SAMI/MissingNodes_SrcCode2014/MissingNodes_Sparse.m

function [ rand_score, purity,   p_triads, missing_nodes_mapping, removed_nodes] = MissingNodes_Sparse( dataFilePath, dataFileName, affinityType, percentKnownPlaceholdersVec, missingNodes )
%UNTITLED2 Summary of this function goes here
%   Detailed explanation goes here
%[SUCCESS,MESSAGE,MESSAGEID] = mkdir('C:\\MissingNodes\\Code\\Results\\',dataFileName);

global g_threshold;
% addpath 'Spectral Clustering' % sigal 13.8.12
% addpath 'mex'% sigal 13.8.12

p_triads = [];
%create a log file for this run
%date_now = clock;
%date_now = strcat(num2str(date_now(1)),'_',num2str(date_now(2)),'_', num2str(date_now(3)),'_', num2str(date_now(4)), num2str(date_now(5)),'_', num2str(date_now(6)));
%diary(strcat('C:\missingnodes\Code\Log\log', date_now,'.log'));

%affinity calculation types
global affinity_calculation_shortest_path;
global affinity_calculation_euclid;
global affinity_calculation_common_friends;
global affinity_calculation_random_clustering;
global affinity_calculation_adamic_adar;
global affinity_calculation_katz_beta_0_5;
global affinity_calculation_katz_beta_0_05;
global affinity_calculation_katz_beta_0_005;

affinity_calculation_shortest_path = 0;
affinity_calculation_euclid = 1;
affinity_calculation_common_friends = 2;
affinity_calculation_random_clustering = 3;
affinity_calculation_adamic_adar = 4;
affinity_calculation_katz_beta_0_5 = 5;
affinity_calculation_katz_beta_0_05 = 6;
affinity_calculation_katz_beta_0_005 = 7;


%percent_known_placeholders_vec = [0.9, 0.8, 0.7, 0.6, 0.5,1];

%%%%% for distance as function of num placeholders %%%%
if nargin < 4
      percent_known_placeholders_vec = [0.5];
else
      percent_known_placeholders_vec = percentKnownPlaceholdersVec;
end

if nargin >= 5
      select_random_missing_nodes = 0;
else
      select_random_missing_nodes = 1;
end
      
compensate_for_unknown_placeholers = 0;

%configuration parameters
%num_values = 100000; %number of values to read from the raw data
%graph_sizes = [400 600 800 1000 1200 1400]; %size of the graph matrix
%graph_sizes = [400 1000]; %size of the graph matrix

num_missing_nodes_arr = 5 : 5 : 30; %number of missing nodes from the network
num_missing_nodes_arr = [11,21,31,41,50]; % 20;
num_missing_nodes_arr = [5 10];
unite_common_friends = 0; %should UNK nodes be united in accordance with the "friend of my friend principle"

cluster_only_missing_nodes = 1;
% if affinity_calculation_type == affinity_calculation_shortest_path || affinity_calculation_type == affinity_calculation_euclid
%     non_neighbors_distance = Inf;
% elseif affinity_calculation_type == affinity_calculation_common_friends
%     non_neighbors_distance = 0;
% end

non_neighbors_distance = 0;

%read the full network, up to num_values links
%disp('reading network information from file...');
fprintf('reading network information from file %s%s ...\n', dataFilePath, dataFileName);
load(strcat(dataFilePath, dataFileName), 'data');

data = sparse(data);

clear('graph');

%rand_score = zeros(2, 2, size(num_missing_nodes_arr,2), 6, 2); %(normalized or not, unite common friends, num missing nodes, affinity calculation, cluster only missing)
%rand_score_sq = rand_score;
%purity = zeros(2, size(num_missing_nodes_arr,2), 6, 2);%(unite common friends, num missing nodes, affinity calculation, cluster only missing)
%purity_sq = purity;
rand_score = [];
purity = [];

graph_size = size(data,1);
%num_missing_nodes_arr = round(num_missing_nodes_arr .* graph_size);

%initialize the data matrix (binary adjacency)
disp('generating network graph...');

actual_graph_size = size(data,1);

original_data = data;
missing_nodes_mapping = [];
for num_missing_nodes_idx = 1 : size(num_missing_nodes_arr,2)
      if select_random_missing_nodes
            num_missing_nodes = num_missing_nodes_arr(1, num_missing_nodes_idx);
      else
            num_missing_nodes = length(missingNodes);
      end
      
