关于RBM中k步对比散度算法CDK的认识

此图摘自受限玻尔兹曼机（RBM）学习笔记（六）对比散度算法，文章关于RBM的介绍非常详细，但是对于我这种小白还是有些地方不知理解对不对~~~如果有误，谢谢大家指正。

以下都是为了方便编写程序进行的理解：

首先外层循环就是为了针对所有样本。在第一层与第二层之间一行伪代码，是为了记录k步采样之前的原始数据，这个时候最好计算一下在已经随机给定各种参数，比如w，a，b的情况下，用S型函数计算的联合概率分布，以便计算后面△的时候使用。

然后第二层循环里面的第一个for循环就是精髓部分，即k步对比散度算法，在这里进行sample_h_given_v之前，要利用前面的参数计算一次negdata，然后再继续训练，就是里面的两行代码了。第一行用negdata使用S型函数计算隐藏层概率，然后可以计算出被激活的隐单元，然后看第二行伪代码，用激活的隐单元再次计算negdata，然后再计算隐藏层概率，不断地循环，循环次数就是对比散度算法中的K了。在重复完毕以后，也就是迭代次数为k时，计算出相关的参数w，a，b。

将上面两步的w，a，b相减就得到△了。

rbm的代码，这个代码中没有太明显体现出上面过程，因为取得是k=1的情况：

rbm.m

% Version 1.000 
%
% Code provided by Geoff Hinton and Ruslan Salakhutdinov 
%
% Permission is granted for anyone to copy, use, modify, or distribute this
% program and accompanying programs and documents for any purpose, provided
% this copyright notice is retained and prominently displayed, along with
% a note saying that the original programs are available from our
% web page.
% The programs and documents are distributed without any warranty, express or
% implied.  As the programs were written for research purposes only, they have
% not been tested to the degree that would be advisable in any important
% application.  All use of these programs is entirely at the user's own risk.

% This program trains Restricted Boltzmann Machine in which
% visible, binary, stochastic pixels are connected to
% hidden, binary, stochastic feature detectors using symmetrically
% weighted connections. Learning is done with 1-step Contrastive Divergence.   
% The program assumes that the following variables are set externally:
% 下面的参数都在外部设置
% maxepoch  -- maximum number of epochs 最大的训练数
% numhid    -- number of hidden units 隐单元个数
% batchdata -- the data that is divided into batches (numcases numdims numbatches)
%总数据被分批处理
% restart   -- set to 1 if learning starts from beginning 

epsilonw      = 0.1;   % Learning rate for weights 权重学习率
epsilonvb     = 0.1;   % Learning rate for biases of visible units 可见层偏置学习率
epsilonhb     = 0.1;   % Learning rate for biases of hidden units  隐单元偏置学习率
weightcost  = 0.0002;   
initialmomentum  = 0.5;  %初始动量
finalmomentum    = 0.9;  %最终动量

[numcases numdims numbatches]=size(batchdata);

if restart ==1,
  restart=0;
  epoch=1;

% Initializing symmetric weights and biases. 
  vishid     = 0.1*randn(numdims, numhid);  %可见层到隐藏层的权重
  hidbiases  = zeros(1,numhid); %隐藏层偏置
  visbiases  = zeros(1,numdims); %可见层偏置

  poshidprobs = zeros(numcases,numhid);  
  neghidprobs = zeros(numcases,numhid);
  posprods    = zeros(numdims,numhid);
  negprods    = zeros(numdims,numhid);
  vishidinc  = zeros(numdims,numhid);
  hidbiasinc = zeros(1,numhid);
  visbiasinc = zeros(1,numdims);
  batchposhidprobs=zeros(numcases,numhid,numbatches);
end

for epoch = epoch:maxepoch,
 fprintf(1,'epoch %d\r',epoch); 
 errsum=0;
 for batch = 1:numbatches,
 fprintf(1,'epoch %d batch %d\r',epoch,batch); 

