parafac.m

多维数据分析,有nPLS,PARAFAC,TURKER等

      for ii=ord:-1:1
         if ii==ord;
            i=1;
         else
            i=ii+1;
         end
         idd=[i+1:ord 1:i-1];
         l_idx2=lidx(idd,:);
         dimx=DimX(idd);
         if ~FixMode(i)
            L1=reshape(Factors(l_idx2(1,1):l_idx2(1,2)),dimx(1),Fac);
            if ord>2
               L2=reshape(Factors(l_idx2(2,1):l_idx2(2,2)),dimx(2),Fac);
               Z=kr(L2,L1);
            else
               Z = L1;
            end
            for j=3:ord-1
               L1=reshape(Factors(l_idx2(j,1):l_idx2(j,2)),dimx(j),Fac);
               Z=kr(L1,Z);
            end
            OldLoad=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
            L=pfls(Z,X,DimX(i),const(i),OldLoad,DoWeight,Weights);
            Factors(lidx(i,1):lidx(i,2))=L(:);
         end
         x=zeros(prod(DimX([1:ii-1 ii+1:ord])),DimX(ii));
         x(:)=X;
         X=x';
         x(:)=Weights;
         Weights=x';
      end
   end
   
   % POSTPROCES LOADINGS (ALL VARIANCE IN FIRST MODE)
   if ~any(FixMode)
     
     A=reshape(Factors(lidx(1,1):lidx(1,2)),DimX(1),Fac);
     for i=2:ord
       B=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
       for ff=1:Fac
         A(:,ff)=A(:,ff)*norm(B(:,ff));
         B(:,ff)=B(:,ff)/norm(B(:,ff));
       end
       Factors(lidx(i,1):lidx(i,2))=B(:);
     end
     Factors(lidx(1,1):lidx(1,2))=A(:);
   end
% APPLY SIGN CONVENTION IF NO FIXED MODES
%  FixMode=1
if ~any(FixMode)&~(any(const==2)|any(const==3))
    Sign = ones(1,Fac);
    for i=ord:-1:2
        A=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
        Sign2=ones(1,Fac);
        for ff=1:Fac
            [out,sig]=max(abs(A(:,ff)));
            Sign(ff) = Sign(ff)*sign(A(sig,ff));
            Sign2(ff) = sign(A(sig,ff));
        end
        A=A*diag(Sign2);
        Factors(lidx(i,1):lidx(i,2))=A(:);
    end 
    A=reshape(Factors(lidx(1,1):lidx(1,2)),DimX(1),Fac);
    A=A*diag(Sign);
    Factors(lidx(1,1):lidx(1,2))=A(:);
end 
   
% Check if nonneg_obeyed
for i=1:ord
  if const(i)==2|const(i)==3
   A=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
   if any(A(:))<0
     nonneg_obeyed=0;
   end
 end
end
   % EVALUATE SOFAR
   % Convert to new format
   clear ff,id1 = 0;
   for i = 1:length(DimX) 
      id2 = sum(DimX(1:i).*Fac);
      ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);
      id1 = id2;
   end
   model=nmodel(ff);
   model = reshape(model,DimX(1),prod(DimX(2:end)));
   if MissMeth  % Missing values present
      connew=model(id);
      X(id)=model(id);
      errold=err;
      errX=X-model;
      if DoWeight==0
         err=sum(sum(errX(idmiss2).^2));
      else
         err=sum(sum((Weights(idmiss2).*errX(idmiss2)).^2));
      end
   else
      errold=err;
      if DoWeight==0
         err=sum(sum((X-model).^2));
      else
         err=sum(sum((Weights.*(X-model)).^2));
      end
   end
   if err/SSX<1000*eps, % Getting close to the machine uncertainty => stop
      disp(' WARNING')
      disp(' The misfit is approaching the machine uncertainty')
      disp(' If pure synthetic data is used this is OK, otherwise if the')
      disp(' data elements are very small it might be appropriate ')
      disp(' to multiply the whole array by a large number to increase')
      disp(' numerical stability. This will only change the solution ')
      disp(' by a scaling constant')
      f = 0;
   else
      f=abs((err-errold)/err);
      if f<crit % Convergence: then check that constraints are fulfilled
         if any(const==2)|any(const==3) % If nnls or unimodality imposed
            for i=1:ord % Extract the 
               if const(i)==2|const(i)==3 % If nnls or unimodality imposed
                  Loadd = Factors(sum(DimX(1:i-1))*Fac+1:sum(DimX(1:i))*Fac);
                  if any(Loadd<0)
                     ConstraintsNotRight=1;
                  else
                     ConstraintsNotRight=0;
                  end
               end
            end
         end
      end
   end