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      %remove random nodes                                                                  %
      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      
      %randomize the missing nodes indexes and sort in descending order
      %disp('selecting random missing nodes...');
      fprintf('selecting %d random missing nodes...\n',num_missing_nodes);

      if select_random_missing_nodes
            [data, missing_nodes_mapping] = RemoveRandomNodes( original_data, num_missing_nodes, missing_nodes_mapping, non_neighbors_distance );
      else
            [data, missing_nodes_mapping] = RemoveRandomNodes( original_data, num_missing_nodes, missing_nodes_mapping, non_neighbors_distance, missingNodes);
      end
      
      data_untouched = data;
      
      for percent_known_placeholders = percent_known_placeholders_vec
            data = data_untouched;
            S = zeros(1, size(data,2));
            num_placeholders_to_remove = 0;
            placeholders_to_remove = [];
            num_placeholders = size(data,1) - actual_graph_size + num_missing_nodes ;
            last_known_node = size(data,1) - num_placeholders;
            
            if percent_known_placeholders < 1

                  num_placeholders_to_remove = round(num_placeholders * (1 - percent_known_placeholders));
                                    
                  while size(placeholders_to_remove, 2) < num_placeholders_to_remove
                      %randomly selecting unique placeholder indexes
                        placeholders_to_remove = unique([placeholders_to_remove, randi(num_placeholders, 1, num_placeholders_to_remove - size(placeholders_to_remove, 2))]);
                  end
                  
                  %rand_vec = rand(1, num_placeholders);
                  %placeholders_to_remove = find(rand_vec > percent_known_placeholders) + last_known_node;
                  
                  placeholders_to_remove = placeholders_to_remove + last_known_node;
                                    
                  %S is the group of neighbors of the unknown placeholders
                  S = data(placeholders_to_remove(1), :);
                  for i = placeholders_to_remove
                        S = S | data(i,:);
                  end
                  
                  %switch from binary vector to list of indexes
                 % S = find(S);
                  
                 data_all_placeholders = data;
                  data(placeholders_to_remove,:) = [];
                  data(:,placeholders_to_remove) = [];
                  
                  num_placeholders = num_placeholders - num_placeholders_to_remove;
            end
            
            
            removed_nodes{num_missing_nodes_idx} = missing_nodes_mapping(1,:); %save the removed nodes in each iteration
            
            
            disp('finding all pairs shortest paths...');
            
            
            
            %if we got an argument for the affinity calculation type then use
            %it. otherwise loop over all the types
            if nargin >= 3
                  affinity_types = affinityType;
            else
                  affinity_types = affinity_calculation_shortest_path: affinity_calculation_katz_beta_0_005;
            end
            
            orig_S = S;
            for affinity_calculation_type = affinity_types
                 for withAttr = 0:1 
                 
                  fprintf('affinity_calculation_type = %d\n', affinity_calculation_type);
                  
                  %data = data_untouched;
                  first_unk_node = actual_graph_size - num_missing_nodes + 1;
                  
                  num_added_nodes = size(data,1) - first_unk_node + 1;
                  
                  % calculate the affinity / similarity matrix
                  fprintf('calculating affinity matrix, type %d...\n', affinity_calculation_type);
                  
                  
                  tic %affinity_calc_time
                  affinity = CalcAffinity( data, affinity_calculation_type, actual_graph_size, num_missing_nodes);
                  affinity_calc_time = toc;%affinity_calc_time
                  
                  %TODO: extend the dimension reduction to adding missing
                  %links / reclustering
                  for reduce_dimensions = [1] %0 must be first because it does not change the affinity matrix
                       
                        reduce_dim_time = 0;
                        if reduce_dimensions == 1
                              tic %ReduceDimensions
                              [affinity, num_placeholders, first_unk_node] = ReduceDimensions(affinity, first_unk_node);
                             reduce_dim_time = toc; %ReduceDimensions
                        end
                        
                        fprintf('calculating true clustering\n');
                        
                        true_clustering = BuildTrueClustering(missing_nodes_mapping, actual_graph_size, num_missing_nodes, percent_known_placeholders, placeholders_to_remove, last_known_node);
                        
