FindNeighborhood

 [Cliques] = FindNeighborhood(MI,sizeconstraint,MIthreshold)
 FindNeighborhood:   Find the neighborhood of each variable using the values of the mutual
                     information
                     Neighbors are those variables whose interaction is above the MIthreshold 
                     Each variable neighborhood is constrained to be at most of size sizeconstraint
 INPUTS:  
 T: Truncation parameter (when T=0, proportional selection is used)
 F: Name of the function that has as an argument a vector or NumbVar variables
 CantGen: Maximum number of generations 
 MaximumFunction:  Maximum of the function that can be used as stop condition when it is known 
 Card: Vector with the dimension of all the variables. 
 Elitism: Number of the current population individuals that pass to the next one.  
---Elistism=-1: The whole selected population (only for truncation) passes to the next generation  
 OUTPUTS
    Cliques: Structure of the model in a list of cliques that defines the neighborhood 
    Each row of Cliques is a clique. The first value is the number of neighbors for variable i. 
    The second, is the number of new variables (one new variable, i).
    Then, neighbor variables are listed and  finally new variables (variable i) are listed
    When Cliques is empty, the model is learned from the data

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

0001 function [Cliques] = FindNeighborhood(MI,sizeconstraint,MIthreshold)
0002 % [Cliques] = FindNeighborhood(MI,sizeconstraint,MIthreshold)
0003 % FindNeighborhood:   Find the neighborhood of each variable using the values of the mutual
0004 %                     information
0005 %                     Neighbors are those variables whose interaction is above the MIthreshold
0006 %                     Each variable neighborhood is constrained to be at most of size sizeconstraint
0007 % INPUTS:
0008 % T: Truncation parameter (when T=0, proportional selection is used)
0009 % F: Name of the function that has as an argument a vector or NumbVar variables
0010 % CantGen: Maximum number of generations
0011 % MaximumFunction:  Maximum of the function that can be used as stop condition when it is known
0012 % Card: Vector with the dimension of all the variables.
0013 % Elitism: Number of the current population individuals that pass to the next one.
0014 %---Elistism=-1: The whole selected population (only for truncation) passes to the next generation
0015 % OUTPUTS
0016 %    Cliques: Structure of the model in a list of cliques that defines the neighborhood
0017 %    Each row of Cliques is a clique. The first value is the number of neighbors for variable i.
0018 %    The second, is the number of new variables (one new variable, i).
0019 %    Then, neighbor variables are listed and  finally new variables (variable i) are listed
0020 %    When Cliques is empty, the model is learned from the data
0021 %
0022 % Last version 8/26/2008. Roberto Santana and Siddarta Shakya (roberto.santana@ehu.es)
0023 
0024 NumbVars = size(MI,1);
0025 epsilon = 1e-200; % It is used to avoid bias when the mutual information is equal
0026 
0027 %for i=2:3:29,
0028 % Cliques(i-1,:) = [2,1,i,i+1,i-1];
0029 % Cliques(i,:) = [2,1,i-1,i+1,i];
0030 % Cliques(i+1,:) = [2,1,i-1,i,i+1];
0031 %end,
0032 %return
0033 
0034 for i=1:NumbVars,   
0035     candidates = find(MI(i,:)>MIthreshold);
0036     ncandidates = size(candidates,2);   
0037     if(ncandidates > sizeconstraint)
0038       [MIvals,VarOrder] = sort(MI(i,candidates)+rand(1,ncandidates)*epsilon,'descend');
0039       %shuffle = randperm(ncandidates);
0040       Cliques(i,1:sizeconstraint+3) = [sizeconstraint,1,candidates(VarOrder(1:sizeconstraint)),i];
0041     elseif(ncandidates > 0)
0042       Cliques(i,1:ncandidates+3) = [ncandidates,1,candidates,i];
0043     else % No neighbor for variable i
0044      Cliques(i,1:3) = [0,1,i];
0045     end,
0046 end,    
0047