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K=1;
X = rand(5,2);
M = mean(X);
C = cov(X);
[U D]=eig(C);
L=diag(D);
[sorted index]=sort(L,'descend');
Xproj=zeros(d,K);
for j=1:K
Xproj(:,j)=U(:,index(j));
end
Y=X*Xproj;
plot(Y1,'d');
axis([4 24 -2 18]);
% Find the first K Principal Components of data X (n rows, d columns)
% X contains n pattern vectors with d features
X= [2.5,0.5,2.2,1.9,3.1,2.3,2.0,1.0,1.5,1.1];
Y= [2.4,0.7,2.9,2.2,3.0,2.7,1.6,1.1,1.6,0.9];
Data = [X;Y]';
mx = mean(X);
my = mean(Y);
Xadj = (X-mean(X));
Yadj = (Y-mean(Y));
DataAdj= [Xadj;Yadj];
Cadj = cov(Xadj,Yadj);
C = cov(X,Y);
[Uadj Dadj]=eig(Cadj);
[U D]=eig(C);
L=diag(D);
[sorted index]=sort(L,'descend');
[FVector index]=sort(U,'descend');
%Final data using both eigenvectors in U
ColAdjData = DataAdj';
FData = FVector * ColAdjData';
OriginalAdjustedData = FVector' * FData;
figure;
plot(X,Y, 'd');
axis equal;
axis([-2 5 -2 5])
figure;
plot(Xadj, Yadj, 'x');
axis([-2 2 -2 2])
figure;
plot(D,'*')
axis([-2 2 -2 2])
figure;
plot(Xadj, Yadj, 'x');
hold on
plot(D,'*')
axis([-2 2 -2 2])
figure;
plot(FData,'d')
axis([-2 2 -2 2])
figure;
plot(OriginalAdjustedData,'r*')
axis([-2 2 -2 2])
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