Finding dependent and independent components from two related data sets

Independent component analysis (ICA) and blind source separation (BSS) are usually applied to a single data set. Both these techniques are nowadays well understood, and several good methods based on somewhat varying assumptions on the data are available. In this paper, we consider an extension of ICA and BSS for separating mutually dependent and independent components from two different but related 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 canonical correlation analysis (CCA) for detecting subspaces of independent and dependent components. Standard ICA and BSS methods can after this be used for final separation of these components. The proposed method performs excellently for synthetic data sets for which the assumed data model holds exactly, and provides meaningful results for real-world robot grasping data. The method has a sound theoretical basis, and it is straightforward to implement and computationally not too demanding. Moreover, the proposed method has a very important by-product: its improves clearly the separation results provided by the FastICA and UniBSS methods that we have used in our experiments. Not only are the signal-to-noise ratios of the separated sources often clearly higher, but CCA preprocessing also helps FastICA to separate sources that it alone is not able to separate.