                        %figure,imshow(affinity,[]), title('Affinity Matrix')
                        for num_clusters_known = [1] %[0 1]
                              
                              k = DetermineNumberOfClusters(num_clusters_known, data_untouched, actual_graph_size, num_missing_nodes, num_added_nodes);

                              last_known_node =  first_unk_node - 1;
                              
                              tic %graph_predict_time
                              [newData, test_clustering] = PredictGraph(affinity, k, data, num_placeholders, affinity_calculation_type, cluster_only_missing_nodes);
                              graph_predict_time = toc; %graph_predict_time
                              
                              if compensate_for_unknown_placeholers == 1
                                    S = orig_S;

                                    if size(newData,1) > size(S,2)
                                        %for breakpoint
                                          tttt = 98;
                                    end
                                    sigma = 1/4;
                                    S = S(1:size(newData,1));
                                    S = S + randn(size(S)) * sigma;
                                    sorted_S = sort(S, 'descend');


                                    %sum over the columns and find the columns which
                                    %indicate at least one neighbor
                                    neighbors_of_new_nodes = find(sum(newData(first_unk_node:size(newData,1), :)));

                                    first_united_node = size(newData,1) - k +1;
                                    newAffinity = CalcAffinityByKatzBeta_Sparse( newData, 0.05, 4  );

                                    %newAffinity = CalculateAffinityByAdamicAdar_Sparse(newData, size(newData,1), 0, 0);
                                    
                                    
                                    newNodesAffinity = newAffinity(first_united_node:size(newAffinity,1), :);
                                    newNodesAffinity(newNodesAffinity>=1) = 0;
                                    newNodesAffinity = newNodesAffinity / max(max(newNodesAffinity));
                                    %newNodesAffinity = newNodesAffinity / 2;

                                    newNodesAffinity(newData(first_united_node:size(newAffinity,1), :) >= 1) = 0;

                                    newNodesAffinity = (newNodesAffinity / max(max(newNodesAffinity)));
                                    %%%%trying to take only the
                                    %%%%k highest affinities
                                    sortedNewNodesAffinity = sort(newNodesAffinity(:), 'descend');
                                    %affinityThreshold = sortedNewNodesAffinity(k + size(neighbors_of_new_nodes, 2));
                                    newNodesAffinity_orig = newNodesAffinity;
                              end
                              
                              if percent_known_placeholders < 1
                                    %calculating as a function
                                    %of number of links added
                                    maxNumLinksToAdd = mean(sum(data(1:last_known_node, 1:last_known_node))) * num_placeholders;
                                    maxNumLinksToAdd = min(maxNumLinksToAdd, 25);
                              else
                                    maxNumLinksToAdd = 0;                                  
                              end
                              %%%%% for distance as
                              %%%%% function of num
                              %%%%% placeholders %%%%
                              
                              %max_neighbors = S >= sorted_S(maxNumLinksToAdd);
                              for numLinksToAdd = 0 : maxNumLinksToAdd
                                    
                                    if compensate_for_unknown_placeholers == 1

                                          newNodesAffinity = newNodesAffinity_orig;

                                          neighbors = [];
                                          if numLinksToAdd > 0

                                                neighbors = find(S >= sorted_S(numLinksToAdd), numLinksToAdd);                                         

                                          end

                                          newDataWithMissingLinks = newData;
                                          newDataForClustering = data;
                                          for neighbor = neighbors
                                                [value, closest_new_node] = max(newNodesAffinity(:,neighbor));
                                                closest_new_node = closest_new_node(1);
                                                newDataWithMissingLinks(first_united_node +  closest_new_node - 1, neighbor) = 1;
                                                newDataWithMissingLinks(neighbor, first_united_node +  closest_new_node - 1) = 1;                                         

                                                newPlaceholder = zeros(1, size(newDataForClustering,2));
                                                newPlaceholder(neighbor) = 1;
                                                newDataForClustering = [newDataForClustering, newPlaceholder';
                                                                                                                  newPlaceholder, 0];    
                                                                                                         
                                                

                                          end                                          
                                          

                                          affinityWithS = CalcAffinity( newDataForClustering, affinity_calculation_type, actual_graph_size, num_missing_nodes);

