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Qdiffmap.m
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clear all;
path2=[ '../Turbulence/Basics'];
addpath(path2);
path3=[ '../Nonequilibrium/'];
addpath(genpath(path3));
path4=[ '../Tenet/TENET/'];
addpath(genpath(path4));
NSUB=1003; %1003
N=62;
LATDIM=7;
Ttrain=800; %550;
Tau=3;
Isubdiag = find(tril(ones(N),-1));
indexregion=[1:31 50:80];
%%% Define Training and test data
% Parameters of the data
TR=0.72; % Repetition Time (seconds)
% Bandpass filter settings
fnq=1/(2*TR); % Nyquist frequency
flp = 0.008; % lowpass frequency of filter (Hz)
fhi = 0.08; % highpass
Wn=[flp/fnq fhi/fnq]; % butterworth bandpass non-dimensional frequency
k=2; % 2nd order butterworth filter
[bfilt,afilt]=butter(k,Wn); % construct the filter
load('hcp1003_REST1_LR_dbs80.mat');
EPS=[1 10 20 30 50 100 150 200 300 400];
THS=[1 2 3 4 5 6];
for ep=1:length(EPS)
for th=1:length(THS)
epsilon=EPS(ep)
Thorizont=THS(th)
for sub=1:NSUB
ts=subject{sub}.dbs80ts;
ts=ts(indexregion,:);
for seed=1:N
ts(seed,:)=detrend(ts(seed,:)-nanmean(ts(seed,:)));
signal_filt(seed,:)=(filtfilt(bfilt,afilt,ts(seed,:)));
end
ts=signal_filt(:,50:end-50);
ts=zscore(ts,[],2);
Tm=size(ts,2);
Kmatrix=zeros(Tm,Tm);
for i=1:Tm
for j=1:Tm
dij2=sum((ts(:,i)-ts(:,j)).^2);
Kmatrix(i,j)=exp(-dij2/epsilon);
end
end
% Dmatrix=diag(sum(Kmatrix,2));
% Ktr=inv(Dmatrix)*Kmatrix*inv(Dmatrix);
Dmatrix=diag(sum(Kmatrix,2));
Pmatrix=inv(Dmatrix)*Kmatrix;
KmatrixTr=Kmatrix(1:Ttrain,1:Ttrain);
DmatrixTr=diag(sum(KmatrixTr,2));
PmatrixTr=inv(DmatrixTr)*KmatrixTr;
[VV,LL]=eig(PmatrixTr);
Phi=VV(:,2:LATDIM+1);
%% CV
TL=Tm-Ttrain;
LAMBDA=LL(2:LATDIM+1,2:LATDIM+1).^Thorizont;
Pcv=Kmatrix(Ttrain+1:end,1:Ttrain);
for r=1:N
tscvestimated=Pcv*Phi*inv(LAMBDA)*Phi'*ts(r,1:Ttrain)';
tscve(r,:)=tscvestimated';
end
FCtrue=corrcoef(ts(:,Ttrain+1:end)');
FCest=corrcoef(tscve');
CORRfitt2(sub)=corr2(FCtrue(Isubdiag),FCest(Isubdiag));
ERRfitt2(sub)=mean((FCtrue(Isubdiag)-FCest(Isubdiag)).^2);
FCtautrue=corr(ts(:,Ttrain+1:Tm-Tau)',ts(:,Ttrain+1+Tau:Tm)');
FCtauest=corr(tscve(:,1:TL-Tau)',tscve(:,1+Tau:TL)');
CORRtaufitt2(sub)=corr2(FCtautrue(:),FCtauest(:));
ERRtaufitt2(sub)=mean((FCtautrue(:)-FCtauest(:)).^2);
[haux,paux,ErrfittFC2(sub)]=kstest2(FCtrue(Isubdiag),FCest(Isubdiag));
