# Functional Connectome of the Human Brain with Total Correlation
## 6 Discussion  
This manuscript presents a higher-order information-theoretic measure to estimate functional connectivity. We estimated Total Correlation with CorEx under different situations. However, the approach has its own pros and cons, which we will discuss later. Furthermore, we found that Total Correlation can be a metric to estimate functional connectivity in the human brain. It can identify some well-known functional connectivities and capture a few unknown nonlinear relationships among brain regions as well. To the best of our knowledge, this is the first time that Total Correlation has been used to estimate larger-scale functional connectivity for a whole-brain AAL atlas with 116 structural ROIs. Total Correlation can also be a tool to find biomarkers to help us diagnose brain-related diseases. Here, we discuss some advantages and limitations of this research now. Firstly, given the curse of dimensionality of fMRI, we need to find a low-dimensional representation that helps us characterize the connectivity. Traditional General Linear Models (GLMs), such as expert-defined ROIs or the ALL atlas, are frequently used to find ROIs in resting-state experiments. However, we should be able to do better with a data-driven approach. Sample sizes and statistical thresholds are known to have a major impact on the statistical power and accuracy of GLM-based ROI selection. Previous research has revealed that the GLM has limited statistical power when inferring from fMRI data [50; 51]. However, we used GLM-based ROI selection in the real fMRI datasets, which may affect the final result when we estimate functional connectivity. Second, CorEx is model-independent, which means no anatomical or functional prior knowledge is required to estimate the ROIs. The method is entirely data-driven; this way, it is possible to analyze networks that have not been investigated and could be a future extension of work. It is also possible to use Total Correlation as a pre-analysis for other techniques such as dynamic causal modeling, which need constraints about the underlying network [52]. What differentiates the CorEx algorithm is that it tries to break the variables into clusters with high TC. In other words, CoRex finds a tree of latent factors that explain Total Correlation, so this tree of clusters based on TC is a more data-driven way to define regions and then connectivity than ROIs predefined by hand. This prioritization of \"modular\" solutions in CorEx was not realized or emphasized in the original research. The second reason why we used CorEx to estimate functional connectivity on larger-scale fMRI datasets is that it is a clustering approach via TC. Furthermore, CorEx estimates Total Correlation via hierarchical maximization correlation between previous layer and current layer variables with a tight information bound that estimates a more accurate relationship among variables in real neural signals. Third, TC is an indirect information quantitative tool that cannot determine the direction of information flow between brain regions. Meanwhile, we discovered some unknown functional connectivity in the real fMRI dataset before. Fourth, given the irregularity of neural time series and the difficulties in quantifying graph signals when brain networks are represented by graphs, we should avoid quantifying too many graph signals. However, there is a metric called permutation entropy that gives us the possibility to quantify the graph signal in complex systems [36]. It could be very interesting to apply this metric to brain networks to check how much information could be obtained from the complex graph signals, which could then help us more deeply understand brain networks in the future. Moreover, as we mentioned the complexity of neural time series, one of the important potential problems is the length of time series, except for the additional dimensional problem.