   if it/showfit-round(it/showfit)==0
      if showfit~=-1,
         ShowPhi=ShowPhi+1;
         if ShowPhi==ShowPhiWhen,
            ShowPhi=0;
            if showfit~=-1,
               disp(' '),
               disp('    Tuckers congruence coefficient'),
               % Convert to new format
               clear ff,id1 = 0;
               for i = 1:length(DimX) 
                  id2 = sum(DimX(1:i).*Fac);ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);id1 = id2;
               end
               [phi,out]=ncosine(ff,ff);
               disp(phi),
               if MissMeth
                  fprintf(' Change in estim. missing values %12.10f',norm(connew-conold)/norm(conold));
                  disp(' ')
                  disp(' ')
               end
               disp(' Sum-of-Squares   Iterations  Explained')
               disp(' of residuals                 variation')
            end
         end
         if DoWeight==0
            PercentExpl=100*(1-err/SSX);
         else
            PercentExpl=100*(1-sum(sum((X-model).^2))/SSX);
         end
         fprintf(' %12.10f       %g        %3.4f    \n',err,it,PercentExpl);
         if Plt==2|Plt==3
            % Convert to new format
            clear ff,id1 = 0;
            for i = 1:length(DimX) 
               id2 = sum(DimX(1:i).*Fac);ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);id1 = id2;
            end
            pfplot(reshape(X,DimX),ff,Weights',[0 0 0 0 0 0 0 1]);
            drawnow
         end
      end
   end
   

   
   % Make safety copy of loadings and initial parameters in temp.mat
   if it/50-round(it/50)==0
      save temp Factors
   end
   
   % JUDGE FIT
   if err>errold
      NumberOfInc=NumberOfInc+1;
   end
   
end % while f>crit


% CALCULATE TUCKERS CONGRUENCE COEFFICIENT
if showfit~=-1 & DimX(1)>1
   disp(' '),disp('   Tuckers congruence coefficient')
   % Convert to new format
   clear ff,id1 = 0;
   for i = 1:length(DimX) 
      id2 = sum(DimX(1:i).*Fac);ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);id1 = id2;
   end
   [phi,out]=ncosine(ff,ff);
   disp(phi)
   disp(' ')
   if max(max(abs(phi)-diag(diag(phi))))>.85
      disp(' ')
      disp(' ')
      disp(' WARNING, SOME FACTORS ARE HIGHLY CORRELATED.')
      disp(' ')
      disp(' You could decrease the number of components. If this')
      disp(' does not help, try one of the following')
      disp(' ')
      disp(' - If systematic variation is still present you might')
      disp('   wanna decrease your convergence criterion and run')
      disp('   one more time using the loadings as initial guess.')
      disp(' ')
      disp(' - Or use another preprocessing (check for constant loadings)')
      disp(' ')
      disp(' - Otherwise try orthogonalising some modes,')
      disp(' ')
      disp(' - Or use Tucker3/Tucker2,')
      disp(' ')
      disp(' - Or a PARAFAC with some modes collapsed (if # modes > 3)')
      disp(' ')
   end
end


% SHOW FINAL OUTPUT

if DoWeight==0
   PercentExpl=100*(1-err/SSX);
else
   PercentExpl=100*(1-sum(sum((X-model).^2))/SSX);
end
if showfit~=-1
   fprintf(' %12.10f       %g        %3.4f \n',err,it,PercentExpl);
   if NumberOfInc>0
      disp([' There were ',num2str(NumberOfInc),' iterations that increased fit']);
   end
end


