MATLAB deeplearning-toolbox CNN

网络结构

卷积层：

cnn.layers = {

struct(‘type’, ‘i’) %input layer

struct(‘type’, ‘c’, ‘outputmaps’, 6, ‘kernelsize’, 5) %convolution layer

struct(‘type’, ‘s’, ‘scale’, 2) %sub sampling layer

struct(‘type’, ‘c’, ‘outputmaps’, 12, ‘kernelsize’, 5) %convolution layer

struct(‘type’, ‘s’, ‘scale’, 2) %subsampling layer

};

输出层：包含10个神经元

实验参数：

opts.batchsize = 50; % 每次训练输入样本的个数

opts.numepochs = 10; % 训练迭代次数

实验结果：

错误率：0.0237

下面画出均方误差随迭代次数改变的曲线：



第一个卷积层提取样本特征：



第二个卷积层提取样本特征：



代码：

test_CNN.m

function test_example_CNN
addpath(genpath('../'));
load mnist_uint8;

% 显示测试集前几个手写字符图像
test_x_0=[];
for i=1:size(test_x,1)
temp=test_x(i,:);
temp=reshape(temp,28,28)';
temp=temp(:);
test_x_0=[test_x_0 temp];
end

figure();
display_network(test_x_0(:,1:10));
set(gca,'position',[0 0 1 1]);

train_x = double(reshape(train_x',28,28,60000))/255;
test_x = double(reshape(test_x',28,28,10000))/255;
train_y = double(train_y');
test_y = double(test_y');

%% ex1 Train a 6c-2s-12c-2s Convolutional neural network
%will run 1 epoch in about 200 second and get around 11% error.
%With 100 epochs you'll get around 1.2% error

rand('state',0)

cnn.layers = {
struct('type', 'i') %input layer
struct('type', 'c', 'outputmaps', 6, 'kernelsize', 5) %convolution layer
struct('type', 's', 'scale', 2) %sub sampling layer
struct('type', 'c', 'outputmaps', 12, 'kernelsize', 5) %convolution layer
struct('type', 's', 'scale', 2) %subsampling layer
};

opts.alpha = 1;
opts.batchsize = 50; % 每次训练输入样本的个数
opts.numepochs = 10; % 训练迭代次数

cnn = cnnsetup(cnn, train_x, train_y);
cnn = cnntrain(cnn, train_x, train_y, opts);
save cnn-conv3_0.mat cnn;
% load cnn.mat;

[er, bad] = cnntest(cnn, test_x, test_y);
disp(['error rate: ' num2str(er)]);
% plot mean squared error
figure; plot(cnn.rL);
assert(er<0.12, 'Too big error');

cnnsetup.m

function net = cnnsetup(net, x, y)
inputmaps = 1;
mapsize = size(squeeze(x(:, :, 1)));
%尤其注意这几个循环的参数的设定
%numel(net.layers)  表示有多少层
for l = 1 : numel(net.layers)   %  layer
if strcmp(net.layers{l}.type, 's')
mapsize = mapsize / net.layers{l}.scale;
%subsampling层的mapsize，最开始mapsize是每张图的大小28*28(这是第一次卷积后的结果，卷积前是32*32)
%这里除以scale，就是pooling之后图的大小，这里为14*14
assert(all(floor(mapsize)==mapsize), ['Layer ' num2str(l) ' size must be integer. Actual: ' num2str(mapsize)]);
for j = 1 : inputmaps %inputmap就是上一层有多少张特征图，通过初始化为1然后依层更新得到
net.layers{l}.b{j} = 0;
end
end
if strcmp(net.layers{l}.type, 'c')
mapsize = mapsize - net.layers{l}.kernelsize + 1;
%这里的mapsize可以参见UFLDL里面的那张图下面的解释
fan_out = net.layers{l}.outputmaps * net.layers{l}.kernelsize ^ 2;
%隐藏层的大小，是一个(后层特征图数量)*(用来卷积的patch图的大小)
for j = 1 : net.layers{l}.outputmaps  %  output map
fan_in = inputmaps * net.layers{l}.kernelsize ^ 2;
%对于每一个后层特征图，有多少个参数链到前层
for i = 1 : inputmaps  %  input map
net.layers{l}.k{i}{j} = (rand(net.layers{l}.kernelsize) - 0.5) * 2 * sqrt(6 / (fan_in + fan_out));
end
net.layers{l}.b{j} = 0;
end
inputmaps = net.layers{l}.outputmaps;
end
end
% 'onum' is the number of labels, that's why it is calculated using size(y, 1). If you have 20 labels so the output of the network will be 20 neurons.
% 'fvnum' is the number of output neurons at the last layer, the layer just before the output layer.
% 'ffb' is the biases of the output neurons.
% 'ffW' is the weights between the last layer and the output neurons. Note that the last layer is fully connected to the output layer, that's why the size of the weights is (onum * fvnum)
fvnum = prod(mapsize) * inputmaps;
onum = size(y, 1);
%这里是最后一层神经网络的设定
net.ffb = zeros(onum, 1);
net.ffW = (rand(onum, fvnum) - 0.5) * 2 * sqrt(6 / (onum + fvnum));
end