                                          if reduce_dimensions == 1
                                                [affinityWithS, num_placeholdersWithS, first_unk_node_with_s] = ReduceDimensions(affinityWithS, first_united_node);
                                          else
                                                num_placeholdersWithS  =  num_placeholders + length(neighbors);  
                                                first_unk_node_with_s = first_united_node;                                          
                                          end

                                          [newPredictedGraph, newClustering] = PredictGraph(affinityWithS, k, newDataForClustering, num_placeholdersWithS, affinity_calculation_type, cluster_only_missing_nodes);



                                          %remap the original data so that
                                          %the known nodes match the
                                          %predicted data and the missing
                                          %nodes match the predicted nodes
                                          %created from each cluster
                                          perm_vector = 1:size(original_data,1);
                                          perm_vector(missing_nodes_mapping(1,:)) = [];
                                          perm_vector = [perm_vector, missing_nodes_mapping(1,:)];
                                          remapped_data = original_data(perm_vector,perm_vector);

                                          [small_data, indices_to_remove] = DecreaseGraphSize(remapped_data, first_united_node : size(remapped_data,1), neighbors); %changed from neighbors to perm(max_neighbors) - to be fair when there are more nieghbors
                                          %small_data2 = DecreaseGraphSize(newData, last_known_node+1 : size(newData,1));
                                          %new_nodes_affinity_sum = sum(sum(newNodesAffinity));

                                          %in case there is an empty cluster, the unrelated nodes may contain node index that does not exist
                                          %in the predicted graph (which may contain less nodes)
                                          indices_to_remove(indices_to_remove > size(newPredictedGraph,2)) = [];


                                          small_data2 = newData;
                                          small_data2(indices_to_remove,:) = [];
                                          small_data2(:,indices_to_remove) = [];
                                          %small_data3 = DecreaseGraphSize(newDataWithMissingLinks, last_known_node+1 : size(newDataWithMissingLinks,1));
                                          small_data3 = newDataWithMissingLinks;
                                          small_data3(indices_to_remove,:) = [];
                                          small_data3(:,indices_to_remove) = [];

                                          small_data4 = newPredictedGraph;
                                          small_data4(indices_to_remove,:) = [];
                                          small_data4(:,indices_to_remove) = [];


                                          %only calculate on
                                          %the first iteration
                                          %to save time
                                          if numLinksToAdd == 0
                                                edit_distance = GraphEditDistance( small_data, small_data2, num_missing_nodes );
                                                edit_distance2 = edit_distance;
                                                edit_distance3 = edit_distance;
                                          else
                                                edit_distance2 = GraphEditDistance( small_data, small_data3, num_missing_nodes );
                                                edit_distance3 = GraphEditDistance( small_data, small_data4, num_missing_nodes );
                                          end
                                    else
                                          perm_vector = 1:size(original_data,1);
                                          perm_vector(missing_nodes_mapping(1,:)) = [];
                                          perm_vector = [perm_vector, missing_nodes_mapping(1,:)];
                                          remapped_data = original_data(perm_vector,perm_vector);

                                          [small_data, indices_to_remove] = DecreaseGraphSize(remapped_data, (size(remapped_data,1) - num_missing_nodes + 1) : size(remapped_data,1), []); %changed from neighbors to perm(max_neighbors) - to be fair when there are more nieghbors
                                          
                                          indices_to_remove(indices_to_remove > size(newData,2)) = [];
                                          small_data2 = newData;
                                          small_data2(indices_to_remove,:) = [];
                                          small_data2(:,indices_to_remove) = [];
                                          
                                          edit_distance = GraphEditDistance( small_data, small_data2, num_missing_nodes );                                          
                                    end
                                    
                                    
                                          
                                    %fprintf('num_links_to_add = %d; missing links distance = %d, new clustering dist = %d\n', numLinksToAdd, full(edit_distance2), full(edit_distance3));
                                    
                                    fprintf('calculating purity\n');
                                   
                                    curr_index = size(purity,2) + 1;
                                    
                                    %purity for actual clustering
                                    try
                                          temp_purity = ClusteringPurity(true_clustering, test_clustering);
                                    catch ME1
                                          temp_purity = 1; % Sigal 12.8.12 - tmp %
                                          ddddd = 1;
                                    end
                                    