% POSTPROCES LOADINGS (ALL VARIANCE IN FIRST MODE)
if Options(4)==0|Options(4)==1
A=reshape(Factors(lidx(1,1):lidx(1,2)),DimX(1),Fac);
for i=2:ord
   B=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
   for ff=1:Fac
      A(:,ff)=A(:,ff)*norm(B(:,ff));
      B(:,ff)=B(:,ff)/norm(B(:,ff));
   end
   Factors(lidx(i,1):lidx(i,2))=B(:);
end
Factors(lidx(1,1):lidx(1,2))=A(:);
if showfit~=-1
   disp(' ')
   disp(' Components have been normalized in all but the first mode')
end
end

% PERMUTE SO COMPONENTS ARE IN ORDER AFTER VARIANCE DESCRIBED (AS IN PCA) IF NO FIXED MODES
if ~any(FixMode)
   A=reshape(Factors(lidx(1,1):lidx(1,2)),DimX(1),Fac);
   [out,order]=sort(diag(A'*A));
   order=flipud(order);
   A=A(:,order);
   Factors(lidx(1,1):lidx(1,2))=A(:);
   for i=2:ord
      B=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
      B=B(:,order);
      Factors(lidx(i,1):lidx(i,2))=B(:);
   end  
   if showfit~=-1
      disp(' Components have been ordered according to contribution')
   end
elseif showfit ~= -1
   disp(' Some modes fixed hence no sorting of components performed')
end

% APPLY SIGN CONVENTION IF NO FIXED MODES


%  FixMode=1
if ~any(FixMode)&~(any(const==2)|any(const==3))
    Sign = ones(1,Fac);
    for i=ord:-1:2
        A=reshape(Factors(lidx(i,1):lidx(i,2)),DimX(i),Fac);
        Sign2=ones(1,Fac);
        for ff=1:Fac
            [out,sig]=max(abs(A(:,ff)));
            Sign(ff) = Sign(ff)*sign(A(sig,ff));
            Sign2(ff) = sign(A(sig,ff));
        end
        A=A*diag(Sign2);
        Factors(lidx(i,1):lidx(i,2))=A(:);
    end 
    A=reshape(Factors(lidx(1,1):lidx(1,2)),DimX(1),Fac);
    A=A*diag(Sign);
    Factors(lidx(1,1):lidx(1,2))=A(:);
    if showfit~=-1
        disp(' Components have been reflected according to convention')
    end
end 

% TOOLS FOR JUDGING SOLUTION
if nargout>3      
   x=X;
   if MissMeth
      x(id)=NaN*id;
   end
   % Convert to new format
   clear ff,id1 = 0;
   for i = 1:length(DimX) 
      id2 = sum(DimX(1:i).*Fac);ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);id1 = id2;
   end
   corcondia=corcond(reshape(x,DimX),ff,Weights,1);
end

if Plt==1|Plt==2|Plt==3
   % Convert to new format
   clear ff,id1 = 0;
   for i = 1:length(DimX) 
      id2 = sum(DimX(1:i).*Fac);ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);id1 = id2;
   end
   if Fac<6&Plt~=3&order>2&ord>2
     pfplot(reshape(X,DimX),ff,Weights,ones(1,8));
   else
     pfplot(reshape(X,DimX),ff,Weights,[1 1 0 1 1 1 1 1]);
     if ord>2
         disp(' Core consistency plot not shown because it requires large memory')
         disp(' It can be made writing pfplot(X,Factors,[Weights],[0 0 1 0 0 0 0 0]');
     else
         disp(' Core consistency not applicable for two-way data')
     end
   end
end

% Show which criterion stopped the algorithm
if showfit~=-1
   if ((f<crit) & (norm(connew-conold)/norm(conold)<MissConvCrit))
      disp(' The algorithm converged')
   elseif it==maxit
      disp(' The algorithm did not converge but stopped because the')
      disp(' maximum number of iterations was reached')
   elseif f<eps
      disp(' The algorithm stopped because the change in fit is now')
      disp(' smaller than the machine uncertainty.')
   else
      disp(' Algorithm stopped for some mysterious reason')
   end
end

% Convert to new format
clear ff,id1 = 0;
for i = 1:length(DimX) 
   id2 = sum(DimX(1:i).*Fac);ff{i} = reshape(Factors(id1+1:id2),DimX(i),Fac);id1 = id2;
end
Factors = ff;