%%%%%%%%% START POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%这个应该属于可见层到隐藏层的联合概率计算
  data = batchdata(:,:,batch);
  poshidprobs = 1./(1 + exp(-data*vishid - repmat(hidbiases,numcases,1)));    %用S函数计算联合概率，P(h=1|v)
  batchposhidprobs(:,:,batc h)=poshidprobs; %第batch批的概率分布
  posprods    = data' * poshidprobs;  %数据乘以概率
  poshidact   = sum(poshidprobs);  %总概率
  posvisact = sum(data);

%%%%%%%%% END OF POSITIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  poshidstates = poshidprobs > rand(numcases,numhid);  %隐藏层状态：0或者1

%%%%%%%%% START NEGATIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%这个部分就是反向计算的部分，从隐藏层到可见层
  negdata = 1./(1 + exp(-poshidstates*vishid' - repmat(visbiases,numcases,1)));  %预测数据
  neghidprobs = 1./(1 + exp(-negdata*vishid - repmat(hidbiases,numcases,1)));    
  negprods  = negdata'*neghidprobs;   %权重的更新
  neghidact = sum(neghidprobs); %隐含层偏置的更新
  negvisact = sum(negdata); %可见层偏置的更新

%%%%%%%%% END OF NEGATIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  err= sum(sum( (data-negdata).^2 ));
  errsum = err + errsum;

   if epoch>5,
     momentum=finalmomentum;
   else
     momentum=initialmomentum;
   end;

%%%%%%%%% UPDATE WEIGHTS AND BIASES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
    vishidinc = momentum*vishidinc + ...
                epsilonw*( (posprods-negprods)/numcases - weightcost*vishid);
    visbiasinc = momentum*visbiasinc + (epsilonvb/numcases)*(posvisact-negvisact);
    hidbiasinc = momentum*hidbiasinc + (epsilonhb/numcases)*(poshidact-neghidact);

    vishid = vishid + vishidinc;
    visbiases = visbiases + visbiasinc;
    hidbiases = hidbiases + hidbiasinc;

%%%%%%%%%%%%%%%% END OF UPDATES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 

  end
  fprintf(1, 'epoch %4i error %6.1f  \n', epoch, errsum); 
end;

再附加一个k=10的情况：

guassianfbm:

% Version 0.100 (Unsupported, unreleased)
%
% Code provided by Graham Taylor and Geoff Hinton
%
% For more information, see:
%    http://www.cs.toronto.edu/~gwtaylor/publications/icml2009
%
% Permission is granted for anyone to copy, use, modify, or distribute this
% program and accompanying programs and documents for any purpose, provided
% this copyright notice is retained and prominently displayed, along with
% a note saying that the original programs are available from our
% web page.
% The programs and documents are distributed without any warranty, expressed or
% implied.  As the programs were written for research purposes only, they have
% not been tested to the degree that would be advisable in any important
% application.  All use of these programs is entirely at the user's own risk.
%
% Train a factored, conditional RBM which has label units that modulate
% each pair of interactions训练一个具有标签单元的分解条件RBM，调节每一对的交互
% CRBM has gaussian visible and binary stochastic hidden units
% CRBM有高斯可见层和二值随机隐藏层
% Standard dev on Gaussian units is fixed to 1
% 高斯单元的标准差固定为1，应该就是标准高斯分布或者标准正态分布
% Feature-factor weights are shared特征-因子权重共享
%
% The program assumes that the following variables are set externally:
% nt        -- order of the model模型组织
% numepochs -- maximum number of epochs最大的训练数
% numhid    -- number of hidden units 隐藏单元个数
% numfeat   -- number of real-valued features between labels and factors
% 标签和因子之间的实参特征数
% numfac    --  number of factors 因子数目
% batchdata --  a matrix of data (numcases,numdims) 帧数*感兴趣关节角
% minibatch -- a cell array of dimension batchsize, indexing the valid
% frames in batchdata
% restart   -- set to 1 if learning starts from beginning 

