[D,R,T] = dimred(X) X = Original vector data. Each row is a data point. Each column is a dimension in the original space. D = Reduced vector data. Each row is a data point. Each column is a dimension in the lower-dimensional space. R = "rotation" matrix to convert data from the the reduced space back into the original data space . Convert D back to X by using X = D*R+T; T = "translation" matrix The narrowest dimension of the data is compressed to zero. you may wish to compute a dimensionality ratio r such as >>g = svd(X); r = min(g) / max(g); or, g = abs(eig(cov(X))); r = min(g)/max(g); and then proceed if r < 1e-6 >> To convert some function F of D back to a function G of X in the higher dimnensional space as follows: X = (original data) [D,R,T] = dimred(X); F = (result of some presumably linear operation perfomed on D) G = F*R+T; % C=round(rand(3)*100)/100; % C=C'*C; % [V,D]=eig(C); % D=diag([0 1 2]); % C=V*D*V'; % mu = [4 4 4]; % X=mvnrnd(mu,C,1000); % mu=repmat(mu,[size(X,1) 1]); % % condition inverse of covariance for plots: % D(1,1)=D(2,2)*1e-6; % CI=inv(V*D*V'); % d=sum((X-mu)'.*(CI*(X-mu)')); % X(d>4,:)=[]; % figure % subplot(2,1,1) % hold on % plot3(X(:,1),X(:,2),X(:,3),'b.') % grid on % view(45,10) % axis equal % axis vis3d % [D,R,T]=dimred(X); % k=convhulln(D); % for n=1:length(k) % plot3(X(k(n,:),1),X(k(n,:),2),X(k(n,:),3),'r-','linew',2); % end % title('Original Data (3D)') % subplot(2,1,2) % plot(D(:,1),D(:,2),'b.') % grid on % axis equal % axis tight % title('Transformed Data (2D)') T = repmat(mean(X),[size(X,1),1]); XX = X-T; [R,N]=eig(XX'*XX); D=XX*R; D=D(:,2:end); Q=[zeros(size(D,2),1) eye(size(D,2))]; R=Q*R'; return does that work???