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Pre-Image by ridge regression given KPCA coordinates
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a = pmg_rr(alg,hyper)
generates a pre-image object; uses ridge regression learning
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hyperparameters:
child=kernel kernel to work with.
kp=kpca kpca object
dn=sample data data pool, if empty uses kp.dat
model:
rmap learnt ridge regression object
mean_x mean of data
rn=sample data coordinates from data pool
stats:
methods:
train calls test
test find the preimage
example:
k=kernel('rbf',0.75);
d=gen(toy2d);
d2=gen(toy2d('l=100'));
[r,kp]=train(kpca({k,'feat=50'}),d2);
p0=pmg_rr;p0.kp=kp; p0.child=k;
p0.dn=d2;
p0.rmap_model_selection=1;
[r,p1]=train(p0,d2);
r2=test(kp,d);
reconstruct=test(p1,r2)
reconstruct.X=reconstruct.X;
clf;
hold on;
colormap white;
plot3(d2.X(:,1),d2.X(:,2),d2.X(:,2)*0+10,'k.');
plot3(d.X(:,1),d.X(:,2),d.X(:,2)*0+10,'rx'); hold on;
plot3(reconstruct.X(:,1),reconstruct.X(:,2),reconstruct.X(:,2)*0+10,'o');
t=text(d.X(1,1),d.X(1,2)+0.005,d.X(1,2)*0+10,sprintf('Ideal Pre-Image'));
set(t,'Fontsize',10);
set(t,'Color',[1,0,0])
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Reference : Learning To Find Pre-Images |