I. Introduction
The role of functional connectivity in understanding the brain has become a prominent topic in neuroscience. The oscillatory neuronal activity happens when the brain encodes sensory information and decodes it to represent perception in-formation, and this cognitive processing is densely related and supported by functional connectivity in the brain, which then drives specific action. Furthermore, functional connectivity can help us to explore brain function further. Nonetheless, it also can help us to find biomarks of mental illness, such as depression [1], autism spectrum disorders [2], bipolar disorder[3], schizophrenia [4] and other psychoses. The previous related re-search shows that a disorder of functional connectivity between specific brain regions could cause the above-mentioned mental illness. Furthermore, several functional connectivity metrics are used to quantify it―the detailed information about the taxonomy of functional connectivity metrics was introduced in Section 2. The functional connectivity metrics are basically divided into two classes: directed and indicted. From an information-theoretical point of view, mutual information has already become a common and powerful way to figure out how indicted functionally linked two regions are, and transfer entropy has become a dominant method in estimating one-way directed functional connectivity. Both information-theoretical approaches have achieved remarkable results in understanding brain function[5], [6]. However, we investigate too much feedforward information flow between brain regions and ignore feedback information coupling between brain re-gions. Furthermore, numerous experiments have demonstrated that feedback information plays an important role in per-ception processing [7], [8]. Meanwhile, feedback information-related studies are also getting more and more attention in both neuroscience and deep learning fields [7], [9]. The di-rected information can achieve the above objective of this research. The directed information proposed by Marko [10] and Massey [11], [12], it can estimate feedforward information, feedback or inverse information, and resonance information, and a lot of research on biological gene networks [13]–[15] and computational neuroscience [16] has already used directed information in a big way. The details of directed information are introduced in Section 3.