Posted by
Noel BONNET on
Jun 28, 2007; 8:48am
URL: http://imagej.273.s1.nabble.com/Need-advice-about-Principal-Component-Analysis-PCA-tp3698972p3698973.html
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/ImageJIt includes the following variants: "raw" PCA, PCA with centering,
Correspondence Analysis.
I hope it helps.
Noel (
[hidden email])