zPhi=zscore(ts(:,Ttrain+1:end)');
for t=1:size(zPhi,1)
fcd=zPhi(t,:)'*zPhi(t,:);
Edgest(:,t)=fcd(Isubdiag)';
end
FCDt=dist(Edgest);
zPhi=zscore(tscve');
for t=1:size(zPhi,1)
fcd=zPhi(t,:)'*zPhi(t,:);
Edgese(:,t)=fcd(Isubdiag)';
end
FCDe=dist(Edgese);
[haux,paux,ErrfittFCD2(sub)]=kstest2(FCDt(:),FCDe(:));
end
CorrFitt(ep,th)=mean(CORRfitt2)
ErrFitt(ep,th)=mean(ERRfitt2);
CorrFittTau(ep,th)=mean(CORRtaufitt2)
ErrFittTau(ep,th)=mean(ERRtaufitt2);
ErrFittFC(ep,th)=mean(ErrfittFC2);
ErrFittFCD(ep,th)=mean(ErrfittFCD2);
end
end
%%%%%% Quatum
% EPS=[0.001 0.005 0.01 0.05 0.1 0.5 1 5 10 50 100];
EPS=[1 10 20 30 50 100 150 200 300];
THS=[1 2 3 4 5 6];
for ep=1:length(EPS)
for th=1:length(THS)
epsilon=EPS(ep)
Thorizont=THS(th)
for sub=1:NSUB
ts=subject{sub}.dbs80ts;
ts=ts(indexregion,:);
for seed=1:N
ts(seed,:)=detrend(ts(seed,:)-nanmean(ts(seed,:)));
signal_filt(seed,:)=(filtfilt(bfilt,afilt,ts(seed,:)));
end
ts=signal_filt(:,50:end-50);
ts=zscore(ts,[],2);
Tm=size(ts,2);
Kmatrix=zeros(Tm,Tm);
for i=1:Tm
for j=1:Tm
dij2=sum((ts(:,i)-ts(:,j)).^2);
Kmatrix(i,j)=exp(complex(0,1)*dij2/epsilon);
end
end
Ktr_t=Kmatrix^Thorizont;
Ptr_t=abs(Ktr_t).^2;
Dmatrix=diag(sum(Ptr_t,2));
Pmatrix=inv(Dmatrix)*Ptr_t;
Ptr_tTr=Ptr_t(1:Ttrain,1:Ttrain);
DmatrixTr=diag(sum(Ptr_tTr,2));
PmatrixTr=inv(DmatrixTr)*Ptr_tTr;
[VV,LL]=eig(PmatrixTr);
Phi=VV(:,2:LATDIM+1);
%% CV
TL=Tm-Ttrain;
LAMBDA=LL(2:LATDIM+1,2:LATDIM+1);
Pcv=Ptr_t(Ttrain+1:end,1:Ttrain);
for r=1:N
tscvestimated=Pcv*Phi*inv(LAMBDA)*Phi'*ts(r,1:Ttrain)';
tscve(r,:)=tscvestimated';
end
tscve=real(tscve);
FCtrue=corrcoef(ts(:,Ttrain+1:end)');
FCest=corrcoef(tscve');
CORRfitt2q(sub)=corr2(FCtrue(Isubdiag),FCest(Isubdiag));
ERRfitt2q(sub)=mean((FCtrue(Isubdiag)-FCest(Isubdiag)).^2);
FCtautrue=corr(ts(:,Ttrain+1:Tm-Tau)',ts(:,Ttrain+1+Tau:Tm)');
FCtauest=corr(tscve(:,1:TL-Tau)',tscve(:,1+Tau:TL)');
CORRtaufitt2q(sub)=corr2(FCtautrue(:),FCtauest(:));
ERRtaufitt2q(sub)=mean((FCtautrue(:)-FCtauest(:)).^2);
[haux,paux,ErrfittFCq2(sub)]=kstest2(FCtrue(Isubdiag),FCest(Isubdiag));
zPhi=zscore(ts(:,Ttrain+1:end)');
for t=1:size(zPhi,1)
fcd=zPhi(t,:)'*zPhi(t,:);
Edgest(:,t)=fcd(Isubdiag)';
end
FCDt=dist(Edgest);
zPhi=zscore(tscve');
for t=1:size(zPhi,1)
fcd=zPhi(t,:)'*zPhi(t,:);