%batchdata is a big matrix of all the frames
%we index it with "minibatch", a cell array of mini-batch indices
numbatches = length(minibatch); %是一组随机数29823-42*12=29319，这里总共有294个numbatches

numdims = size(batchdata,2);  % visible dimension可见层也就是感兴趣层维数58
numlabels = size(labeldata,2);% 10个标签

%Setting learning rates学习率的设置
%Corresponding to the "undirected" observation model无向观察模型
epsilonvisfac=single(1e-2);   %无向观察模型学习率0.01，可见层(输出层)到因子层(output-factors)
%only one set of featfac parameters
%shared between undirected, A & B models下面就是AB模型之间的共享
epsilonfeatfac=single(1e-2);%feature到因子层三个权值共享一个，所以只有一个学习率0.01
epsilonhidfac=single(1e-2);%隐藏层到因子层，hidden-factor是0.01

%Corresponding to the "directed" Autoregressive model两个有向自回归子模型
%A，也就是最下面那个蓝色的连接的三个地方里面的km(v<t到m)和im(v=t到m)
epsilonpastfacA=single(1e-3);  %这一个代表的就是过去的与最下面的因子称为m的连接0.001
epsilonvisfacA=single(1e-3);   %这一个代表的就是现在的与最下面的因子称为m的连接0.001

%Corresponding to the "directed" past->hidden model
%对应有向的过去到隐藏层模型，从图中可以看到那个绿色的(也就是B)连接了past和hidden
epsilonpastfacB=single(1e-2); %从past连接到B  是0.01
epsilonhidfacB=single(1e-2); %从B连接到hid    是0.01

epsilonlabelfeat=single(1e-3); %从标签层到特征层的学习率0.001

epsilonvisbias=single(1e-2);  %可见层偏置学习率0.01
epsilonhidbias=single(1e-2);  %隐含层偏置学习率0.01
%epsilonvishid=1e-3;  %gated biases

%currently we use the same weight decay for all weights当前，把所有的权重设置为一个
%but no weight decay for biases没有偏置的权重衰减
wdecay = single(0.0002);

mom = single(0.9);       %momentum used only after 5 epochs of training

if restart==1,  
  restart=0;
  epoch=1;
 
  %weights  
  visfac = single(0.01*randn(numdims,numfac));%可见层到因子层权重58*200(58是第二次预处理得到的关节数)
  featfac = single(0.01*randn(numfeat,numfac));%特征层到因子层的权重100*200(预定义的numfeat=100)
  hidfac = single(0.01*randn(numhid,numfac));%隐藏层到因子层之间的权重600*200(预定义的隐藏层数目600)
    
  %Note the new parameterization of pastfac:
  %First numdims rows correspond to time t-nt  %往回看的帧数，第一帧=当前帧-后退的帧数
  %Last numdims rows correspond to time t-1    %往回看的帧数，最后帧=当前帧-1
  pastfacA = single(0.01*randn(nt*numdims,numfac)); %（12*58）*200=696*200维对于A那一个子模型，蓝色的那个，过去到因子层
  visfacA = single(0.01*randn(numdims,numfac));     %58*200对于A那一个子模型，蓝色的那个，可见层到因子层
  
  pastfacB = single(0.01*randn(nt*numdims,numfac)); %696*200维对于B那一个子模型，绿色的那个，过去到因子层
  hidfacB = single(0.01*randn(numhid,numfac));      %600*200对于B那一个子模型，绿色的那个，隐藏层到因子层
      
  %matrix where rows are per-label features
  labelfeat = single(0.01*randn(numlabels,numfeat));  %10*100的维数标签-特征对
  
  %biases
  visbiases = zeros(1,numdims,'single');  %可见层偏置1*58
  hidbiases = zeros(1,numhid,'single');   %隐藏层偏置1*600
  %vishid = 0.01*randn(numdims,numhid);
     
  clear posdataprod pospastprod poshidprod posvishidprod posvisact poshidact
  clear negdataprod negpastprod neghidprod negvishidprod negvisact neghidact

