Component Ordering in Independent Component Analysis Based on Data Power

With Independent Component Analysis (ICA) the objective is to separate multidimensional data into independent components. A well known problem in ICA is that since both the independent components and the separation matrix have to be estimated, neither the ordering nor the amplitudes of the components can be determined. One suggested method for solving these ambiguities in ICA is to measure the data power of a component, which indicates the amount of input data variance explained by an independent component. This method resembles the eigenvalue ordering of principle components. We will demonstrate theoretically and with experiments that strong sources can be estimated with higher accuracy than weak components. Based on the selection by data power, a method is developed for estimating independent components in high dimensional spaces. A test with synthetic data shows that the new algorithm can provide higher accuracy than the usual PCA dimension reduction.