                                    purity(curr_index).score = temp_purity;
                                    purity(curr_index).score_sq = temp_purity^2;
                                    purity(curr_index).edit_distance = edit_distance;
                                    if compensate_for_unknown_placeholers == 1
                                          purity(curr_index).numLinksToAdd = numLinksToAdd;                                          
                                          purity(curr_index).edit_distance_missing_links = edit_distance2;
                                          purity(curr_index).edit_distance_new_clustering = edit_distance3;
                                          fprintf('numLinksToAdd - %d\nedit_distance - %d\nedit_distance_missing_links - %d\nedit_distance_new_clustering - %d\n', numLinksToAdd, full(edit_distance), full(edit_distance2), full(edit_distance3)); 
                                    end
                                    purity(curr_index).withAttr = withAttr;
                                    purity(curr_index).unite_common_friends = unite_common_friends;
                                    purity(curr_index).num_missing_nodes_idx = num_missing_nodes_idx;
                                    purity(curr_index).num_missing_nodes = num_missing_nodes_arr(num_missing_nodes_idx);
                                    purity(curr_index).affinity_calculation_type = affinity_calculation_type;
                                    purity(curr_index).cluster_only_missing_nodes = cluster_only_missing_nodes;
                                    purity(curr_index).num_clusters_known = num_clusters_known;
                                    purity(curr_index).num_placeholders = num_placeholders;
                                    purity(curr_index).num_placeholders_to_remove = num_placeholders_to_remove;
                                    purity(curr_index).iteration = 1;
                                    purity(curr_index).test_clustering = test_clustering;
                                    purity(curr_index).true_clustering = true_clustering;
                                    purity(curr_index).graph_size = graph_size;
                                    purity(curr_index).inverse_purity = 1; % Sigal 12.8.12 - tmp % CalculateInversePurity(true_clustering, test_clustering);
                                    purity(curr_index).NMI = 0; %CalcNormalizedMutualInformation(true_clustering, test_clustering);
                                    purity(curr_index).removed_nodes = removed_nodes;
                                    purity(curr_index).percent_known_placeholders = percent_known_placeholders;
                                    purity(curr_index).reduce_dimensions = reduce_dimensions;
                                    purity(curr_index).missing_nodes_mapping = missing_nodes_mapping;
                                    purity(curr_index).compensate_for_unknown_placeholers = compensate_for_unknown_placeholers;  
                                    purity(curr_index).affinity_calc_time = affinity_calc_time;
                                    purity(curr_index).reduce_dim_time = reduce_dim_time;
                                    purity(curr_index).graph_predict_time = graph_predict_time;
                                    
                                    if compensate_for_unknown_placeholers == 0
                                          break
                                    end
                              end
                              %
                              %                     purity(unite_common_friends+1, num_missing_nodes_idx,  affinity_calculation_type+1, cluster_only_missing_nodes+1)  = ...
                              %                         purity(unite_common_friends+1, num_missing_nodes_idx,  affinity_calculation_type+1, cluster_only_missing_nodes+1) + temp_purity;
                              %
                              %                     purity_sq(unite_common_friends+1, num_missing_nodes_idx,  affinity_calculation_type+1, cluster_only_missing_nodes+1)  = ...
                              %                         purity_sq(unite_common_friends+1, num_missing_nodes_idx,  affinity_calculation_type+1, cluster_only_missing_nodes+1) + temp_purity^2;
                              %

                              
                              %fprintf('affinity_calculation_type = %d, unite_common_friends = %d\n', affinity_calculation_type, unite_common_friends);
                              %fprintf('Graph size: %d, Number of missing nodes: %d, Purity: %f \n' ,graph_size, num_missing_nodes, temp_purity);
                              %fprintf('============================================\n\n\n');
                              
                              %clear U;
                              
                              clear eigValues;
                              clear eigVectors;
                              
