Assignment 2 Problem 3

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Dragon
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Assignment 2 Problem 3

Beitrag von Dragon » 15. Nov 2008 18:41

I try to project a mouth image in the subspace of eigen-mouths.
If I substract the mean mouth and then project the images of the reconstructed images get black.
If I don't do this I get an reasonable result. Image below. Or is it wrong?

Have I to substract the mean befor the projection? Or where is my fault?

Addtionaly I wanted to ask what the log-likelihood is? log(p(x|Omega))?

Last question is what to do at the second bullet of this Problem.
Can anyone explain this to me?
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>flo<
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Re: Assignment 2 Problem 3

Beitrag von >flo< » 16. Nov 2008 15:26

I think your results are reasonable. You have to subtract the mean when doing PCA. Compare for slides 69 and 70 for example projections.

The log-likelihood is the log of p(x|omega), yes :-)

The second bullet is just plotting the eigenvalues. Compare for slide 56 for an example how this could look like.

Dragon
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Re: Assignment 2 Problem 3

Beitrag von Dragon » 16. Nov 2008 15:36

I have substracted the mean when doing the PCA. Thats clear to me.

But if I choose a mouth m and want to project it in the eigenmouthspace,
have I then to substract the mean from m before doing the projection?
If looked to the slides 69 and 70 before and I thought they told me to do it this way.

Last question I think you are talking of the second bullet in problem 2.
I meant the second bullet in problem 3.
"Draw six random samples..."

>flo<
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Re: Assignment 2 Problem 3

Beitrag von >flo< » 16. Nov 2008 16:42

Dragon hat geschrieben:I have substracted the mean when doing the PCA. Thats clear to me.

But if I choose a mouth m and want to project it in the eigenmouthspace,
have I then to substract the mean from m before doing the projection?
If looked to the slides 69 and 70 before and I thought they told me to do it this way.
You definitely have to subtract the mean before projecting, yes. The mean here is the same mean that you used in order to compute the principal components.
Last question I think you are talking of the second bullet in problem 2.
I meant the second bullet in problem 3.
"Draw six random samples..."
Oh sorry. I got confused because both problems deal with PCA.

Essentially you are doing the same as in the reconstruction of the images. There you took the projections of the images and you projected them back from the subspace into the "full" space. Now you use random factors instead of the projected images. Compare for the Matlab manual of the function randn on how to draw Gaussian random samples. When you choose the variance think about what the results of PCA (eigenvectors and eigenvalues) mean. Remember that you can sample for each direction independently. I hope I could help?

Dragon
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Re: Assignment 2 Problem 3

Beitrag von Dragon » 16. Nov 2008 18:48

Essentially you are doing the same as in the reconstruction of the images. There you took the projections of the images and you projected them back from the subspace into the "full" space. Now you use random factors instead of the projected images. Compare for the Matlab manual of the function randn on how to draw Gaussian random samples. When you choose the variance think about what the results of PCA (eigenvectors and eigenvalues) mean. Remember that you can sample for each direction independently. I hope I could help?
Yes I think now I know how to do this.

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