Parallel Analysis

This technique is used to decide the dimension for PCA. I know little about its theory and I am searching for some related materials.

The current algorithm I am applying for my experiments is very simple. It is only required to do a PCA once more. For example, X is the data matrix whose vectors are samples. Then each row of X should be randomly permuted when the new PCA is applied to it. Then compare the eigenvalues (sorted in the descending order) of the two. The dimension for PCA is the number of eigenvalues that the second PCA gets and are smaller than those the first PCA gets correspondingly.

According to the experiments result, with the dimension determined by the parallel analysis, the data and projected data yield very similar results with linear algorithms.