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get_HC_IC_BD.m
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get_HC_IC_BD.m
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function [Clusters_Params allIC_BD allClust_BD] = get_HC_IC_BD(vectors, params)
% Get the parameters from the structure
eta = params.expectation;
theta_cl = params.natural;
weight = params.weight';
k = length(weight);
cp = params.cp;
label = params.label;
%% Perform hierarchical clustering
numberOfCluster = k;
LNF = zeros(numberOfCluster,1);
DLNF = zeros(numberOfCluster,1);
for j = 1:numberOfCluster
normEta(j) = sqrt(eta(j, :) * eta(j, :)');
normTheta(j) = getThetaFromEta(normEta(j));
LNF(j) = log((4*pi*sinh(normTheta(j))) / normTheta(j));
DLNF(j) = (eta(j, :) * theta_cl(j, :)') - LNF(j);
end
clear j;
% Compute distance among clusters
indx = 1;
Div_G = zeros(1, (numberOfCluster*(numberOfCluster-1))/2);
distMat = zeros(size(Div_G));
for i = 1 : numberOfCluster-1
for j = i+1 : numberOfCluster
% Left sided distance
Div_G(indx) = DLNF(i) - DLNF(j) - ( (eta(i,:) - eta(j,:)) * theta_cl(j,:)');
distMat(indx) = weight(i) * weight(j) * Div_G(indx);
indx = indx+1;
end
end
clear i j;
% Apply hierarchical clustering (use matlab function 'linkage')
Z = linkage(distMat,'average'); % 'average distance'
Clusters_Params = cell(1, numberOfCluster);
%% Perform clustering
for numClust = numberOfCluster : -1 : 1
ucp = zeros(size(vectors,1), numClust);
% Do initial clustering
T = cluster(Z,'maxclust',numClust);
isConsidered = zeros(size(T));
% Allocate updated cluster parameter vectors
Up_eta = zeros(numClust, size(eta,2));
Up_theta_cl = zeros(numClust, size(theta_cl,2));
Up_weight = zeros(numClust, 1);
update_mu = zeros(numClust, size(eta,2));
update_kappa = zeros(1,numClust);
subset_cl = cell(1, numClust);
indx=1;
numClMerge = 0;
% Find the merged clusters and Update cluster centroid (usign Bregman centroid)
for i=1:numberOfCluster
if(isConsidered(i)), continue; end
cl_label = T(i);
% get the associated subsets of original cluster
subset_cl{indx} = find(T==cl_label);
isConsidered(subset_cl{indx}) = 1;
% Merge the subset and update centroid and weight
if(length(subset_cl{indx}) > 1)
% Left sided Bregman centroid computation with expectation
% parameters
Up_weight(indx) = sum(weight(subset_cl{indx}));
Up_eta(indx,:) = sum(bsxfun(@times, weight(subset_cl{indx}), eta(subset_cl{indx},:))) ./ Up_weight(indx);
% Convert to source parameters (mu, kappa) from expectation parameter
% (eta)
normUp_eta(indx) = sqrt(Up_eta(indx, :) * Up_eta(indx, :)');
normUp_theta(indx) = getThetaFromEta(normUp_eta(indx));
% Compute R(normTheta)
R_norm_Up_theta(indx) = ((1/tanh(normUp_theta(indx))) - (1/normUp_theta(indx))) / normUp_theta(indx);
Up_theta_cl(indx, :) = Up_eta(indx, :) ./ R_norm_Up_theta(indx);
update_kappa(indx) = normUp_theta(indx);
update_mu(indx, :) = Up_theta_cl(indx, :) ./ normUp_theta(indx);
ucp(:, indx) = sum(cp(:, subset_cl{indx}),2);
for ijk = 1:length(subset_cl{indx})
numClMerge = numClMerge + length(find(label == subset_cl{indx}(ijk)));
end
else
% no update
Up_weight(indx) = weight(subset_cl{indx});
Up_eta(indx,:) = eta(subset_cl{indx},:);
% Convert to source parameters (mu, kappa) from expectation parameter
% (eta)
normUp_eta(indx) = sqrt(Up_eta(indx, :) * Up_eta(indx, :)');
normUp_theta(indx) = getThetaFromEta(normUp_eta(indx));
% Compute R(normTheta)
R_norm_Up_theta(indx) = ((1/tanh(normUp_theta(indx))) - (1/normUp_theta(indx))) / normUp_theta(indx);
Up_theta_cl(indx, :) = Up_eta(indx, :) ./ R_norm_Up_theta(indx);
update_kappa(indx) = normUp_theta(indx);
update_mu(indx, :) = Up_theta_cl(indx, :) ./ normUp_theta(indx);
ucp(:, indx) = cp(:, subset_cl{indx});
end
indx = indx + 1;
end
Clusters_Params{numClust}.src_params.mu = update_mu;
Clusters_Params{numClust}.src_params.kappa = update_kappa;
Clusters_Params{numClust}.weight = Up_weight;
Clusters_Params{numClust}.exp_params = Up_eta;
Clusters_Params{numClust}.nat_params = Up_theta_cl;
%% Compute Information Criterion values
clear prms
prms.mu = update_mu;
prms.kappa = update_kappa;
prms.weight = Up_weight';
% --> Get the class number for each component
clear sufStat_minus_expectParam Log_Normalizing_Function gradDLNF innerProdTerm divergence
for j=1:numClust
normEta2(j) = sqrt(Up_eta(j, :) * Up_eta(j, :)');
normTheta2(j) = getThetaFromEta(normEta2(j));
R_norm_theta2(j) = ((1/tanh(normTheta2(j))) - (1/normTheta2(j))) / normTheta2(j);
theta_cl2(j, :) = Up_eta(j, :) ./ R_norm_theta2(j);
Log_Normalizing_Function(j) = log((4*pi*sinh(normTheta2(j))) / normTheta2(j));
Dual_Log_Normalizing_Function(j) = (Up_eta(j, :) * theta_cl2(j, :)') - Log_Normalizing_Function(j);
gradDLNF(j,:) = theta_cl2(j, :);
sufStat_minus_expectParam(:, :, j) = bsxfun(@minus, vectors , Up_eta(j, :));
innerProdTerm(:,j) = sufStat_minus_expectParam(:, :, j) * gradDLNF(j,:)';
divergence(:,j) = -(Dual_Log_Normalizing_Function(j) + innerProdTerm(:,j));
end
% Hard clustering
[~, allClust_BD(:, numClust)] = min(divergence,[], 2);
valIC2 = getICvalues_phi_beta_vmfmm(vectors, prms, allClust_BD(:, numClust), ucp);
allIC_BD.BIC(numClust) = valIC2.BIC;
allIC_BD.ICL(numClust) = valIC2.ICL;
allIC_BD.AIC(numClust) = valIC2.AIC;
allIC_BD.Beta_min(numClust) = valIC2.beta_min;
allIC_BD.Beta_range(numClust,:) = valIC2.beta_range;
allIC_BD.Beta_range_actVal(numClust,:) = valIC2.beta_range_actVal;
allIC_BD.tE(numClust) = -sum(sum(ucp .* log2(ucp)));
allIC_BD.numMerge(numClust) = numClMerge;
end