Compress

   Gaussian mixutre compression.

   Compresses a Gaussian mixture so that it includes only 'm' components.
   We first remove components with tiny weigth and then we apply the 
   compression by Goldberger and Roweis (see Appendix A in the paper).

   Note that this can be applied to both normalized and unnormalized
   mixtures.

   Both Gaussian-based beliefs and alpha-elements are compressed. So, this 
   is one of the fundamental methods of this toolbox. Any improvement in
   this function results in a large speed up in the global planner.

0001 function gmC=Compress(gm,m)
0002 %   Gaussian mixutre compression.
0003 %
0004 %   Compresses a Gaussian mixture so that it includes only 'm' components.
0005 %   We first remove components with tiny weigth and then we apply the
0006 %   compression by Goldberger and Roweis (see Appendix A in the paper).
0007 %
0008 %   Note that this can be applied to both normalized and unnormalized
0009 %   mixtures.
0010 %
0011 %   Both Gaussian-based beliefs and alpha-elements are compressed. So, this
0012 %   is one of the fundamental methods of this toolbox. Any improvement in
0013 %   this function results in a large speed up in the global planner.
0014 
0015   if (gm.n<=m) || (m==0) % if gmC is not already compressed or not to be compressed
0016     gmC=gm;
0017   else
0018     % This is to ensure all weights are positive, in [0,1], and sum 1
0019     gmN=Normalize(gm);
0020 
0021     % Remove remove non-important components (to speed up next step)
0022     %   - gmLC is the sub-set of gmN with relemant components
0023     %   - mapLC is the index of the elements of gmN used to form gmLC
0024     [gmLC mapLC]=RemoveSmallComponents(gmN,0.1/gmN.n);
0025     
0026     % Use the Goldberger and Roweis compression
0027     %   - gmC is the compressed mixture
0028     %   - mapC are pointers from eleements in gmLC to elements in gmC
0029     %     (this allow to identify the elements in gmLC aggregated to form
0030     %     an element in gmC)
0031     [gmC mapC]=CompressGR(Normalize(gmLC),m,1e-5,50);
0032  
0033     % Recover the original weigths summing the weights of the input
0034     % components assigned to each  output component
0035     gmC.w=zeros(1,gmC.n);
0036     for i=1:gmC.n
0037       ndx=(mapC==i);
0038       gmC.w(i)=sum(gm.w(mapLC(ndx)));
0039     end
0040 
0041     % Caution: at this point gmC is not normalized any more
0042     gmC=RemoveSmallComponents(gmC,1e-3);
0043  end