CompressGR

   Gaussian mixture compression using the Golberger and Roweis method.

   Compresses a normalized Gaussian mixture so that it includes at most
   'm' elements.
   This function implements the method by Golberger and Roweis described
   in appendix A of the paper.

   Parameters
     gm: The normalized mixture to compress
     m: The maximum number of components in  the output compressed
         normalized mixture.
     epsilon: Convergence criterion. If the relative error between two
              iterations changes less than epsilon we stop the process.
     MaxIterations: If the process iterates more times than this threshold
                    the compression process is stopped.
   Output:
     gmC: The output normalized mixture.
     map: Map between components in the input mixtures and those in the
          output one (This in \pi in Table 3 in Appendix A in the paper).

0001 function [gmC map]=CompressGR(gm,m,epsilon,MaxIterations)                                                    
0002 %   Gaussian mixture compression using the Golberger and Roweis method.
0003 %
0004 %   Compresses a normalized Gaussian mixture so that it includes at most
0005 %   'm' elements.
0006 %   This function implements the method by Golberger and Roweis described
0007 %   in appendix A of the paper.
0008 %
0009 %   Parameters
0010 %     gm: The normalized mixture to compress
0011 %     m: The maximum number of components in  the output compressed
0012 %         normalized mixture.
0013 %     epsilon: Convergence criterion. If the relative error between two
0014 %              iterations changes less than epsilon we stop the process.
0015 %     MaxIterations: If the process iterates more times than this threshold
0016 %                    the compression process is stopped.
0017 %   Output:
0018 %     gmC: The output normalized mixture.
0019 %     map: Map between components in the input mixtures and those in the
0020 %          output one (This in \pi in Table 3 in Appendix A in the paper).
0021 
0022   if (gm.n<=m)
0023     % 'gm' is already compressed
0024     gmC=gm;
0025     map=1:gm.n; %trivial mapping one to one
0026   else
0027     
0028     gmC=GetLargestComponents(gm,m);
0029     % gmC=GetRandomComponents(gm,m);
0030     % gmC=GetFirstComponents(gm,m);
0031 
0032     % default fake distance
0033     d=inf;
0034     
0035     % default mapping (just to allocate space)
0036     map=1:gm.n;
0037     
0038     iteration=1;
0039     stop=false;
0040     while ~stop
0041 
0042       %Compute the mapping from 'gm' to 'gmC
0043       for i=1:gm.n
0044         f=gm.g{i};
0045         [md map(i)]=min(cellfun(@(g)GaussianKL(f,g),gmC.g));
0046       end
0047 
0048       %Update 'gmC'
0049       for j=1:m
0050         % get the components of gm that are close to the j component of gmC
0051         ndx=(map==j);
0052         sw=sum(gm.w(ndx));
0053         if sw>0
0054           gmC.w(j)=sw;
0055           gmC.g{j}=FuseComponents(GMixture(gm.w(ndx)/sw,gm.g(ndx)));
0056         else
0057           % None of the components of gm is close to this component of gmC
0058           % Replace with one random component from gm
0059           m1=ceil(rand*gm.n);
0060           gmC.w(j)=gm.w(m1);
0061           gmC.g{j}=gm.g{m1};
0062         end
0063       end
0064       gmC=Normalize(gmC);
0065 
0066       % Update the distance from 'gmC' to 'gm'
0067       d1=d; 
0068       d=cellfun(@(f,g)(GaussianKL(f,g)),gm.g,gmC.g(map))*gm.w';
0069 
0070       iteration=iteration+1;
0071       
0072       stop=((d<epsilon)||(abs(d1-d)/d<epsilon));
0073 
0074       if (~stop)
0075         if (d1<d)
0076           error('Increasing distance');
0077         end
0078         if (iteration>MaxIterations)
0079           error('Too slow convergence');
0080         end
0081       end
0082     end
0083 
0084   end