  %keep previous updates around for momentum  %为当前状态保存前面的更新信息
  visfacinc = zeros(size(visfac),'single');   %可见层到因子层的信息
  featfacinc = zeros(size(featfac),'single'); %特征层到因子层的信息
  hidfacinc = zeros(size(hidfac),'single');   %隐藏层到因子层的信息
  
  pastfacAinc = zeros(size(pastfacA),'single');  %过去到因子层A(最下面蓝色的)的信息
  visfacAinc = zeros(size(visfacA),'single');    %可见层到因子层A(最下面蓝色)的信息
  
  pastfacBinc = zeros(size(pastfacB),'single');  %过去层到因子层B(中间绿色的)的信息
  hidfacBinc = zeros(size(hidfacB),'single');    %隐藏层到因子层B(中间绿色的)的信息
  
  labelfeatinc = zeros(size(labelfeat),'single'); %标签层到特征层
  
  visbiasinc = zeros(size(visbiases),'single');   %可见层偏置
  hidbiasinc = zeros(size(hidbiases),'single');   %隐藏层偏置
  %vishidinc = zeros(size(vishid));    
end

%Main loop
for epoch = epoch:maxepoch,  %1到200 训练周期
  errsum=0; %keep a running total of the difference between data and recon
  for batch = 1:numbatches,     %1到294因为总共294个小批，每个小批100个数据帧，最后一个19个数据

%%%%%%%%% START POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
    numcases = length(minibatch{batch});   %除了最后一次是19，其他都是100
    mb = minibatch{batch}; %caches the indices  找到对应批次的内容，里面存的是随机数，前面定义过
    
    past = zeros(numcases,nt*numdims,'single'); %initialization  100*696
    
    data = single(batchdata(mb,:));%把随机数对应的那个帧的数据取出来一般来说是100*58维的(每批100帧，每帧58个维度)
    %use pastindex to index the appropriate frames in batchdata
    %(for each frame in the minibatch) depending on the delay
    %past = reshape(batchdata(pastindex,:),numcases,nt*numdims);    
    %past = batchdata(mb-1,:); %one step in the past
    
    %Easiest way to build past is by a loop
    %Past looks like [ [data time t-nt] ... [data time t-1] ] 
    for hh=nt:-1:1 %note reverse order 100个随机帧的前面12个帧信息的综合，即100*(12*58维)
      past(:,numdims*(nt-hh)+1:numdims*(nt-hh+1)) = batchdata(mb-hh,:) + randn(numcases,numdims);
    end

    %get the features from the one-hot labels
    labels = labeldata(mb,:);  %100*10维度从单热度编码中获取特征，说白了就是根据标签找到对应的特征，这句话的功能是根据这个随机帧mb找到它的风格标签
    features = labels*labelfeat; %根据标签找到对应的哪一个风格，lables每一行只有一个1，乘以labelfeat就可以找到对应的行了
    
    
    %DEBUG
    %past = double(rand(size(past))>0.5);
    %calculate inputs to factors (will be used many times)
    yvis = data*visfac; %summing over numdims当前批的帧100*58维度，乘以，输出层到因子层的权重58*200维
    yfeat = features*featfac; %summing over numfeat特征层100*100维度，乘以特征层到因子层的偏置100*200维，feature是100*100的原因在于每批100帧，每帧100个特征数目
        
    ypastA = past*pastfacA;     %summing over nt*numdims  过去的100帧前面的12帧数据100*(12*58)维，乘以，输入层(前N帧)到因子层的权重696*200
    yfeatA = features*featfac;  %summing over numfeat     特征层100*100乘以特征到因子的权重100*200
    yvisA = data*visfacA;       %summing over numdims     当前100帧100*58维，乘以，输出层到因子层的偏置58*200
    
    ypastB = past*pastfacB;     %summing over nt*numdims  过去帧100*696维，乘以，过去帧到因此层的维度696*200
    yfeatB = features*featfac;  %summing over numfeat     特征100*100维，乘以，特征到因子层的权重维度100*200
        
    yvisfeat = yvis.*yfeat; %used twice, so cache         先存着，因为要用两次
    ypastfeatB = ypastB.*yfeatB; %used twice, so cache    先存着，因为要用两次
    
