## 4 Methods
### Performance Evaluation  
The performance evaluation of the algorithm was performed using the **k-fold** cross-validation technique, as defined by [78]. The first step is to organize the objects randomly and divide them into subsets of data, where each object belongs to only one subset. The next \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Oibjects** & **\% Objects** & **Accuracy** & **Level 2** & **Level 3** & **Level 4** & **Level 5** \\ \hline
25 & 0.1\% & 78.743\% & 2 & 8 & 15 & 5 \\
74 & 0.3\% & 78.145\% & 2 & 5 & 4 & 0 \\
123 & 0.5\% & 77.982\% & 2 & 4 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: TESSOM accuracy with variation in number of objects. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Value** & **Accuracy** & **Level 2** & **Level 3** & **Level 4** & **Level 5** & **Level 6** \\ \hline
0.5 & 79.205\% & 4 & 14 & 33 & 19 & 0 \\
0.6 & 79.069\% & 3 & 11 & 23 & 14 & 3 \\
0.7 & 79.209\% & 3 & 9 & 20 & 18 & 2 \\
0.8 & 78.743\% & 2 & 8 & 15 & 5 & 0 \\
0.9 & 78.294\% & 1 & 4 & 6 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: TESSOM accuracy with entropy variation. step is the execution of **TESSOM** training, using \(k-1\) subgroups for training and \(1\) group for tests, performing a loop of \(k\) interactions, always using different groups for tests and returning the group used previously for training. The macro flowchart for executing the processing is presented in Figure 10.  
During the training of the **TESSOM** tree, other algorithms were also used with the same subsets of objects generated by \(k\)-_folds_, as represented in Figure 10, with the collection of needed results and information. The algorithms are presented in Table 5, all with supervised training and are available for use by the library **caret**; they were also used by [79; 80; 81; 82; 83]. (Supervised training: during training, the labeling is considered in order to perform error corrections and increase the accuracy of the model.) The reason for choosing algorithms in Table 5 for comparison is the wider use of these algorithms in research on the same topic (analysis of hemogram variables). Other algorithms based on SOM trees are related to this research, but are focused on other types of data, For example, BTASOM is used for analysis of temporal data [44] or image analysis [84]. These algorithms have different parameterizations, and the choice was made according to experiments to better adapt them to this work, or as indicated in the literature. The used parameterizations were:  
* **kNN**, with \(k=7\), after studying the error curve with other values, using the dataset for the experiment;
* **MLP (Multilayer Perceptron)**: 14 neurons of the hidden layer (13 variables + 1) and number of epochs = 1000 were the parameters, and there was stabilization of the model with the best results;
* **Random forest**: the number of 100 trees was defined as the best value for the algorithm according to [85; 86]. For the testing phase (prediction evaluation), a test was included using the \(kNN\) algorithm with the complete base and using the parameterization defined above through  
Figure 10: Process for experiment execution, based on cross-validation by [78]. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Algorithm** & **Type** & **Based on** & **XAI** \\ \hline kNN & Classifier & Distances & No \\ Multilayer Perceptron (MLP) & Neural Network & Perceptron & No \\ Random Forest & Classifier & Decision Trees & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification of comparative algorithms. the **class** library. The purpose of using this library is to allow comparing the results of the testing phase of the **TESSOM** algorithm and the **care** library. Two types of results were evaluated: the training results and the results obtained by the **TESSOM** model.