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facebook_randWalk.m
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load('facebook/facebook.txt')
addpath('RandomWalks')
facebook=facebook+1;%change to 1 based indexing
n=max(facebook(:));
[ D, edges ] = preprocess_D(facebook,n);
%% generate underlying signals
load Facebook_data_inhomogeneous2
%load Facebook_data_homogeneous
%load Facebook_data_inhomogeneous;%Facebook_data_randomwalk.mat;
y=y/norm(y)*sqrt(n);%scale it up to order \sqrt(n)
%( Comment this out if it is the inhomogeneous data. but not homogeneous one)
%%
%0 based k
k=1;%O should be L
O=construct_O( D,k );
%% Get parameters of the experiments
rng(43651243)
SnR_list=[30,25,20,15,10,5,0,-5,-10];%in dB
% 10 log (signal_sigma^2/noise_sigma^2)
sigma_list=sqrt(10.^(-SnR_list/10));%/sqrt(n);
%sigma_list=[0.01,0.1,0.3,0.5,0.7,0.9];
lambdalist=-7:0.2:3;
lambdalist=exp(lambdalist);%exp(lambdalist);
sz=length(lambdalist);
%sigma_list=[0.01, 0.05];
szz=length(sigma_list);
mse_list=zeros(szz,1);
mse_listL=zeros(szz,1);
mse_listW=zeros(szz,1);
mse_list1=zeros(szz,1);
mse_list2=zeros(szz,1);
%filtered=zeros(n,szz,sz,5);
rep=5;
% the master result
mse_all=zeros(sz,szz,5,rep);
base=norm(D,1);
mse_table=zeros(szz,rep);
mse_table1=zeros(szz,rep);
mse_table2=zeros(szz,rep);
mse_tableL=zeros(szz,rep);
mse_tableW=zeros(szz,rep);
%pre-generate all the noise
Z=zeros(n,rep,szz);
for i=1:length(sigma_list)
Z(:,:,i)=randn(n,rep)*sigma_list(i);
end
%% k=0
for ii=1:rep
for i=1:szz
%% gtf k=0
mse_list_inner=zeros(sz,1);
reg_weight=zeros(sz,1);
z=Z(:,ii,i);
yhat=y+z;
for j=1:sz % over all lambda
m=size(D,1);
scalefactor=base/norm(O,1);%mean(sum(abs(O),2);
lambda=scalefactor*lambdalist(j); rho=10*lambda;
[ x ,history1] = gtf_admm_v2( yhat,edges,k-1,lambda,rho);
%[ x,history ] = gtf_proj_newton1( yhat,edges,k,lambda);
mse_list_inner(j)=norm(x-y)^2/n;
reg_weight(j)=norm(O*x);
end
loglog(lambdalist,mse_list_inner);
hold on;
mse_all(:,i,1,ii)=mse_list_inner;
mse_list(i)=min(mse_list_inner);
drawnow;
%save('temp.mat');
end
%% To compare against the Laplacian smoother
for i=1:szz
z=Z(:,ii,i);
yhat=y+z;
mse_list_inner=zeros(sz,1);
reg_weight=zeros(sz,1);
for j=1:sz
scalefactor=base/norm(O,1);%base/norm(O,'fro')^2;
lambda=lambdalist(j)*scalefactor;
%lambda=exp(j/2*log(lambdalist(j)));
x=Laplacian_smoother(yhat,edges,lambda,0,0);
mse_list_inner(j)=norm(x-y)^2/n;
end
loglog(lambdalist,mse_list_inner);
hold on;
mse_all(:,i,2,ii)=mse_list_inner;
mse_listL(i)=min(mse_list_inner);
drawnow;
end
% %% To compare against James's Wavelets
%
% %load FacebookWavletBasis.mat %got matrix B
%
%
% for i=1:szz
%
% z=Z(:,ii,i);
% yhat=y+z;
%
% mse_list_inner=zeros(sz,1);
% reg_weight=zeros(sz,1);
%
% for j=1:sz
%
% scalefactor=base/norm(O,1);%base/norm(O,'fro')^2;
