Re: Need advice about Principal Component Analysis (PCA)

Posted by dksamuel on Jun 28, 2007; 9:21am
URL: http://imagej.273.s1.nabble.com/Need-advice-about-Principal-Component-Analysis-PCA-tp3698972p3698974.html

Dear all
As far as PCA is concerned there are 2 good ppts from
http://www.ggebiplot.com/ the help file and demo programs help to understand
these terms better (but are not data for Images) with regards Samuel

On 6/28/07, Noel BONNET <[hidden email]> wrote:

>
> Hello,
>
> I agree with the comments given by Michael previously.
>
> Some additional answers:
> 1c. PCA (or any Multivariate Statistical Analysis variant) provides
> eigen-vectors (eigen-images when the data set is composed of a series of
> images) and scores (the weights of the different eigen-images in the
> original images). What is conserved if the product of the two signs (the
> sign of one eigen-image and the sign of the associated score). So, one
> sign
> appear more or less randomly (depending on the algorithm used for
> computing
> the eigenvectors), but the contribution of each eigen-image to the
> original
> images is not random at all!!!
>
> 2. There are many variants of PCA:
> - "raw" PCA (no centering, no normalization)
> - PCA with centering
> - PCA with normalization
> - PCA With centering and normalization
> - Correspondence Analysis (double normalization, on images and on pixels)
> There are also two ways for performing PCA:
> - either the objects are the images and the features are the intensities
> associated to the different pixels
> - or the objects are the pixels and the features are the values of these
> pixels in the different images.
> If you want to perform centering, you have to subtract the mean values ob
> the OBJECTS (which is equivalent to the answer by Michael if your objects
> are the images)
>
> 3. The order of the eigenvectors is always fixed by a decreasing order of
> the eigenvalues, because a large eigenvalue means an important
> significance
> (considering that information is represented by a large variance).
>
> 4. Give me your email adress and I will send you data with results.
>
> 5. I recommend my own pluging for ImageJ (of course!), available at:
> http://www.univ-reims.fr/INSERM514/ImageJ
>
> It includes the following variants: "raw" PCA, PCA with centering,
> Correspondence Analysis.
>
> I hope it helps.
>
>
> Noel ([hidden email])
>