    %pass 3-way term + gated biases + hidbiases through sigmoid 
    %从图中可以看到，隐藏层是由f和n这两个因子决定的，所以发现连接的是yfeat和yvis和hidfac，ypastB和yfeatB和hidfacB
    %联合概率使用S函数，指数值为两个连接到hidden layer的因子与hidden layer本身的偏置和，符号是S函数自带的
    poshidprobs = 1./(1 + exp(-yvisfeat*hidfac'  ...
      -ypastfeatB*hidfacB' - repmat(hidbiases,numcases,1)));
      %-data*vishid - repmat(hidbiases,numcases,1)));  repmat按照行重复
    
    %Activate the hidden units    激活隐单元
    hidstates = single(poshidprobs > rand(numcases,numhid)); %全是0和1
    
    yhid = hidstates*hidfac;%找到激活的单元，把权重保留，其他的权重置零
    yhid_ = poshidprobs*hidfac; %smoothed version  %概率乘以隐藏层到因子层的权值
    
    yhidB_ = poshidprobs*hidfacB; %smoothed version  %概率乘以隐藏层到因子层n(也就是B)的权值
    
    %these are used multiple times, so cache
    yvishid_ = yvis.*yhid_;  
    yvispastA = yvisA.*ypastA;
    ypasthidB_ = ypastB.*yhidB_;
    yfeatpastA = yfeatA.*ypastA;                    
    
    %Calculate statistics needed for gradient update
    %Gradients are taken w.r.t neg energy
    %Note that terms that are common to positive and negative stats
    %are left out
    posvisprod = data'*(yfeat.*yhid_); %smoothed
    posfeatprod = features'*(yvishid_); %smoothed
    poshidprod = poshidprobs'*(yvisfeat); %smoothed
    
    posvisAprod = data'*(yfeatpastA);
    posfeatAprod = features'*(yvispastA);
    pospastAprod =  past'*(yvisA.*yfeatA);
   
    pospastBprod = past'*(yfeatB.*yhidB_); %smoothed
    posfeatBprod =  features'*(ypasthidB_); %smoothed
    poshidBprod =  poshidprobs'*(ypastfeatB);
    
    %Now the gradients for the label/feature matrix
    %First find the grad terms w.r.t. the features
    %Then backpropagate (it's linear, so simply matrix multiply)
    %There are three terms, since the features gate the undirected & two
    %sets of directed connections
%     posfeatgrad = (yvishid_)*featfac' + ...
%       (yvispastA)*featfac' + ...
%       (ypasthidB_)*featfac'; 
    
   posfeatgrad = (yvishid_ + yvispastA + ypasthidB_)*featfac';  %计算梯度
    
    
    %posvishidprod = data'*poshidprobs;
    posvisact = sum(data,1);
    poshidact = sum(poshidprobs,1);  %smoothed             
    
%%%%%%%%% END OF POSITIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%% START NEGATIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
%10步对比散度算法
  for cdn = 1:cdsteps    
    %Activate the visible units
    %Collect 3-way terms + vis biases + gated biases 
    %note use of stochastic hidstates
    %Mean-field version (do not add Gaussian noise)        
    negdata = (yfeat.*yhid)*visfac' + ...
      (yfeatpastA)*visfacA' + ...
      repmat(visbiases,numcases,1);    %应该是通过f和m两个因子重构的输出值100*58维
    
    yvis = negdata*visfac;
    yvisfeat = yvis.*yfeat; %used twice, so cache     
    
    %pass 3-way term + gated biases + hidbiases through sigmoid 
    neghidprobs = 1./(1 + exp(-yvisfeat*hidfac'  ...
      -ypastfeatB*hidfacB' - repmat(hidbiases,numcases,1)));