Edgese(:,t)=fcd(Isubdiag)';
end
FCDe=dist(Edgese);
[haux,paux,ErrfittFCDq2(sub)]=kstest2(FCDt(:),FCDe(:));
end
CorrFittq(ep,th)=mean(CORRfitt2q)
ErrFittq(ep,th)=mean(ERRfitt2q);
CorrFittTauq(ep,th)=mean(CORRtaufitt2q)
ErrFittTauq(ep,th)=mean(ERRtaufitt2q);
ErrFittFCq(ep,th)=mean(ErrfittFCq2);
ErrFittFCDq(ep,th)=mean(ErrfittFCDq2);
end
end
%% PCA
for sub=1:NSUB
ts=subject{sub}.dbs80ts;
ts=ts(indexregion,:);
for seed=1:N
ts(seed,:)=detrend(ts(seed,:)-nanmean(ts(seed,:)));
signal_filt(seed,:)=(filtfilt(bfilt,afilt,ts(seed,:)));
end
ts=signal_filt(:,50:end-50);
ts=zscore(ts,[],2);
[CoePCA,PhiPCA,llpca,tss,exp,mu]=pca(ts(:,1:Ttrain)');
%% CV
PhiPCAcv=ts(:,1+Ttrain:end)'*CoePCA;
tscve=PhiPCAcv(:,1:LATDIM)*CoePCA(:,1:LATDIM)'+mu;
FCtrue=corrcoef(ts(:,Ttrain+1:end)');
FCest=corrcoef(tscve);
CORRfitt2pca(sub)=corr2(FCtrue(Isubdiag),FCest(Isubdiag));
ERRfitt2pca(sub)=mean((FCtrue(Isubdiag)-FCest(Isubdiag)).^2);
FCtautrue=corr(ts(:,Ttrain+1:Tm-Tau)',ts(:,Ttrain+1+Tau:Tm)');
FCtauest=corr(tscve(1:TL-Tau,:),tscve(1+Tau:TL,:));
CORRtaufitt2pca(sub)=corr2(FCtautrue(:),FCtauest(:));
ERRtaufitt2pca(sub)=mean((FCtautrue(:)-FCtauest(:)).^2);
[haux,paux,ErrfittFCPCA2(sub)]=kstest2(FCtrue(Isubdiag),FCest(Isubdiag));
zPhi=zscore(ts(:,Ttrain+1:end)');
for t=1:size(zPhi,1)
fcd=zPhi(t,:)'*zPhi(t,:);
Edgest(:,t)=fcd(Isubdiag)';
end
FCDt=dist(Edgest);
zPhi=zscore(tscve');
for t=1:size(zPhi,1)
fcd=zPhi(t,:)'*zPhi(t,:);
Edgese(:,t)=fcd(Isubdiag)';
end
FCDe=dist(Edgese);
[haux,paux,ErrfittFCDPCA2(sub)]=kstest2(FCDt(:),FCDe(:));
end
CorrFittPCA=mean(CORRfitt2pca)
ErrFittPCA=mean(ERRfitt2pca);
CorrFittTauPCA=mean(CORRtaufitt2pca)
ErrFittTauPCA=mean(ERRtaufitt2pca);
ErrFittFCPCA=mean(ErrfittFCPCA2);
ErrFittFCDPCA=mean(ErrfittFCDPCA2);
figure(1)
subplot(1,2,1)
imagesc(CorrFitt(2:10,:));
axis('square')
subplot(1,2,2)
imagesc(CorrFittq(2:9,:));
axis('square')
CorrFittPCA
figure(2)
subplot(1,2,1)
imagesc(ErrFitt(2:10,:));
zlim([0 0.25]);
axis('square')
subplot(1,2,2)
imagesc(ErrFittq(2:9,:));
zlim([0 0.25]);
axis('square')
ErrFittPCA
save results_diffmaps.mat CorrFittPCA CorrFittTauPCA ErrFittPCA ErrFittTauPCA ...
CorrFitt CorrFittTau ErrFitt ErrFittTau ...
CorrFittq CorrFittTauq ErrFittq ErrFittTauq ...
ErrFittFC ErrFittFCD ErrFittFCq ErrFittFCDq ErrFittFCPCA ErrFittFCDPCA;