Geometrical interpretation of the PCA subspace approach for overdetermined blind source separation

Abstract

We discuss approaches for blind source separationwhere we can use more sensors than sources to obtain a betterperformance. The discussion focuses mainly on reducing thedimensions of mixed signals before applying independent componentanalysis. We compare two previously proposed methods. The firstis based on principal component analysis, where noise reduction isachieved. The second is based on geometric considerations andselects a subset of sensors in accordance with the fact that a lowfrequency prefers a wide spacing, and a high frequency prefers anarrow spacing. We found that the PCA-based method behavessimilarly to the geometry-based method for low frequencies in theway that it emphasizes the outer sensors and yields superiorresults for high frequencies. These results provide a betterunderstanding of the former method.