    if cdn == 1
      %Calculate reconstruction error计算重构误差
      err= sum(sum( (data(:,:,1)-negdata).^2 ));
      errsum = err + errsum;
    end
 
    if cdn == cdsteps     
      yhidB_ = neghidprobs*hidfacB; %smoothed version 
      yhid_ = neghidprobs*hidfac; %smoothed version
      yvishid_ = yvis.*yhid_;
      yvisA = negdata*visfacA;       %summing over numdims
      yvispastA = yvisA.*ypastA;
      ypasthidB_ = ypastB.*yhidB_;
      %last cd step -- Calculate statistics needed for gradient update
      %Gradients are taken w.r.t neg energy
      %Note that terms that are common to positive and negative stats
      %are left out
      %对于f因子层的三个连接，每一条连接都是用另外两条的数据得到
      negvisprod = negdata'*(yfeat.*yhid_); %smoothed 
      negfeatprod = features'*(yvishid_); %smoothed
      neghidprod = neghidprobs'*(yvisfeat); %smoothed

      %对于m因子层的三个连接
      negvisAprod = negdata'*(yfeatpastA);
      negfeatAprod = features'*(yvispastA);
      negpastAprod =  past'*(yvisA.*yfeatA);

      %对于n因子层的三个连接
      negpastBprod = past'*(yfeatB.*yhidB_); %smoothed
      negfeatBprod =  features'*(ypasthidB_); %smoothed
      neghidBprod =  neghidprobs'*(ypastfeatB);

      %Now the gradients for the label/feature matrix
      %First find the grad terms w.r.t. the features
      %Then backpropagate (it's linear, so simply matrix multiply)
      %There are three terms, since the features gate the undirected & two
      %sets of directed connections
%       negfeatgrad = (yvishid_)*featfac' + ...
%         (yvispastA)*featfac' + ...
%         (ypasthidB_)*featfac';

      negfeatgrad = (yvishid_ + yvispastA + ypasthidB_)*featfac';
      
      %negvishidprod = data'*neghidprobs;
      negvisact = sum(negdata,1);
      neghidact = sum(neghidprobs,1);  %smoothed

    else
      %Stochastically sample the hidden units
      hidstates = single(neghidprobs > rand(numcases,numhid));      
      yhid = hidstates*hidfac;
    end 
  end
      
     
 

%%%%%%%%% END NEGATIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
    if epoch > 5 %use momentum
        momentum=mom;
    else %no momentum
        momentum=0;
    end
    
%%%%%%%%% UPDATE WEIGHTS AND BIASES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
visfacinc = momentum*visfacinc + ...
  epsilonvisfac*( ( posvisprod - negvisprod)/numcases - wdecay*visfac);
featfacinc = momentum*featfacinc + ...
  epsilonfeatfac*((posfeatprod + posfeatAprod + posfeatBprod ...
  - negfeatprod - negfeatAprod - negfeatBprod)/numcases - wdecay*featfac);
% featfacinc = momentum*featfacinc + ...
%   epsilonfeatfac*( (posfeatprod - negfeatprod)/numcases - wdecay*featfac);
hidfacinc = momentum*hidfacinc + ...
  epsilonhidfac*( (poshidprod - neghidprod)/numcases - wdecay*hidfac);   %前面一个参数应该是学习率，后面那个wdecay应该是权重衰减率

visfacAinc = momentum*visfacAinc + ...
  epsilonvisfacA*( (posvisAprod - negvisAprod)/numcases - wdecay*visfacA);
% featfacAinc = momentum*featfacAinc + ...
%   epsilonfeatfacA*( (posfeatAprod - negfeatAprod)/numcases - wdecay*featfacA);
pastfacAinc = momentum*pastfacAinc + ...
  epsilonpastfacA*( (pospastAprod - negpastAprod)/numcases - wdecay*pastfacA);

hidfacBinc = momentum*hidfacBinc + ...
  epsilonhidfacB*( (poshidBprod - neghidBprod)/numcases - wdecay*hidfacB);
% featfacBinc = momentum*featfacBinc + ...
%   epsilonfeatfacB*( (posfeatBprod - negfeatBprod)/numcases - wdecay*featfacB);
pastfacBinc = momentum*pastfacBinc + ...
  epsilonpastfacB*( (pospastBprod - negpastBprod)/numcases - wdecay*pastfacB);

labelfeatinc = momentum*labelfeatinc + ...
  epsilonlabelfeat*( labels'*(posfeatgrad - negfeatgrad)/numcases - wdecay*labelfeat);

