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fitgmm_sdp.m
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fitgmm_sdp.m
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function [Priors, Mu, Sigma, est_labels, stats] = fitgmm_sdp(S, Y, est_options)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Copyright (C) 2018 Learning Algorithms and Systems Laboratory, %
% EPFL, Switzerland %
% Author: Nadia Figueroa %
% email: nadia.figueroafernandez@epfl.ch %
% website: http://lasa.epfl.ch %
% %
% This work was supported by the EU project Cogimon H2020-ICT-23-2014. %
% %
% Permission is granted to copy, distribute, and/or modify this program %
% under the terms of the GNU General Public License, version 2 or any %
% later version published by the Free Software Foundation. %
% %
% This program is distributed in the hope that it will be useful, but %
% WITHOUT ANY WARRANTY; without even the implied warranty of %
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General%
% Public License for more details %
% %
% If you use this code in your research please cite: %
% "" %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Parse Options
est_type = est_options.type;
max_gaussians = est_options.maxK;
do_plots = est_options.do_plots;
[M,N] = size(Y);
if isempty(est_options.fixed_K)
fixed_K = 0;
else
fixed_K = est_options.fixed_K;
end
if est_type ~= 1
if isempty(est_options.samplerIter)
if est_type == 0
samplerIter = 20;
end
if est_type == 2
samplerIter = 200;
end
dataset_name = 'Test data';
else
samplerIter = est_options.samplerIter;
dataset_name = est_options.dataset_name;
end
end
if isempty(est_options.true_labels)
true_labels = [];
else
true_labels = est_options.true_labels;
end
switch est_type
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%% Option 0: Cluster SDP matrices with SPCM-CRP-MM %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case 0
% Setting sampler/model options (i.e. hyper-parameters, alpha, Covariance matrix)
options = [];
options.type = 'full'; % Type of Covariance Matrix: 'full' = NIW or 'Diag' = NIG
options.T = samplerIter; % Sampler Iterations
options.alpha = 1; % Concentration parameter [0 - 2]
% Standard Base Distribution Hyper-parameter setting
if strcmp(options.type,'diag')
lambda.alpha_0 = M; % G(sigma_k^-1|alpha_0,beta_0): (degrees of freedom)
lambda.beta_0 = sum(diag(cov(Y')))/M; % G(sigma_k^-1|alpha_0,beta_0): (precision)
end
if strcmp(options.type,'full')
lambda.nu_0 = M; % IW(Sigma_k|Lambda_0,nu_0): (degrees of freedom)
lambda.Lambda_0 = eye(M)*sum(diag(cov(Y')))/M; % IW(Sigma_k|Lambda_0,nu_0): (Scale matrix)
lambda.Lambda_0 = 1/(M) * diag(diag(cov(Y'))); % IW(Sigma_k|Lambda_0,nu_0): (Scale matrix)
end
lambda.mu_0 = mean(Y,2); % hyper for N(mu_k|mu_0,kappa_0)
lambda.kappa_0 = 1; % hyper for N(mu_k|mu_0,kappa_0)
% Run Collapsed Gibbs Sampler
options.lambda = lambda;
options.verbose = 1;
[Psi, Psi_Stats] = run_ddCRP_sampler(Y, S, options);
est_labels = Psi.Z_C';
%%%%%%%% Visualize Collapsed Gibbs Sampler Stats %%%%%%%%%%%%%%
if do_plots
if exist('h1b','var') && isvalid(h1b), delete(h1b);end
options = [];
options.dataset = dataset_name;
options.true_labels = true_labels;
options.Psi = Psi;
[ h1b ] = plotSamplerStats( Psi_Stats, options );
end
%%%%%%%%%% Extract Learned GMM models %%%%%%%%%%%%%
est_labels = Psi.Z_C';
N = size(Y,2);
unique_labels = unique(est_labels);
est_K = length(unique_labels);
Priors = zeros(1, est_K);
singletons = zeros(1, est_K);
for k=1:est_K
assigned_k = sum(est_labels==unique_labels(k));
Priors(k) = assigned_k/N;
singletons(k) = assigned_k < round(N*0.01);
end
Mu = Psi.Theta.Mu(:,unique_labels);
Sigma = Psi.Theta.Sigma(:,:,unique_labels);
if any(singletons)
singleton_idx = find(singletons == 1);
Mu(:,singleton_idx) = [];
Sigma(:,:,singleton_idx) = [];
unique_labels(singleton_idx) = [];
Priors = [];
est_K = length(Mu);
for k=1:est_K
assigned_k = sum(est_labels==unique_labels(k));
Priors(k) = assigned_k/N;
end
end
clear stats
stats.Psi = Psi;
stats.Psi_Stats = Psi_Stats;
[~, est_labels] = my_gmm_cluster(Y, Priors, Mu, Sigma, 'hard', []);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%% Option 1: Cluster SDP matrices with GMM-EM + BIC Model Selection %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case 1