cnntrain.m

function net = cnntrain(net, x, y, opts)
m = size(x, 3);
numbatches = m / opts.batchsize;
if rem(numbatches, 1) ~= 0
error('numbatches not integer');
end
net.rL = [];
for i = 1 : opts.numepochs
disp(['epoch ' num2str(i) '/' num2str(opts.numepochs)]);
tic;
kk = randperm(m);
for l = 1 : numbatches
batch_x = x(:, :, kk((l - 1) * opts.batchsize + 1 : l * opts.batchsize));
batch_y = y(:,    kk((l - 1) * opts.batchsize + 1 : l * opts.batchsize));

net = cnnff(net, batch_x);
net = cnnbp(net, batch_y);
net = cnnapplygrads(net, opts);
if isempty(net.rL)
net.rL(1) = net.L;
end
net.rL(end + 1) = 0.99 * net.rL(end) + 0.01 * net.L;
end
toc;
end

end

cnnff.m

function net = cnnff(net, x)
n = numel(net.layers);
net.layers{1}.a{1} = x;
inputmaps = 1;

for l = 2 : n   %  for each layer
if strcmp(net.layers{l}.type, 'c')
%  !!below can probably be handled by insane matrix operations
for j = 1 : net.layers{l}.outputmaps   %  for each output map
%  create temp output map
z = zeros(size(net.layers{l - 1}.a{1}) - [net.layers{l}.kernelsize - 1 net.layers{l}.kernelsize - 1 0]);
for i = 1 : inputmaps   %  for each input map
%  convolve with corresponding kernel and add to temp output map
%  做卷积，参考UFLDL，这里是对每一个input的特征图做一次卷积，再加起来
z = z + convn(net.layers{l - 1}.a{i}, net.layers{l}.k{i}{j}, 'valid');
end
%  add bias, pass through nonlinearity
%  加入bias
net.layers{l}.a{j} = sigm(z + net.layers{l}.b{j});
end
%  set number of input maps to this layers number of outputmaps
inputmaps = net.layers{l}.outputmaps;
elseif strcmp(net.layers{l}.type, 's')
%  downsample
for j = 1 : inputmaps
%这里有点绕绕的，它是新建了一个patch来做卷积，但我们要的是pooling，所以它跳着把结果读出来，步长为scale
%这里做的是mean-pooling
z = convn(net.layers{l - 1}.a{j}, ones(net.layers{l}.scale) / (net.layers{l}.scale ^ 2), 'valid');   %  !! replace with variable
net.layers{l}.a{j} = z(1 : net.layers{l}.scale : end, 1 : net.layers{l}.scale : end, :);
end
end
end
%  收纳到一个vector里面，方便后面用~~
%  concatenate all end layer feature maps into vector
net.fv = [];
for j = 1 : numel(net.layers{n}.a)
sa = size(net.layers{n}.a{j});
net.fv = [net.fv; reshape(net.layers{n}.a{j}, sa(1) * sa(2), sa(3))];
end
%  最后一层的perceptrons，数据识别的结果
net.o = sigm(net.ffW * net.fv + repmat(net.ffb, 1, size(net.fv, 2)));

end

cnnbp.m

function net = cnnbp(net, y)
n = numel(net.layers);
%  error
net.e = net.o - y;
%  loss function
net.L = 1/2* sum(net.e(:) .^ 2) / size(net.e, 2);
%从最后一层的error倒推回来deltas
%和神经网络的bp有些类似
%%  backprop deltas
net.od = net.e .* (net.o .* (1 - net.o));   %  output delta
net.fvd = (net.ffW' * net.od);              %  feature vector delta
if strcmp(net.layers{n}.type, 'c')         %  only conv layers has sigm function
net.fvd = net.fvd .* (net.fv .* (1 - net.fv));
end
%和神经网络类似，参看神经网络的bp

