IVA and ICA: Use of diversity in independent decompositions

Starting with a simple linear generative model and the assumption of statistical independence of the underlying components, independent component analysis (ICA) decomposes a given set of observations by making use of the diversity in the data. Most of the ICA algorithms introduced to date have made use of one of the two types of diversity, non-Gaussianity or sample dependence. We first discuss the main results for ICA in terms of identifiability and performance with these two types of diversity, and then introduce independent vector analysis (IVA), generalization of ICA for decomposition of multiple datasets at a time. We show that the role of diversity in this case parallels that in ICA, and discuss identifiability conditions and performance bounds in a maximum likelihood framework.