# A Deep Learning Model for Data-Driven Discovery of Functional Connectivity
## 4 Discussion  
The richness of results in the three presented categories highlights the benefits of the proposed method. High classification performance shows that the model can accurately classify the subjects and, hence, it can be trusted with the other two interpretative results of the paper. Functional connectivity between the regions shown in the paper is of paramount importance, as it highlights how brain regions are connected to each other and the variation between classes. Learning functional connectivity end-to-end through classification training frees the model from depending on an external method. The sparse weight matrix of subjects with SZ shows that connectivity remains significant between considerably fewer regions than for healthy controls. Notably, the attention based functional connectivity cannot be interpreted as the conventional correlation based symmetric connectivity. Because of the inherent asymmetry in keys and values, the obtained graph is directed, but it is also prediction based rather than simply correlation. We expect that a further investigation into the obtained graph structure will bring more results and deeper interpretations. The sparsity is to be further explored and seen in the context of the regions selected, as shown in the last section of results. The final regions selected by the model strengthens our hypotheses that not all regions are equally important for identifying a particular brain disorder. Reducing the brain regions by almost 80% helps in identifying the important regions for the classification of SZ. The regions selected by our model, such as cerebellum, temporal lobe, caudate, SMA, etc., have been linked to the disease by multiple previous studies, hence reassuring the correctness of our model [27; 28; 29; 30]. We see an immediate benefit of using GNNs to study functional connectivity and our BrainGNN model specifically. The data-driven model almost eliminates manual decisions transitioning graph construction and region selection into the data-driven realm. With this BrainGNN opens up a new direction to the existing studies of connectivity, and we expect further model introspection to yield insight into the spatio-temporal biomarkers of schizophrenia. Further reducing the selected regions and how they different across subjects belonging to different class is also left for future work. We envision great benefits to the interpretability and elimination of manual processing and decisions in a future extension of the model that would enable it to work directly from the voxel-level, not only connecting and selecting ROIs, but also constructing them.  
Conceptualization, U.M., S.P.; methodology, U.M.; software, U.M.; validation, U.M.; formal analysis, U.M.; investigation, U.M.; resources, V.D.C.; data curation, Z.F., U.M.; writing--original draft preparation, U.M.; writing--review and editing, U.M., S.P., Z.F.; visualization, U.M.; supervision, S.P.; project administration, S.P., V.D.C.; funding acquisition, S.P., V.D.C. All authors have read and agreed to the published version of the manuscript.  
This study was in part supported by NIH grants 2 RF1 MH121885, 1R01 AG063153, and 2R01 EB006841.  
Figure 6: (a) Histogram of regions selected after the last pooling layer of GNN. 2 nd fold of the cross validation gives this figure. All the 23 regions are selected an equal number of times (16). It further signifies the important of these regions, showing that, for all subjects across both classes, these 23 regions are always selection. (b) mapping the 23 regions back on the brain across the three anatomical planes. 100 th time point is selected for these brain scans. X axis shows different slices of the plane.