Canonical information flow decomposition among neural structure subsets - Takahashi, Daniel Y.; Baccalá, Luiz A.; Sameshima, Koichi (Frontiers in Neuroinformatics, 2014)
Partial directed coherence (PDC) and directed coherence (DC) which describe complementary aspects of the directed information flow between pairs of univariate components that belong to a vector of simultaneously observed time series have recently been generalized as bPDC/bDC respectively to portray the relationship between subsets of component vectors (Takahashi, 2009;  Faes and Nollo, 2013). This generalization is specially important for neuroscience applications as one often wishes to address the link between the set of time series from an observed ROI (region of interest) with respect to series from some other physiologically relevant ROI. bPDC/bDC are limited, however, in that several time series within a given subset may be irrelevant or  may even interact opposingly with respect to one another leading to interpretation difficulties. To address this, we propose an alternative measure, termed cPDC/cDC, employing canonical decomposition to reveal the main frequency domain modes of interaction between the vector subsets. We also show bPDC/bDC and cPDC/cDC are related and possess mutual information rate interpretations. Numerical examples and a real data set illustrate the concepts. The present contribution provides what is seemingly the first canonical decomposition of information flow in  the frequency domain.