# Functional Connectome of the Human Brain with Total Correlation
## 7 Conclusions  
We introduced Total Correlation to capture multivariate large-scale interactions within brain regions. They were experimentally verified as effective steps for reconstructing multivariate relationships in the brain. In this study, CorEx was adopted to estimate Total Correlation. The CorEx approach can capture functional connectivity characteristics when going beyond pairwise brain regions. On the other hand, we evaluated the method with resting-state fMRI datasets. We found that multivariable relationships cannot be detected if we use pairwise correlation and mutual information quantities only. More generally, multivariate relationships can be clustered only if we use Total Correlation. Therefore, Total Correlation measures are significant to find complicated functional connectivity among brain regions. Furthermore, we showed that Total Correlation can estimate functional connectivity in the real neural dataset and find biomarkers for diagnosing brain diseases.  
In the future, we plan to use the functional connectivity relationships discovered by Total Correlation as an input to existing Graph Neural Networks (GNNs) [54] for the purpose of interpretable brain disease diagnosis, such that practitioners or doctors can identify the most informative subgraphs (or modules) to the decision (e.g., autism patients or healthy control groups). In this regard, quantitative measures to define differences between graphs [55] and the extension of analytical results in [25] to a larger number of nodes will be critical to assess and improve the qualitative results presented here. The recently proposed approaches (e.g., [56; 57]) all rely on pairwise relationships estimated by the linear correlation coefficient as the input, which ignores high-order dependence essentially. In this sense, we believe our approach has the potential to improve the explanation performances of existing GNNs on brains.  
Conceptualization, methodology, software, and validation, Q.L., writing --original draft preparation, writing--review, and editing, Q.L., G.V.S., S.Y. and J.M. The contribution of J.M. was focused on the definition of the paper scope about large-scale connectomes, the relation with analytical results in [25], and the criticism of performance measures. All authors have read and agreed to the published version of the manuscript.  
Q-L- and J-M- were partially funded by the Spanish/European grants from GVA/AEI/FEDER/EU: MICINN PID2020-118071 GB-I00, MICINN PDC2021-121522-C21, and GVA Grisolia-P/2019/035. G.V.S. acknowledges support from the Defense Advanced Research Projects Agency (DARPA) under Award FA8750-17-C-0106. S.Y. was funded by the Research Council of Norway under Grant No. 309439. Finally, we thank the organizers of the HCP and ACPI for providing these interesting dataset used in these studies.  
All the human data used in this research is an open-source dataset, and therefore, this study does not relate to any ethics.  
The data and code needed to reproduce the results presented here are available at [[https://forms.gle/1](https://forms.gle/1) DXDpEpi/AodQ77q7]([https://forms.gle/1](https://forms.gle/1) DXDpEpi/AodQ77q7) accessed on 6 November 2022.  
The authors declare no conflict of interest.