I trying to detecting whether a data set of time series has a global change in frequencies. Calculating the average (or median) pairwise coherence, I feel, misses the point because I am trying to get a measure of network (i.e. multivariate, more than pairwise) coherence. I found a group[1] that uses the relative magnitude of the first singular value to all others to calculate what they call global coherence. The singular values come from a singular value decomposition (SVD) of a matrix of pairwise coherences. Searching online didn't show up much more. Any thoughts? Wong KFK, Mukamel EA, Salazar AF, Pierce ET, Harrell PG, Walsh JL, Sampson A, Brown EN, Purdon PL. 2011. Robust time-varying multivariate coherence estimation: application to electroencephalogram recordings during general anesthesia. Conference proceedings : Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society Conference 2011: 47258.
Calculation of Multivariate Coherence
matrices;data analysis
It seems that, at the risk of writing a truism, any multivariate measure must be sensitive to all the independent components of a system.The relative ratio of the first singular values to the sum of all singular values is one such measure. Another is the determinant of the matrix of singular values. Using SVD does assume that the system can be completely described by parts that are separable into linearly interacting entities.In sum, in as much as global coherence captures the essence of a multivariate measurement and is not too sensitive to noise other ones will just be variations on a theme rather than refinements.