一、Rbm阅读材料

    http://en.wikipedia.org/wiki/Restricted_Boltzmann_machine

    http://deeplearning.net/tutorial/rbm.html

二、Rbm训练的基本原理

三、Rbm代码分析

   

% 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
% 训练RBM，可视层是二值的，随机的；隐藏层也一样；它们之间的连接是对称连接.
% visible, binary, stochastic pixels are connected to
% hidden, binary, stochastic feature detectors using symmetrically  
% weighted connections. Learning is done with 1-step Contrastive Divergence.
% 学习只采用一次的CD.
% The program assumes that the following variables are set externally:
%下面的变量是外部设置的.
% maxepoch  -- maximum number of epochs
%@这个变量有待后面分析
% numhid    -- number of hidden units 
%隐藏单元的数量
% batchdata -- the data that is divided into batches (numcases numdims numbatches)
%训练集被分成块：样本个数*样本的特征维数
% restart   -- set to 1 if learning starts from beginning 
%有待理解@（如果学习从头开始，把这个变量设置为1？）

epsilonw      = 0.1;   % Learning rate for weights 
                       %控制权值的学习率
epsilonvb     = 0.1;   % Learning rate for biases of visible units
                       %控制可视单元的偏置的学习率
epsilonhb     = 0.1;   % Learning rate for biases of hidden units 
                       %控制隐藏单元偏置的学习率
weightcost  = 0.0002;  %@权值代价（有待理解）
initialmomentum  = 0.5;%@能量初始值
finalmomentum    = 0.9;%@最终能量值

[numcases numdims numbatches]=size(batchdata);
%@有左边输出变量有三个，这说明batchdata是三维的，第三维块的个数

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

% Initializing symmetric weights and biases. %初始化对称权值和偏置
  vishid     = 0.1*randn(numdims, numhid);
  %编程时，一定先给所采用的变量设定初始的矩阵来存贮
  %可视层与隐藏层之间的权值矩阵:行为输入的维数numdims,列为隐藏单元的总数
  hidbiases  = zeros(1,numhid);%隐藏层的偏置，维数等于隐藏单元的总数
  
  visbiases  = zeros(1,numdims);%可视层的偏置，维数等于可视单元的总数

  poshidprobs = zeros(numcases,numhid);
  %@pos、probs、numcases代表的含义有待求解
  %@猜测一下，poshidprobs是用来存放正样本训练集（numcases)通过各个隐藏单元的输出值
  neghidprobs = zeros(numcases,numhid);
  %@猜测一下，neghidprobs是用来存放负样本训练集（numcases)通过各个隐藏单元的输出值(概率）
  posprods    = zeros(numdims,numhid);
  %@猜测一下，posprobs是用来存放正样本最终训练出来的权值矩阵numdims,numhid
  negprods    = zeros(numdims,numhid);
  %@猜测一下，posprobs是用来存放负样本最终训练出来的权值矩阵numdims,numhid
  vishidinc  = zeros(numdims,numhid);
  %@“inc"有待理解，vishidinc是用来存放权值矩阵的中间值？
  hidbiasinc = zeros(1,numhid);
  %@“inc"有待理解，hidbiasinc是用来存放隐藏层的偏置？
  visbiasinc = zeros(1,numdims);
  %@“inc"有待理解，visbiasinc是用来存放可视层的偏置？
  batchposhidprobs=zeros(numcases,numhid,numbatches);
  %@batchposhidprobs有待理解
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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%@这个相当对隐藏层采样，然后求解<vh>0,因为<vh>0是就正的，所以取STRAT POSITIVE PHASE
%对于自编码器来说，这应该是编码阶段
  data = batchdata(:,:,batch);
  poshidprobs = 1./(1 + exp(-data*vishid - repmat(hidbiases,numcases,1)));    
  batchposhidprobs(:,:,batch)=poshidprobs;
  %batchposhidprobs存放着每个样对每个隐藏层单元状态为1的概率输出值，每块有100*1000个数
  %（对第一层来说）
  posprods    = data‘ * poshidprobs;
  poshidact   = sum(poshidprobs);%把100个样本得出的隐藏层单元输出值加起来
  posvisact = sum(data);%把块100个样本数据的各个特征加起来

%%%%%%%%% END OF POSITIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  poshidstates = poshidprobs > rand(numcases,numhid);
%判断隐藏层单元输出值是否大于一个随机矩阵中对应元素的值。如果大于随机矩阵中对应元素的值，将值改为1.
%即是把隐藏层单元输出值转化为0，1二值状态

%%%%%%%%% START NEGATIVE PHASE  %%%%%%%%%%%%%%%%%%%%%%    %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%@这个相当对隐藏层采样，然后求解<vh>1,因为<vh>1是就负的，所以取STRAT NEGTIVE PHASE
%对于自编码器来说，这应该是解码阶段
  negdata = 1./(1 + exp(-poshidstates*vishid‘ - repmat(visbiases,numcases,1)));
  %有点像求条件概率P3（RBM) h0->v1->h1(poshidstates以隐藏层单元输出的二值作为马尔科夫链的起始值，可视层第一次采样的数据？
  neghidprobs = 1./(1 + exp(-negdata*vishid - repmat(hidbiases,numcases,1)));    
  negprods  = negdata‘*neghidprobs;%@采样得到的可视层数据值乘以采样得到的隐藏层单元输出值得出啥？
  neghidact = sum(neghidprobs);
  negvisact = sum(negdata); 

%%%%%%%%% END OF NEGATIVE PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  err= sum(sum( (data-negdata).^2 ));
  %h0->v1 原始输入数据跟正负采样后产生的可视层数据的差，即是求重构误差
  errsum = err + errsum;

   if epoch>5,
     momentum=finalmomentum;
   else
     momentum=initialmomentum;
   end;
%能量大小的选择跟epoch的大小有关
%%%%%%%%% UPDATE WEIGHTS AND BIASES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%求完<vh>0和<vh>1后，就可以求解权值的增量了
    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); 
  %最后求出每个epoch的errsum
end;