%两个偏置
visbiasinc = momentum*visbiasinc + ...
  (epsilonvisbias/numcases)*(posvisact - negvisact);
hidbiasinc = momentum*hidbiasinc + ...
  (epsilonhidbias/numcases)*(poshidact - neghidact);


visfac = visfac + visfacinc;
featfac = featfac + featfacinc;
hidfac = hidfac + hidfacinc;

visfacA = visfacA + visfacAinc;
pastfacA = pastfacA + pastfacAinc;  %没有featfacA和featfacB的原因是参数feat-fac的参数共享

hidfacB = hidfacB + hidfacBinc;
pastfacB = pastfacB + pastfacBinc;

labelfeat = labelfeat + labelfeatinc;

%sfigure(34); imagesc(labelfeat); colormap gray; axis off     
%drawnow;

visbiases = visbiases + visbiasinc;
hidbiases = hidbiases + hidbiasinc;
    
%%%%%%%%%%%%%%%% END OF UPDATES  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    
  end
    
  %every 10 epochs, show output   每十个周期输出一次
  if mod(epoch,10) ==0
      fprintf(1, 'epoch %4i error %6.1f  \n', epoch, errsum);
      
      if 0%mod(epoch,100)==0
      
      %show hiddens      要播放的帧
      plotindex = 101:500; %frames of batchdata that we will plot
      nc = length(plotindex);
      
      data = batchdata(plotindex,:);      
      
      past = zeros(nc,nt*numdims); %initialization用过去的十二帧初始化
      for hh=nt:-1:1 %note reverse order
        %past(:,numdims*(hh-1)+1:numdims*hh) = initdata(hh:end-(nt-hh+1),:);
        past(:,numdims*(nt-hh)+1:numdims*(nt-hh+1)) = batchdata(plotindex-hh,:);   %在batchdata中把对应的帧(101-500)保存
      end
      
      labels = labeldata(plotindex,:);
      features = labels*labelfeat;     
      
      yvis = data*visfac; %summing over numdims
      yfeat = features*featfac; %summing over numfeat

      ypastB = past*pastfacB;     %summing over nt*numdims
      yfeatB = features*featfac; %summing over numfeat

      yvisfeat = yvis.*yfeat; %used twice, so cache
      ypastfeatB = ypastB.*yfeatB; %used twice, so cache

      %pass 3-way term + gated biases + hidbiases through sigmoid
      poshidprobs = 1./(1 + exp(-yvisfeat*hidfac'  ...
        -ypastfeatB*hidfacB' - repmat(hidbiases,nc,1)));

      sfigure(32); imagesc(poshidprobs'); colormap gray; axis off;      

      yhid_ = poshidprobs*hidfac; %smoothed version
      ypastA = past*pastfacA;     %summing over nt*numdims
      yfeatA = features*featfac;  %summing over numfeat
      yfeatpastA = yfeatA.*ypastA;       
      
      %look at mean-field reconstruction
      negdata = (yfeat.*yhid_)*visfac' + ...
        (yfeatpastA)*visfacA' + ...
        repmat(visbiases,nc,1);      
      
      sfigure(33);clf
      subplot(2,1,1); plot(data(:,7)); hold on; plot(negdata(:,7),'r');
      subplot(2,1,2); plot(data(:,18)); hold on; plot(negdata(:,18),'r');
      
      %sfigure(34); imagesc(labelfeat); colormap gray; axis off         
      
      %Hinton plots of parameters
      %Likely do not want to plot all dims, all hiddens, all factors
      maxdims = 30; maxhid = 100; maxfac = 50;
      maxpast = 2; %how many time steps in past to plot (pastfac)
      
