# Functional Connectome of the Human Brain with Total Correlation
## 1 Introduction  
The human brain is a complex system comprised of interconnected functional units. Millions of neurons in the brain interact with each other at both a structural and functional level to drive efficient inference and processing in the brain. Furthermore, the functional connectivity among these regions also reveals how they interact with each other in specific cognitive tasks. Functional connectivity refers to the statistical dependency of activation patterns between various brain regions that emerges as a result of direct and indirect interactions [1, 2]. It is usually measured by how similar neural time series are to each other, and it shows how the time series statistically interact with each other. A variety of ways to analyze functional connectivity exist. A seedwise analysis can be performed by selecting a seed-driven hypothesis and analyzing its statistical dependencies with all other voxels outside its limits. It is a common tool for studying how different parts of the brain are connected to one another. Connectivity is determined by calculating the correlation between the time series of each voxel in the brain and the time series of a single seed voxel. Another option is to perform a wide analysis of the voxel or Region Of Interest (ROI), where statistical dependencies on all voxels or ROIs are studied [3]. Structural connectivity refers to the anatomical organization of the brain by means of fiber tracts [4]. The sharing of communication between neurons in multiple regions is coordinated dynamically via changes in neural oscillation synchronizations [5]. When it comes to the brain connectome, functional connectivity refers to how different areas of the brain communicate with one another during task-related or resting-state activities [6]. The use of information-theoretic metrics can efficiently detect their interaction in dynamical brain networks, and it is widely used in the field of neuroscience [7], for instance to quantify information encoding and decoding in the neural system [8, 9, 10, 11], measure visual information flow in the biological neural networks [12, 13] and color information processingin the neural cortex [14], and so on. However, although functional connectivity has already become a hot research topic in neuroscience [15; 16], systematic studies on the information flow or the redundancy and synergy amongst brain regions remain limited. One extreme type of redundancy is full synchronization, where the state of one neural signal may be used to predict the status of any other neural signal, and this concept of redundancy is thus viewed as an extension of the standard notion of correlation to more than two variables [17]. Synergy, on the other hand, is analogous to those statistical correlations that govern the whole, but not its constituent components [18]. High-order brain functions are assumed to require synergies, which give simultaneous local independence and global cohesion, but are less suitable for them under high synchronization situations, such as epileptic seizures [19]. Most functional connectivity approaches until now have mainly concentrated on pairwise relationships between two regions. The conventional approach used to estimate indirect functional connectivity among brain regions is the Pearson Correlation (CC) [20] and Mutual Information (I) [8; 21; 22; 23]. However, real brain network relationships are often complex, involving more than two regions, and the pairwise dependencies measured by correlation or mutual information cannot reflect these multivariate dependencies. Therefore, recent studies in neuroscience focus on the development of information-theoretic measures that can handle more than two regions simultaneously such as Total Correlation [24; 25]. Total Correlation (TC) [26] (also known as multi-information [27; 28; 29]) mainly describes the amount of dependence observed in the data and, by definition, can be applied to multiple multivariate variables.