Dynamic interactions in terms of senders, hubs, and receivers (SHR) using the singular value decomposition of time series: Theory and brain connectivity applications

Understanding of normal and pathological brain function requires the identification and localization of functional connections between specialized regions. The availability of high time resolution signals of electric neuronal activity at several regions offers information for quantifying the connections in terms of information flow. When the signals cover the whole cortex, the number of connections is very large, making visualization and interpretation very difficult. We introduce here the singular value decomposition of time-lagged multiple signals, which localizes the senders, hubs, and receivers (SHR) of information transmission. Unlike methods that operate on large connectivity matrices, such as correlation thresholding and graph-theoretic analyses, this method operates on the multiple time series directly, providing 3D brain images that assign a score to each location in terms of its sending, relaying, and receiving capacity. The scope of the method is general and encompasses other applications outside the field of brain connectivity.