                        end
                  end
                  clear('affinity');
                 end   
            end
      end
end
end


function [affinity] = CalcAffinity( data, affinity_calculation_type, actual_graph_size, num_missing_nodes)
global affinity_calculation_shortest_path;
global affinity_calculation_euclid;
global affinity_calculation_common_friends;
global affinity_calculation_random_clustering;
global affinity_calculation_adamic_adar;
global affinity_calculation_katz_beta_0_5;
global affinity_calculation_katz_beta_0_05;
global affinity_calculation_katz_beta_0_005;


if affinity_calculation_type == affinity_calculation_euclid
      sp_mat = graphallshortestpaths(data);
      %remove INF values
      max_value = max(sp_mat(sp_mat ~= Inf)) + 1;
      sp_mat_euclid = sp_mat;
      sp_mat_euclid(sp_mat == Inf) = max_value;
      affinity = CalculateAffinity(sp_mat_euclid);
      %affinity = exp(-(sp_mat.^2))/(2 * 0.3^2);
elseif affinity_calculation_type == affinity_calculation_shortest_path
      %                 max_value = max(sp_mat(sp_mat ~= Inf)) + 1;
      %                 sp_mat_euclid = sp_mat;
      %                 sp_mat_euclid(sp_mat == Inf) = max_value;
      %                 affinity = (sp_mat_euclid + 1).^(-affinity_exp_factor);
      
      
      %affinity = spfun(affinityFunc, data);
      affinity = graphallshortestpaths(data);
      affinity = affinity .^ -2;
      
      affinity(affinity == Inf) = 1; %added on 05/11/11
      
elseif affinity_calculation_type == affinity_calculation_common_friends
      affinity = CalcAffinityByCommonNeighbors_Sparse(data, actual_graph_size, num_missing_nodes);
      %affinity = CalcAffinityByCommonNeighbors(data, actual_graph_size, num_missing_nodes);
elseif affinity_calculation_type == affinity_calculation_random_clustering
      affinity = data; %just a placeholder...
elseif affinity_calculation_type == affinity_calculation_adamic_adar
      affinity =  CalculateAffinityByAdamicAdar_Sparse( data, actual_graph_size, num_missing_nodes, 1  );
      if nnz(affinity) < 5
            x = 8;
      end
elseif affinity_calculation_type == affinity_calculation_katz_beta_0_5
      affinity = CalcAffinityByKatzBeta_Sparse( data, 0.5, 3  );
elseif affinity_calculation_type == affinity_calculation_katz_beta_0_05
      affinity = CalcAffinityByKatzBeta_Sparse( data, 0.05, 4 );
elseif affinity_calculation_type == affinity_calculation_katz_beta_0_005
      affinity = CalcAffinityByKatzBeta_Sparse( data, 0.005, 4 );
end

end

function [test_clustering] = SpectralClustering(affinity, k, num_placeholders, affinity_calculation_type, cluster_only_missing_nodes)

global affinity_calculation_shortest_path;
global affinity_calculation_euclid;
global affinity_calculation_common_friends;
global affinity_calculation_random_clustering;
global affinity_calculation_adamic_adar;
global affinity_calculation_katz_beta_0_5;
global affinity_calculation_katz_beta_0_05;
global affinity_calculation_katz_beta_0_005;

first_unk_node = size(affinity,1) - num_placeholders + 1;

diagonal = sum(affinity, 2); %sum the rows
D = sparse(diag(diagonal)); %D is the matrix whose diagonal is the sum of the rows of A
clear('diagonal');

fprintf('Calculating NL\n');

D = sqrt(D);
NL1 = D * affinity * D;
clear('D');

fprintf('calculating U\n');

fail = 0;
try
      [nEigVec,eigValues] = eigs(NL1,k);
catch ME1
      opts.tol = 1e-1;
      try
            [nEigVec,eigValues] = eigs(NL1,k, 'LM', opts);
      catch ME2
            fail = 1;
      end
end

% select k largest eigen vectors
if fail == 0
      U = [];
      % construct the normalized matrix U from the obtained eigen vectors
      for i=1:size(nEigVec,1)
            n = sqrt(sum(nEigVec(i,:).^2));
            U(i,:) = nEigVec(i,:) ./ n;
      end

      
      num_samples = size(affinity,1) - first_unk_node + 1;
      
      if cluster_only_missing_nodes == 1
            
            U(1:first_unk_node - 1 ,:) = []; %cluster only the missing nodes
            
      end
      
      fprintf('kmeans clustering\n');