em_type = 'matlab';
if fixed_K == 0
repetitions = 10;
[bic_scores, k] = fit_gmm_bic(Y, max_gaussians, repetitions, em_type, do_plots);
stats.bic_scores = bic_scores;
stats.best_k = k;
else
k = fixed_K;
stats.best_k = k;
end
switch em_type
case 'matlab'
% Train GMM with Optimal k
warning('off', 'all'); % there are a lot of really annoying warnings when fitting GMMs
%fit a GMM to our data
GMM_full = fitgmdist([Y]', k, 'Start', 'plus', 'CovarianceType','full', 'Regularize', .000001, 'Replicates', 10);
warning('on', 'all');
% Extract Model Parameters
Priors = GMM_full.ComponentProportion;
Mu = transpose(GMM_full.mu);
Sigma = GMM_full.Sigma;
case 'nadia'
cov_type = 'full'; Max_iter = 500;
[Priors0, Mu0, ~, Sigma0] = my_gmmInit(Y, k, cov_type);
[Priors, Mu, Sigma, ~] = my_gmmEM(Y, k, cov_type, Priors0, Mu0, Sigma0, Max_iter);
end
[~, est_labels] = my_gmm_cluster(Y, Priors, Mu, Sigma, 'hard', []);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%% Option 2: Cluster SDP matrices CRP MM sampler (CRP-GMM) %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
case 2
% CRP-GMM (Frank-Wood's implementation) which is a Gibbs Sampler
[class_id, mean_record, covariance_record, K_record, lP_record, alpha_record] = sampler(Y, samplerIter);
[max_val, max_id] = max(lP_record);
est_K = K_record(max_id);
est_labels = class_id(:,max_id);
samplerIter = length(lP_record);
% Gather Stats
clear stats
stats.lP_record = lP_record;
stats.K_record = K_record;
stats.Mu_record = mean_record;
stats.Sigma_record = covariance_record;
stats.samplerIter = samplerIter;
% Visualization and plotting options
if do_plots
figure('Color',[1 1 1])
subplot(2,1,1)
semilogx(1:samplerIter, lP_record'); hold on;
semilogx(max_id, lP_record(max_id),'ko','MarkerSize',10);
grid on
xlabel('Gibbs Iteration','Interpreter','LaTex','Fontsize',20); ylabel('LogPr','Interpreter','LaTex','Fontsize',20)
xlim([1 samplerIter])
legend({'$p(Z|Y, \alpha, \lambda)$'},'Interpreter','LaTex','Fontsize',14)
title(sprintf('CRP-GMM Sampling results, optimal K=%d at iter=%d', est_K, max_id), 'Interpreter','LaTex','Fontsize',20)
subplot(2,1,2)
stairs(K_record, 'LineWidth',2);
set(gca, 'XScale', 'log')
xlim([1 samplerIter])
xlabel('Gibbs Iteration','Interpreter','LaTex','Fontsize',20); ylabel('$\Psi$ = Estimated K','Interpreter','LaTex','Fontsize',20);
end
% Extract Learnt cluster parameters
unique_labels = unique(est_labels);
est_K = length(unique_labels);
Priors = zeros(1, est_K);
singletons = zeros(1, est_K);
for k=1:est_K
assigned_k = sum(est_labels==unique_labels(k));
Priors(k) = assigned_k/N;
singletons(k) = assigned_k < 2;
end
Mu = mean_record {max_id};
Sigma = covariance_record{max_id};
% Remove Singleton Clusters
if any(singletons)
[~, est_labels] = my_gmm_cluster(Y, Priors, Mu, Sigma, 'hard', []);
unique_labels = unique(est_labels);
est_K = length(unique_labels);
Mu = Mu(:,unique_labels);
Sigma = Sigma(:,:,unique_labels);
Priors = [];
for k=1:est_K
assigned_k = sum(est_labels==unique_labels(k));
Priors(k) = assigned_k/N;
end
end
[~, est_labels] = my_gmm_cluster(Y, Priors, Mu, Sigma, 'hard', []);
% CRP-GMM (Mo-Chens's implementation) which is a COLLAPSED Gibbs Sampler
if est_K == 1
fprintf(2, 'It seems that the Gibbs Sampler did not converge.. trying Collapsed Gibbs Sampler...\n');
[est_labels, Theta, w, ll, k_s] = mixGaussGb(Y, samplerIter);
[Priors, Mu, Sigma] = gmmOracle(Y, est_labels);
[max_val, max_id] = max(ll);
est_K = length(Priors);
clear stats
stats.collapsed.ll = ll;
stats.collapsed.ll = k_s;
if do_plots
figure('Color',[1 1 1])
subplot(2,1,1)
semilogx(1:samplerIter, ll); hold on;
semilogx(max_id, ll(max_id),'ko','MarkerSize',10);
grid on;
xlabel('Collapsed Gibbs Iteration','Interpreter','LaTex','Fontsize',20); ylabel('LogPr','Interpreter','LaTex','Fontsize',20)
xlim([1 samplerIter])
legend({'$p(Z|Y, \alpha, \lambda)$'},'Interpreter','LaTex','Fontsize',14)
title(sprintf('CRP-GMM Sampling results, optimal K=%d at iter=%d', est_K, max_id), 'Interpreter','LaTex','Fontsize',20)
subplot(2,1,2)
stairs(K_record, 'LineWidth',2);
set(gca, 'XScale', 'log')
xlim([1 samplerIter])
xlabel('Collapsed Gibbs Iteration','Interpreter','LaTex','Fontsize',20); ylabel('$\Psi$ = Estimated K','Interpreter','LaTex','Fontsize',20);
end
end
end
end