FactAffinityElim

 [Cliques,deep]=FactAffinityElim(MI,vars,sizeconstraint,p,deep)
 FactAffinityElim:        Finds a set of cliques from a matrix of mutual information
                          using affinity propagation. The application of
                          the algorithm is recursive.
 INPUTS
 vars:              vars that will be involved in the factorization (initially all the
                    variables
 sizeconstraint: Maximum size of the factors involved in the factorization
 p: Preference parameter for affinity propagation
 deep: Parameter to control the recursive calls
 OUTPUTS
 Cliques: Structure of the model in a list of cliques that defines the (chain shaped)  junction tree. 
          Each row of Cliques is a clique. The first value is the number of overlapping variables. 
          The second, is the number of new variables.
          Then, overlapping variables are listed and  finally new variables are listed.

 Last version 8/26/2008. Roberto Santana (roberto.santana@ehu.es)

0001 function [Cliques,deep]=FactAffinityElim(MI,vars,sizeconstraint,p,deep)
0002 % [Cliques,deep]=FactAffinityElim(MI,vars,sizeconstraint,p,deep)
0003 % FactAffinityElim:        Finds a set of cliques from a matrix of mutual information
0004 %                          using affinity propagation. The application of
0005 %                          the algorithm is recursive.
0006 % INPUTS
0007 % vars:              vars that will be involved in the factorization (initially all the
0008 %                    variables
0009 % sizeconstraint: Maximum size of the factors involved in the factorization
0010 % p: Preference parameter for affinity propagation
0011 % deep: Parameter to control the recursive calls
0012 % OUTPUTS
0013 % Cliques: Structure of the model in a list of cliques that defines the (chain shaped)  junction tree.
0014 %          Each row of Cliques is a clique. The first value is the number of overlapping variables.
0015 %          The second, is the number of new variables.
0016 %          Then, overlapping variables are listed and  finally new variables are listed.
0017 %
0018 % Last version 8/26/2008. Roberto Santana (roberto.santana@ehu.es)
0019 
0020 
0021 if deep>=10
0022    MI = MI + mean(MI(:))*rand(size(MI)); 
0023 end
0024 
0025 
0026 n = size(MI,1);
0027 outvars = [];
0028 
0029 [idx,netsim,dpsim,expref,unconverged]=apcluster(MI,p,'dampfact',0.5); %Find the clusters of the MI matrix
0030 nconv = 0;
0031 while(unconverged & nconv<10)
0032   [idx,netsim,dpsim,expref,unconverged]=apcluster(MI+min(MI(:))*rand(size(MI)),p,'dampfact',0.9);
0033   nconv = nconv+1
0034 end
0035 
0036 Cliques = [];
0037 nclusters = length(unique(idx));
0038 exemplars = unique(idx);
0039 for i=1:nclusters
0040  clusters{i} = find(idx==exemplars(i));
0041  clustsize = size(clusters{i},1);
0042 
0043  if(clustsize>sizeconstraint)
0044     outvars = [outvars,clusters{i}'];
0045  else
0046    %vars(clusters{i}')'
0047    Cliq = [0,clustsize,vars(clusters{i}'),zeros(1,sizeconstraint-clustsize)];
0048    Cliques = [Cliques;Cliq];
0049  end
0050 end
0051 if(~isempty(outvars)) 
0052   if(isempty(Cliques))  
0053    deep = deep + 1;
0054   end,
0055 
0056   MI1 = MI(:,outvars);
0057   MI1 = MI1(outvars,:);
0058   p = median(MI1); %median(MI1(:));
0059   %p=  min(MI1(:))+(max(MI1(:))-min(MI1(:)))*rand();  % Set preference to median similarity
0060   [Cliques1,deep]=FactAffinityElim(MI1,vars(outvars),sizeconstraint,p,deep);
0061   Cliques = [Cliques;Cliques1];
0062 end
0063 
0064 
0065