Wc_gradFilter + conv2(images(:, :, imageNum), convError(:, :, filterNum, imageNum), 'valid');    end    Wc_grad(:, :, filterNum) = (1/numImages).*Wc_gradFilter;endWc_grad = Wc_grad + weightDecay * Wc;%% Unroll gradient into grad vector for minFuncgrad = [Wc_grad(:) ; Wd_grad(:) ; bc_grad(:) ; bd_grad(:)];end

minFuncSGD.m

function [opttheta] = minFuncSGD(funObj,theta,data,labels,...                        options)% Runs stochastic gradient descent with momentum to optimize the% parameters for the given objective.%% Parameters:%  funObj     -  function handle which accepts as input theta,%                data, labels and returns cost and gradient w.r.t%                to theta.%  theta      -  unrolled parameter vector%  data       -  stores data in m x n x numExamples tensor%  labels     -  corresponding labels in numExamples x 1 vector%  options    -  struct to store specific options for optimization%% Returns:%  opttheta   -  optimized parameter vector%% Options (* required)%  epochs*     - number of epochs through data%  alpha*      - initial learning rate%  minibatch*  - size of minibatch%  momentum    - momentum constant, defualts to 0.9%%======================================================================%% Setupassert(all(isfield(options,{'epochs','alpha','minibatch'})),...        'Some options not defined');if ~isfield(options,'momentum')    options.momentum = 0.9;end;epochs = options.epochs;alpha = options.alpha;minibatch = options.minibatch;m = length(labels); % training set size% Setup for momentummom = 0.5;momIncrease = 20;velocity = zeros(size(theta));%%======================================================================%% SGD loopit = 0;for e = 1:epochs        % randomly permute indices of data for quick minibatch sampling    rp = randperm(m);        for s=1:minibatch:(m-minibatch+1)        it = it + 1;        % increase momentum after momIncrease iterations        if it == momIncrease            mom = options.momentum;        end;        % get next randomly selected minibatch        mb_data = data(:,:,rp(s:s+minibatch-1));        mb_labels = labels(rp(s:s+minibatch-1));        % evaluate the objective function on the next minibatch        [cost grad] = funObj(theta,mb_data,mb_labels);                % Instructions: Add in the weighted velocity vector to the        % gradient evaluated above scaled by the learning rate.        % Then update the current weights theta according to the        % sgd update rule                %%% YOUR CODE HERE %%%        velocity = mom*velocity+alpha*grad;         theta = theta-velocity;        fprintf('Epoch %d: Cost on iteration %d is %f\n',e,it,cost);    end;    % aneal learning rate by factor of two after each epoch    alpha = alpha/2.0;end;opttheta = theta;end

运行结果：

本文作者：linger

本文链接：http://blog.csdn.net/lingerlanlan/article/details/41390443