## 5 Results  
The experiment was executed with the full dataset using the _k-fold_ process, with parameter \(k\) set to 10. The results obtained for accuracy are presented in Table 6, which contains the results obtained for the training data, the prediction using the majority label of the neuron for the calculation and the _kNN_ prediction, which is performed by generating a _kNN_ classification on the objects of the neurons that were not expanded, to apply the test objects and perform the prediction. With Figure 12 it is possible to evaluate the **ROC** curve for the TESSOM algorithm, which presents an **AUC** of 0.973 for training (green line) and 0.749 for model tests (prediction--red \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Average** & **Standard Deviation** \\ \hline Training & 79.028\% & 0.4197\% \\ Prediction & 76.315\% & 2.9985\% \\ kNN Prediction & 75.378\% & 3.2374\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: **TESSOM** training accuracy data. Figure 11: Interpretation of data from the confusion matrix. line). Given the curves obtained bu _MLP_, _kNN_ and _Random Forest_, presented in Figure 13, the gain obtained through the use of TESSOM can be identified. The execution times of each algorithm in seconds are shown in Table 7. It is important to note that for prediction, TESSOM presents higher times because it involves two methods, and one of the methods internally has _kNN_ training that uses the objects in the neuron to perform the prediction. The accuracy values obtained for all models trained and used for validation are identified in two tables: in Table 8 are the results obtained by using the training data, and in Table 9 the results obtained using the test set are presented. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Algorithm** & **Train** & **Prediction** \\ \hline TESSOM & 26.907153 & 6.354581 \\ kNN & 1.078941 & 0.022347 \\ Multilayer Perceptron (MLP) & 8.653341 & 0.008462 \\ Random Forest & 36.464645 & 0.022636 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Algorithms execution times (seconds). Figure 12: TESSOM ROC curve for training and testing. Figure 13: ROC curves for _MLP_, _kNN_ and _Random Forest_ models. By evaluating the obtained results, one can observe that the **TESSOM** model presented better accuracy levels of \(\approx\)2% in comparison to the other algorithms used in the training phase. In addition, its prediction accuracy is equivalent to that of other models, when considering the standard deviation. However, the objective of these experiments was to analyze the performance of the proposed algorithm in comparison to other alternatives, emphasizing that the greatest contribution to be presented is in the possibility of interpreting the **TESSOM** results. Next, the results of the **TESSOM** tree are analyzed, following the interpretation process described in Section 3.2 to identify useful results for the COVID-19 study. **TESSOM**, as the name implies, generates a tree structure that can be interpreted in a top-down manner. The first SOM model generated is considered as the root node (or level 1) of the model. Models derived from the subsets of data identified by their neurons are level 2, and so on. In Figure 14, all results obtained at the different levels of the **TESSOM** tree, up to the third level, are presented. To demonstrate the use of **TESSOM** as an aid to identify variables that contribute to the identification of positive cases of COVID-19, the analysis focuses on neurons with percentages of positive cases higher than 80%, and whose volume of associated objects is higher than 50. These values are defined because a low number of objects may not statistically represent relevant information, considering that the total set has 2453 objects. When performing the analysis of the results shown in Figure 14, it could be seen that at level 1, neuron 4 had an entropy of \(\approx\)0.62 and a percentage of positives of \(\approx\)84.7%, according to Table 10. Therefore, the analysis started at this neuron.