## 3 Results and Discussion  
This study used the CoCoMac BCN dataset in order to build a computational tool that is able to select the best ANN topologies for BCN connectivity prediction. A recent study conducted by [PERSON] et al. [64] has reviewed The Human Connectome Project, an amazing five-year enterprise devoted to characterize brain connectivity and function in healthy adult human beings. [PERSON] [65] discussed the need for computational methods to disentangle the relationships between anatomical and functional connections. However, we have to deal with the estimation of data reliability and the presence of contradictory reports to develop new BCN models. Consequently, there is a need for computational tools for data mining using integrated large sets of partially redundant or inconsistent data in brain maps [66]. More often, data on BCN have to be systematically re-evaluated (collated) [67]. ANNs can discriminate between the correct connectivity for nodes (n\({}_{\text{j}}\)) in complex systems (Lij) from the incorrect and/or randomly distributed links. In order to be able to select the best ANN topology for BCN node connectivity prediction, we propose the Net-Net AutoML method. This tool represents a classifier based on Shannon entropies (Sh\({}_{\text{k}}\)) of BCN pairs of nodes and ANN topology. In the first step, the BCN was turned into numerical input parameters (Sh\({}_{\text{k}}\)(ANN) values) for all pairs of nodes to feed alternative ANN classifiers. Next, we trained different ANNs to predict the BCN connectivity. In the final step, we joined all the data (Sh\({}_{\text{k}}\) values of BCNs and ANNs) of selected pre-trained cases to search the best AutoML classifier using twelve Machine Learning methods. Table 1 shows the values of Sh\({}_{\text{k}}\)(ANN) for 10 different topologies. As previously explained, Sh\({}_{\text{k}}\)(A\({}_{\text{i}}\)) and Sh\({}_{\text{k}}\)(B\({}_{\text{i}}\)) were used as inputs and Lij = 1 (BCN links) or Lij = 0 as outputs. At that point, we used Multilayer Perceptron (MLP) and Liner Neural Network (LNN) as topologies with the default values provided by STATISTICA after its automatic algorithm based on feature selection and topology modification to improve them. In order to obtain a better generalization, the future studies should use more ANN topologies and/or different configurations thereof. We may need to use a High Performance Computing (HPC) service if we want to test a high number of ANNs for many complex systems [68; 69; 70; 71; 72; 73]. Thus, our final classifier is based on entropies for different nodes of the BCN--Sh\({}_{\text{k}}\)(A\({}_{\text{i}}\)) and Sh\({}_{\text{k}}\)(B\({}_{\text{j}}\))--and entropies of different ANNs topologies--Sh\({}_{\text{k}}\)(ANN). The best Net-Net AutoML model determined the scores \({}^{\text{q}}\)S(Lij) for a given ANN topology to predict the connectivity of BCN pair of nodes. This study presents a proof-of-concept model that fits very well, 500,740 outcomes obtained with 10 different ANNs. Twelve ML classifiers were tested and the AUROC values were calculated using a 10-fold cross-validation (see Table 2). The best model was obtained with RF10 (RF based on 10 trees) and AUROC was 0.9983 \(\pm\) 0.0001. Figure 2 shows the box-plot for the AUROC values of 12 ML methods (10-fold CV). The boxplot suggests that the AUROC values for all ML methods were stable within each fold. In addition, the difference between the RF and the other methods (box-plots are far from overlapping) proved to be statistically significant. All the Net-Net classifiers obtained good performance with an AUROC value greater than 0.90. An interesting result was provided by the simple KNN method with a mean AUROC value of 0.9958, still less than RF10 with a mean AUROC value of 0.9983. The linear methods (LDA and LogR) can provide models with a mean AUROC value \(>\) 0.92 and 0.95. The change to a tree-based method provided a better AUROC with values greater than 0.99, except for Ada.