ICA by PCA approach: Relating higher-order statistics to second-order moments

It is well known that principal component analysis (PCA) only considers the second-order statistics and that independent component analysis (ICA) exploits higher-order statistics of the data. In this paper, for whitened data, we give an elegant way to incorporate higher-order statistics implicitly in the form of second-order moments, and show that ICA can be performed by PCA following a simple transformation. This method is termed P-ICA. Kurtosis-based P-ICA is equivalent to the fourth-order blind identification (FOBI) algorithm [2]. Analysis of the transformation form enables us to give the robust version of P-ICA, which exploits the trade-off of all even order statistics of sources. Experimental comparisons of P-ICA with the prevailing ICA methods are presented. The main advantage of P-ICA is that it enables any PCA system, especially the dedicated hardware, to perform ICA after slight modification.