Finding dependent and independent components from related data sets: A generalized canonical correlation analysis based method

In this paper, we consider an extension of independent component analysis (ICA) and blind source separation (BSS) techniques to several related data sets. The goal is to separate mutually dependent and independent components or source signals from these data sets. This problem is important in practice, because such data sets are common in real-world applications. We propose a new method which first uses a generalization of standard canonical correlation analysis (CCA) for detecting subspaces of independent and dependent components. For two data sets, this reduces to using standard CCA. Any ICA or BSS method can then be used for final separation of these components. The proposed method performs well for difficult synthetic data sets containing different types of source signals. It provides interesting and meaningful results for real-world robot grasping data and functional magnetic resonance imaging (fMRI) data. The method is straightforward to implement and computationally not too demanding. The proposed method clearly improves the separation results of several well-known ICA and BSS methods compared with the situation in which CCA or generalized CCA is not used. Not only are the signal-to-noise ratios of the separated sources often clearly higher, but our method also helps these ICA and BSS methods to separate sources that they alone cannot separate.