      %undirected model
      sfigure(35); 
      subplot(3,1,1); hinton(visfac(1:maxdims,1:maxfac));
      subplot(3,1,2); hinton(featfac(:,1:maxfac));
      subplot(3,1,3); hinton(hidfac(1:maxhid,1:maxfac));
      set(gcf,'Name','undirected')      
           
      %autoregressive model
      sfigure(36);
      %for past, we only want to plot maxdims & maxpast
      %i don't know how to do this without a loop
      pastrows = [];
      for kk=maxpast:-1:1 %note reverse
        %select maxdims rows corresponding to time step kk
        pastrows = [pastrows; pastfacA(end-kk*numdims+1:...
          end-kk*numdims+maxdims, 1:maxfac)];
      end      
      subplot(3,1,1); hinton(pastrows);
      %subplot(3,1,2); hinton(featfacA(:,1:maxfac));
      subplot(3,1,3); hinton(visfacA(1:maxdims,1:maxfac));
      set(gcf,'Name','autoregressive')           
      
      %directed vis -> hid model
      sfigure(37);
      %see comment above
      pastrows = [];
      for kk=maxpast:-1:1 %note reverse
        %select maxdims rows corresponding to time step kk
        pastrows = [pastrows; pastfacB(end-kk*numdims+1:...
          end-kk*numdims+maxdims, 1:maxfac)];
      end     
      subplot(3,1,1); hinton(pastrows);
      %subplot(3,1,2); hinton(featfacB(:,1:maxfac));
      subplot(3,1,3); hinton(hidfacB(1:maxhid,1:maxfac));
      set(gcf,'Name','directed')   
      
      %labelfeat and biases
      sfigure(34);
      subplot(3,1,1); hinton(visbiases(1:maxdims));
      subplot(3,1,2); hinton(hidbiases(1:maxhid));
      subplot(3,1,3); hinton(labelfeat);
      set(gcf,'Name','labelfeat and biases')
      
      
%       %Could see a plot of the weights every 10 epochs
%       sfigure(33);
%       subplot(2,3,1); hinton(visfac);
%       subplot(2,3,2); hinton(pastfac);
%       subplot(2,3,3); hinton(hidfac);
%       subplot(2,3,4); hinton(vishid);
%       subplot(2,3,5); hinton(visbiases);
%       subplot(2,3,6); hinton(hidbiases);
%       drawnow;
%       sfigure(34);
%       subplot(3,1,1); imagesc(data'); colormap gray; axis off
%       subplot(3,1,2); imagesc(poshidprobs',[0 1]); colormap gray; axis off
%       subplot(3,1,3); imagesc(negdata',[0 1]); colormap gray; axis off
%       drawnow;
      %figure(3); weightreport
      %drawnow;
      end      
  end
  %Checkpoint models 
  %最终得到的就是可见层-因子层权重、特征曾-因子层权重、隐藏层-因子层权重、过去-因子层A(或者称为m)的权重、可见层-因子层A的权重
  %过去-因子层B的权重、隐藏层-因子层B的权重、标签-特征的权重；可见层偏置，隐藏层偏置、k步采样、隐藏层单元个数、周期数、训练帧数
  if mod(epoch,snapshotevery) ==0  %每100帧来一张快照
    snapshot_file = [snapshot_path '_ep' num2str(epoch) '.mat'];
    save(snapshot_file, 'visfac','featfac','hidfac', ...
      'pastfacA','visfacA', ...
      'pastfacB','hidfacB', ...
      'labelfeat','visbiases','hidbiases', ...
      'cdsteps', 'numhid','numfac','epoch', 'nt');
  end

  drawnow; %update any plots你可以理解为把当前需要画的东西都画到屏幕上。一般用于循环内，显示动画效果。看看文档的例子吧http://cn.mathworks.com/help/matlab/ref/drawnow.html
end