%  reshape feature vector deltas into output map style
sa = size(net.layers{n}.a{1});
fvnum = sa(1) * sa(2);
for j = 1 : numel(net.layers{n}.a)
net.layers{n}.d{j} = reshape(net.fvd(((j - 1) * fvnum + 1) : j * fvnum, :), sa(1), sa(2), sa(3));
end
%这是算delta的步骤
%这部分的计算参看Notes on Convolutional Neural Networks，其中的变化有些复杂
%和这篇文章里稍微有些不一样的是这个toolbox在subsampling(也就是pooling层)没有加sigmoid激活函数
%所以这地方还需仔细辨别
%这这个toolbox里的subsampling是不用计算gradient的，而在上面那篇note里是计算了的
for l = (n - 1) : -1 : 1
if strcmp(net.layers{l}.type, 'c')
for j = 1 : numel(net.layers{l}.a)
net.layers{l}.d{j} = net.layers{l}.a{j} .* (1 - net.layers{l}.a{j}) .* (expand(net.layers{l + 1}.d{j}, [net.layers{l + 1}.scale net.layers{l + 1}.scale 1]) / net.layers{l + 1}.scale ^ 2);
end
elseif strcmp(net.layers{l}.type, 's')
for i = 1 : numel(net.layers{l}.a)
z = zeros(size(net.layers{l}.a{1}));
for j = 1 : numel(net.layers{l + 1}.a)
z = z + convn(net.layers{l + 1}.d{j}, rot180(net.layers{l + 1}.k{i}{j}), 'full');
end
net.layers{l}.d{i} = z;
end
end
end
%参见paper，注意这里只计算了'c'层的gradient，因为只有这层有参数
%%  calc gradients
for l = 2 : n
if strcmp(net.layers{l}.type, 'c')
for j = 1 : numel(net.layers{l}.a)
for i = 1 : numel(net.layers{l - 1}.a)
net.layers{l}.dk{i}{j} = convn(flipall(net.layers{l - 1}.a{i}), net.layers{l}.d{j}, 'valid') / size(net.layers{l}.d{j}, 3);
end
net.layers{l}.db{j} = sum(net.layers{l}.d{j}(:)) / size(net.layers{l}.d{j}, 3);
end
end
end
%最后一层perceptron的gradient的计算
net.dffW = net.od * (net.fv)' / size(net.od, 2);
net.dffb = mean(net.od, 2);

function X = rot180(X)
X = flipdim(flipdim(X, 1), 2);
end
end

cnnapplygrads.m

function net = cnnapplygrads(net, opts)
for l = 2 : numel(net.layers)
if strcmp(net.layers{l}.type, 'c')
for j = 1 : numel(net.layers{l}.a)
for ii = 1 : numel(net.layers{l - 1}.a)
net.layers{l}.k{ii}{j} = net.layers{l}.k{ii}{j} - opts.alpha * net.layers{l}.dk{ii}{j};
end
net.layers{l}.b{j} = net.layers{l}.b{j} - opts.alpha * net.layers{l}.db{j};
end
end
end

net.ffW = net.ffW - opts.alpha * net.dffW;
net.ffb = net.ffb - opts.alpha * net.dffb;
end

cnntest.m

function [er, bad] = cnntest(net, x, y)
%  feedforward
net = cnnff(net, x);

for l = 2 : numel(net.layers)  %  for each layer
if strcmp(net.layers{l}.type, 'c')
for k = 1 : 10  %  显示十个样本的特征图像
w=[];
for j = 1 : net.layers{l}.outputmaps   %  for each output map
w1 = reshape(net.layers{l}.a{j}(:,:,k), size(net.layers{l}.a{j},1), size(net.layers{l}.a{j},1))';
w1 = w1(:);
w = [w1 w];

end
figure();
display_network (w);
end
end
end

[~, h] = max(net.o);
[~, a] = max(y);
bad = find(h ~= a);

er = numel(bad) / size(y, 2);
end