An independent component ordering and selection procedure based on the MSE criterion

Principal components (PCs) by construction have a natural ordering based on their cumulative proportion of variance explained. However, most ICA algorithms for finding independent components (ICS) are arbitrary, which limit the use of ICA in pattern discovery and dimension reduction. To solve this problem, we propose an efficient IC ordering approach and prove that this method guarantees to find the optimal ordering of ICs based on the MSE criterion. Furthermore, we employ the cross validation method to select the number of dominant ICs. Simulation experiments show that the proposed IC ordering and selection procedure is efficient and effective, which can be used to identify the dominant ICs as well as to reduce the number of ICs.