GLL_package_v2.0 committed

This version of the GLL package includes examples from the following papers (see README.txt): 
[1] H. E. Egilmez, E. Pavez, and A. Ortega, "Graph learning from data under Laplacian and structural constraints," IEEE Journal of Selected Topics in Signal Processing, 2017.

[2] H. E. Egilmez, E. Pavez, and A. Ortega, "Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification," IEEE Transactions on Signal and Information Processing over Networks, 2018.

Author: hegilmez

demo_us_temperature.m

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+clear all
+close all
+
+% load us temperature data
+load('us_temp_data.mat');
+
+% sample covariance
+S = cov(data_2d_state,1);
+
+% initializaions
+filter_type = 'exp';
+beta = 0.5; % filter parameter
+graph_filter_ideal = @(x)(graph_filter_fwd(x,beta,filter_type) );
+[U,sigma_sq_C] = createBasis(S,'descend');
+max_sigma=(max(sigma_sq_C));
+sigma_orig = sigma_sq_C/max_sigma;
+
+% step I: prefilter
+sigma_sq_C = sigma_sq_C/max_sigma; sigma_sq_C(sigma_sq_C <= 10^-10) = 0;
+lambdas_current = graph_filter_inv(sigma_sq_C,beta,filter_type);
+orig_sigmas = 1./lambdas_current; orig_sigmas(orig_sigmas==Inf)=0;
+S_prefiltered = U * diag(orig_sigmas) * U';
+
+% step II: graph learning 
+Laplacian = estimate_cgl(S_prefiltered,ones(size(S_prefiltered)),0.000,10^-5,10^-7,40);
+
+% step III: filter parameter estimation (for a desired filter type a filter parameter selection step)
+%  Note: for exponential filter filter parameter selection step can be skipped, 
+%        becayse the output graphs are scaled versions of eachother for different beta parameter
+%        please refer to the paper for further details
+
+% show resulting graph on the US map
+draw_us_temp_graph(Laplacian, center_vector);

functions/generateFilteredModel.m

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+function [h_L,h_L_SquareRootMtx] = generateFilteredModel(L,graph_filter)
+
+[U,lambdas_L] = createBasis(L,'ascend'); lambdas_L(lambdas_L<= 10^-10)=0;
+sigmas_C = graph_filter(lambdas_L); sigmas_C(sigmas_C <= 10^-10) = 0; 
+
+h_L = U * diag(sigmas_C) * U'; h_L = 0.5*(h_L + h_L');
+h_L_SquareRootMtx =  U * diag(sigmas_C.^(0.5));
+end

functions/graph_filter_fwd.m

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+function sigma_sq = graph_filter_fwd(lambdas,beta,filter_type)
+
+if sum([lambdas(:);beta]<0)>0 % if there are negative values
+    error('Error: graph_filter_fwd negative frequency of beta value!');
+end
+    
+if isequal(filter_type,'exp')
+    
+    sigma_sq = exp(-beta*lambdas);
+    
+elseif isequal(filter_type,'fscale')
+    
+    sigma_sq = 1./(beta*lambdas);
+
+elseif isequal(filter_type,'fshift')
+    
+     sigma_sq = 1./(beta + lambdas);
+     
+elseif isequal(filter_type,'vshift')
+    
+     sigma_sq = (1./(lambdas)) + beta;
+     sigma_sq(sigma_sq == Inf) = beta;
+
+elseif isequal(filter_type,'hop')
+    
+    sigma_sq = 1./(lambdas.^beta);
+    
+else
+    error('Error: graph_filter_fwd wrong filter_type');
+
+end
+
+    sigma_sq(sigma_sq <= 10^-10) = 0;
+    sigma_sq(sigma_sq == Inf) = 0;
+
+    
+end

functions/graph_filter_inv.m

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+function lambdas = graph_filter_inv(sigma_sq,beta,filter_type)
+
+if sum([sigma_sq(:);beta]<0)>0 % if there are negative values
+    error('Error: graph_filter_inv negative variance or beta value!');
+end
+
+if isequal(filter_type,'exp')
+    
+    lambdas = -log(sigma_sq)/beta;
+    
+elseif isequal(filter_type,'fscale')
+    
+    lambdas = 1./(beta*sigma_sq);
+    lambdas(sigma_sq <= 10^-10) = 0;
+    
+elseif isequal(filter_type,'fshift')
+    
+    lambdas = 1./(sigma_sq - beta);
+    lambdas(sigma_sq <= 10^-10) = 0;
+    
+elseif isequal(filter_type,'vshift')
+    
+    lambdas = 1./(sigma_sq - beta);
+    
+elseif isequal(filter_type,'hop')
+    
+    lambdas = 1./(sigma_sq.^(1/beta));
+    lambdas(sigma_sq <= 10^-10) = 0;
+    
+else
+    error('Error: graph_filter_inv wrong filter_type');
+    
+end
+lambdas(lambdas <= 10^-10) = 0;
+end