a-pca-apuntes-5

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lOMoARcPSD|3741347 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
lOMoARcPSD|3741347 
 
 
 
 
 
 
function [Y W Val Vec]=A_pca(X,d) 
 
 
[n p]=size(X); 
Xpp=X; 
 
if n>p 
P=Xpp'*Xpp; %outter product pxp 
else 
P=Xpp*Xpp'; %inner product nxn 
end 
 
[Vec Val]=eig(P); 
Val = abs(diag(Val)); 
Val = Val./sum(Val); 
%organizar de mayor a menor 
[Val ival]=sort(Val,'descend'); 
Vec = Vec(:,ival); 
 
if d == 0 %valores propios mayores a la media de la suma de los valores 
propios 
ivald = Val >= mean(Val); 
W = Vec(:,ivald); 
elseif d > 0 && d < 1 
va = 0; 
W = []; 
i = 1; 
while va < d 
W = [W,Vec(:,i)]; 
va = va+Val(i); 
i=i+1; 
end 
 
elseif d >= 1 
W = Vec(:,1:d); 
end 
 
if n<p 
W = Xpp'*W*diag(Val(1:size(W,2)).^-.5); 
%W = W*diag(Val(1:size(W,2))).^-.5; 
end 
 
for i = 1 : size(W,2) 
W(:,i) = W(:,i)/norm(W(:,i)); 
end 
Y = Xpp*W;