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extremal_optimization.m
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extremal_optimization.m
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%function [dendogram Qmonitor best_iteration best_group Iab] =
%extremal_optimization(W,max_steps,full_clustering_flag,plot_flag,division_threshold,observed_groups)
function [dendogram Qmonitor best_iteration best_group Iab] = extremal_optimization(W,max_steps,full_clustering_flag,plot_flag,division_threshold,observed_groups)
if ~exist('full_clustering_flag','var')
full_clustering_flag=true;
end
if ~exist('plot_flag','var')
plot_flag=true;
end
if ~exist('division_threshold','var')
division_threshold = 1;
end
Qthreshold = .1;
N = size(W,1);
if max_steps <2
max_steps= ceil(log2(N));
end
Qmonitor = nan*ones(1,max_steps);
dendogram = cell(max_steps,1);
for current_step=1:max_steps
if current_step==1
aleaf = dendogram_leaf([],1:N);
dendogram{current_step} = {aleaf};
Qmonitor(current_step) = 0;
else
new_leaves = 0;
current_layer = cell(new_leaves);
for parent_leaf_index=1:length(dendogram{current_step-1})
parent_leaf = dendogram{current_step-1}{parent_leaf_index};
if length(parent_leaf.group) > division_threshold
[group1 group2 Qcurr] = extremal_optimization_split(parent_leaf.group,W);
if full_clustering_flag
if ~isempty(group1)
new_leaves = new_leaves +1;
leaf1 = dendogram_leaf(parent_leaf,group1);
current_layer{new_leaves} = leaf1;
end
if ~isempty(group2)
new_leaves = new_leaves + 1;
leaf2 = dendogram_leaf(parent_leaf,group2);
current_layer{new_leaves} = leaf2;
end
elseif Qcurr>Qthreshold
aleaf = dendogram_leaf(parent_leaf,parent_leaf.group);
new_leaves = new_leaves +1;
current_layer{new_leaves} = aleaf;
end
else
aleaf = dendogram_leaf(parent_leaf,parent_leaf.group);
new_leaves = new_leaves +1;
current_layer{new_leaves} = aleaf;
end
end
dendogram{current_step} = current_layer;
current_partition = get_groups(current_layer);
Qmonitor(current_step) = get_modularity(current_partition,W);
if plot_flag
figure(1)
plot(Qmonitor)
title('Modularity Q');
drawnow;
figure(2)
community_graph(current_partition,W)
title('Community Graph');
drawnow;
figure(3)
clf
group_indices=cat(2,current_partition{:});
imagesc(W(group_indices,group_indices));
title('W colormap');
drawnow;
end
end
end
best_iteration = find(Qmonitor==max(Qmonitor),1);
best_group = get_groups(dendogram{best_iteration});
if exist('observed_groups','var')
Iab = get_normalized_mutual_information(observed_groups,best_group);
end
end
%% GET GROUPS
function groups = get_groups(current_layer)
g = length(current_layer);
groups = cell(g,1);
for i=1:g
aleaf = current_layer{i};
groups{i} = aleaf.group;
end
end
%% APPLY EXTREMAL OPTIMIZATION GIVEN A SUBGRAPH
function [max_group1 max_group2 Qmax] = extremal_optimization_split(parent_group,W)
%A = W>0;
Nt = length(parent_group);
N = size(W,1);
Qmax = -1*inf;
total_edges = sum(sum(triu(W(parent_group,parent_group))));
indices = parent_group(randperm(Nt));
e = zeros(2);
group1 = sort(indices(1:ceil(Nt/2)));
group2 = sort(indices(ceil(Nt/2)+1:Nt));
while true
e(1,1) = sum(sum((W(group1,group1))))/2;
e(2,2) = sum(sum((W(group2,group2))))/2;
e(1,2) = sum(sum(W(group1,group2)));
e(2,1) = e(1,2);
e(isnan(e))=0;
e=e./total_edges;
a = sum(e,2);
aux_indices_group1 = 1:length(group1);
aux_indices_group2 = length(group1)+1:length(parent_group);
Qcurrent=get_modularity2({aux_indices_group1 aux_indices_group2},W([group1 group2],[group1 group2]));
if isnan(Qcurrent)
Qcurrent=0;
end
%Qcurrent = sum(diag(e)-a.^2);
%Qlamda = (total_edges/2)*sum(lamdas.*degree(A(indices,indices)));
try
if Qcurrent>Qmax
Qmax=Qcurrent;
max_group1 = group1;
max_group2 = group2;
converge_countdown = N;
else
converge_countdown=converge_countdown-1;
end
if converge_countdown==0
break;
end
catch ME
ME.stack;
end;
% TO VECTORISE
lamdas = zeros(Nt,1);
try
for index_iterator =1:length(indices)
if isempty(group2(group2==indices(index_iterator)))
lamdas(index_iterator) = sum(W(indices(index_iterator),group1))...
/sum(W(indices(index_iterator),parent_group))...
- a(1);
else
lamdas(index_iterator) = sum(W(indices(index_iterator),group2))...
/sum(W(indices(index_iterator),parent_group))...
- a(2);
end
end
catch ME
ME.stack;
end
lamdas(isnan(lamdas))=0;
[worst_node_indices worst_nodes] = find_minimums(indices,lamdas,ceil(length(indices)));
worst_selector = ceil(abs(2.5*randn(1)));
if worst_selector>length(worst_node_indices)
worst_selector = length(worst_node_indices);
end
worst_fit = worst_node_indices(worst_selector);
if ~isempty(group1(group1==worst_fit))
group1(group1==worst_fit)=[];
group2 = sort([group2 worst_fit]);
else
group2(group2==worst_fit)=[];
group1 = sort([group1 worst_fit]);
end
end
end