% lambda=lambdalist(j)*scalefactor;
%
% yrot=B*yhat;
% yrot=max(0,yrot-lambda*sqrt(2*log(n)))...%soft thresholding
% + min(0,yrot+lambda*sqrt(2*log(n)));
% %)(abs(yrot)<lambda*sqrt(2*log(n)));
% x=B'*yrot;
%
%
%
% mse_list_inner(j)=norm(x-y)^2/n;
% end
% loglog(lambdalist,mse_list_inner);
%
%
% hold on;
%
% mse_all(:,i,3,ii)=mse_list_inner;
% mse_listW(i)=min(mse_list_inner);
% drawnow;
% end
%% k=1
k=1;
for i=1:szz
z=Z(:,ii,i);
yhat=y+z;
mse_list_inner=zeros(sz,1);
reg_weight=zeros(sz,1);
for j=1:sz
m=size(D,1);
scalefactor=base/norm(O,1);%mean(sum(abs(O),2);
lambda=scalefactor*lambdalist(j); rho=10*lambda;
[ x ,history1] = gtf( yhat,edges,k,lambda,rho);
%[ x,history ] = gtf_proj_newton1( yhat,edges,k,lambda);
mse_list_inner(j)=norm(x-y)^2/n;
reg_weight(j)=norm(O*x);
end
loglog(lambdalist,mse_list_inner);
hold on;
mse_all(:,i,4,ii)=mse_list_inner;
mse_list1(i)=min(mse_list_inner);
drawnow;
%save('temp.mat');
end
%% k=2
k=2;
for i=1:szz
z=Z(:,ii,i);
yhat=y+z;
mse_list_inner=100*ones(sz,1);
reg_weight=zeros(sz,1);
for j=1:sz
m=size(D,1);
scalefactor=base/norm(O,1);%mean(sum(abs(O),2);
lambda=scalefactor*lambdalist(j); rho=0.5*lambda;
[ x ,history1] = gtf( yhat,edges,k,lambda,rho);
%[ x,history ] = gtf_proj_newton1( yhat,edges,k,lambda);
mse_list_inner(j)=norm(x-y)^2/n;
reg_weight(j)=norm(O*x);
end
loglog(lambdalist,mse_list_inner);
hold on;
mse_all(:,i,5,ii)=mse_list_inner;
mse_list2(i)=min(mse_list_inner);
drawnow;
end
%%
mse_table(:,ii) =mse_list;
mse_table1(:,ii)= mse_list1;
mse_table2(:,ii)=mse_list2;
mse_tableL(:,ii)=mse_listL;
mse_tableW(:,ii)=mse_listW;
save('temp.mat');
end % end rep
%%
%save('Exp_Facebook_RandomWalk_last.mat')
%save('Exp_Facebook_results.mat','y','sigma_list','mse_list','mse_list2','mse_list3')
%%
h=figure;
% plot the relative denoising performance in dB, the maller the better of
% course.
% plot(-SnR_list,10*log(mse_list'./sigma_list.^2)/log(10)','ro-',...
% -SnR_list,10*log(mse_list1'./sigma_list.^2)/log(10)','r*-',...
% -SnR_list,10*log(mse_list2'./sigma_list.^2)/log(10)','r^-',...
% -SnR_list,10*log(mse_listL'./sigma_list.^2)/log(10)','kx--',...
% -SnR_list,10*log(mse_listW'./sigma_list.^2)/log(10)','bs-.','linewidth',2,'markersize',12);
plot(-SnR_list,10*log(mse_list')/log(10)','ro-',...
-SnR_list,10*log(mse_list1')/log(10)','r*-',...
-SnR_list,10*log(mse_list2')/log(10)','r^-',...
-SnR_list,10*log(mse_listL')/log(10)','kx--',...%'linewidth',2,'markersize',12);% -SnR_list,10*log(mse_b2')/log(10)','b*-',...
'linewidth',2,'markersize',12);
xlabel('Noise Level: -SnR in (dB)','fontsize',14)
ylabel('Denoising Performance in dB','fontsize',14)
ylabel('Denoised -SnR in dB','fontsize',14)
lg=legend('Trend filtering k=0','Trend filtering k=1',...
'Trend filtering k=2','Laplacian smoothing');
set(lg,'fontsize',14,'location','best')
grid on;