      % perform kmeans clustering on the matrix U
      fail = 1;
      while fail > 0
            try
                  currK = k;
                  [IDX,C, SUMD, D] = kmeans(U,currK,  'EmptyAction', 'singleton'); %in case of an empty cluster just drop it
                  fail = 0;
            catch ME1
                  fail = fail + 1;
                  if fail < 100
                        disp('error in kmeans clustering. trying again...');
                  else
                        %give up on clustering and select random clusters...
                        IDX = randi(currK, size(U));
                        fail = 0;
                  end
            end
      end
      
      test_clustering = IDX(size(IDX,1) - num_samples + 1  : size(IDX,1));
      
      
      %if it's random just replace everything...
      if affinity_calculation_type == affinity_calculation_random_clustering
            test_clustering = randi(k, size(test_clustering,1), size(test_clustering,2));
      end
      

else
      disp('Failed in finding eigenvectors - using random!');
      if cluster_only_missing_nodes == 0
            num_samples = size(affinity,1);
      else
            num_samples = num_placeholders;
      end
      test_clustering = randi(k, num_samples, 1);
end
end

function [newData, test_clustering] = PredictGraph(affinity, k, data, num_placeholders, affinity_calculation_type, cluster_only_missing_nodes)

last_known_node =  size(data,1) - num_placeholders;
first_unk_node =  last_known_node + 1;

[test_clustering] = SpectralClustering(affinity, k, num_placeholders, affinity_calculation_type, cluster_only_missing_nodes);

newNodes = CreateNewNodesFromClusters(data, test_clustering);

newData = [data(1:last_known_node,1:last_known_node),       newNodes(:, 1:last_known_node)';...
                              newNodes(:,1:last_known_node),                                       zeros(size(newNodes,1))];

end

function [k] = DetermineNumberOfClusters(num_clusters_known, data_untouched, actual_graph_size, num_missing_nodes, num_added_nodes)

%determine k - the number of clusters
if num_clusters_known == 1
      k = num_missing_nodes;
elseif num_clusters_known == 0
      k = mean(sum(data_untouched(1 : actual_graph_size - num_missing_nodes, 1 : actual_graph_size - num_missing_nodes)));
      %fprintf('Average number of neighbors for known nodes = %d, number of added nodes = %d\n', k, num_added_nodes);
      k = round(num_added_nodes / floor(k));
      fprintf('Rounding k to %d\n', k);
      fprintf('Actual number of clusters = %d\n', num_missing_nodes);
elseif num_clusters_known == 2
      k = mean(sum(data_untouched(1 : actual_graph_size - num_missing_nodes, 1 : actual_graph_size - num_missing_nodes)));
      %fprintf('Average number of neighbors for known nodes = %d, number of added nodes = %d\n', k, num_added_nodes);
      k = 2*round(num_added_nodes / k);
      fprintf('Guessing upper limit for k: %d\n', k);
      fprintf('Actual number of clusters = %d\n', num_missing_nodes);
end

end


function [affinity, num_placeholders, first_unk_node] = ReduceDimensions(affinity, first_unk_node)

num_placeholders = size(affinity,1) - first_unk_node + 1;
affinity_sum = sum(affinity(first_unk_node:size(affinity,1),:)); %the sum of the affinity of placeholders to all other nodes
nodes_to_keep = (affinity_sum > 0); %keep only nodes which have some affinity to the placeholders
nodes_to_keep(first_unk_node:size(affinity,1)) = 1; %keep all the placeholders even if for some reason they have a sum of zero...

affinity = affinity(nodes_to_keep, nodes_to_keep);

first_unk_node = size(affinity,1) - num_placeholders + 1;

end

function [true_clustering] = BuildTrueClustering(missing_nodes_mapping, actual_graph_size, num_missing_nodes, percent_known_placeholders, placeholders_to_remove, last_known_node)

true_clustering = []; %zeros(size(test_clustering, 1), 1);

for i = 2 : size(missing_nodes_mapping, 1)
      for j = 1 : size(missing_nodes_mapping,2)
            if missing_nodes_mapping(i,j) ~= 0
                  true_clustering(missing_nodes_mapping(i,j) - actual_graph_size + num_missing_nodes, 1) = j; % missing_nodes_mapping(1, j);
            end
      end
end

if percent_known_placeholders < 1
      true_clustering(placeholders_to_remove - last_known_node) = [];
end

end