Why are the Eigenvalues and Eigenvectors from PCAG (PCA from genes) and PCAE (PCA from experiments) the same?
A. To compute the principal components, the m Eigenvalues and their corresponding Eigenvectors are calculated from the (m x m) distance matrix using Singular Value Decomposition (SVD). m = number of experiments. n = number o genes. Genesis uses this method for both cases (genes AND experiments)! See also answer to question (3). Q. PCAE (PCA from experiments): If I load a data set with 30 genes and 5 conditions, I expect to see 30 components with 30 dimensions each and not only 5 components. Furthermore, the Eigenvalues should be different from those that I get with PCAG (PCA form genes). A. This is correct, and the straightforward implementation did exactly calculate the SVD of the (n x n) distance matrix. In this case we get the expected n components, where n is the number of genes. However, the disadvantage of this method is, that it is very computational intensive, since n is usually quite large. And here is the trick. It is due to a mathematical tick possible to calculate the resul
