Extending ICA for finding jointly dependent components from two related data sets

In this paper, we introduce some methods for finding mutually corresponding dependent components from two different but related data sets in an unsupervised (blind) manner. The basic idea is to generalize cross-correlation analysis by taking into account higher-order statistics. We propose independent component analysis (ICA) type extensions for the singular value decomposition of the cross-correlation matrix. They extend cross-correlation analysis in a similar manner as ICA extends standard principal component analysis for covariance matrices. We present experimental results demonstrating the usefulness of the proposed methods both for artificially generated data and for a cryptographic problem.