###### Abstract
For example, for COVID-19 cases, literature shows that there are far more data tied to positive diagnoses than negative ones. In part, this is since asymptomatic patients usually do not seek testing [5; 14; 20]. Therefore, a significant number of artificial intelligence algorithms have prediction results biased by class imbalance, which requires, in many of them, the application of other techniques that aim to pre-process the base in order to achieve balance, such as the prototype generation technique [21; 22] or bias adjustment [23]. In addition, it should also be noted that some patients with different diagnoses may present with comorbidities, and when performing a test such as a blood test, some test factors may coincide, leading to situations in which the data indicate overlapping diagnostic outcomes--that is, the decisions are not simple. As far as this problem is concerned, artificial intelligence algorithms are particularly good generators of decision boundaries. However, in order to achieve this goal in some situations, complex mathematical operations are needed, and that makes it difficult to provide an explainable decision. This is the case with neural networks, support vector machines and other algorithms that generate a decision boundary [4; 24]. The motivation for this work was two-fold. The paper [1] proposed a method based on a neural network of self-organizing maps (SOM) applied to blood counts of 599 patients diagnosed positively or negatively with COVID-19 from Albert Einstein hospital in Sao Paulo, whose results are explainable by humans, considering the paradigms defined for **XAI** (_explainable AI_) [25; 26]. Therefore, SOM visualization methods were explored to identify the relevance of each of the 13 blood test factors (biological variables) by inspecting each neuron using linear discriminant analysis, to discover the most preponderant factors for the correct diagnosis. The second source of motivation was the idea of attempting to exploit SOM in a similar way to AI algorithms based on decision trees, such as _random forest_ and _XGBoost_. These algorithms analyze each variable of a dataset (in this case, CBC variables) in order to model the best combination of these factors based on the entropy measurement in order to maximize the accuracy for diagnosis prediction. These models may provide a clearer understanding on how a decision is made, through the interpretation of the variables in order of relevance from the top to the bottom of the tree. Disadvantageously, although the relevance of each variable can be discovered, the algorithm in many cases ends up selecting a set of variables which does not allow a complete analysis of the variables and their relationships. Furthermore, these algorithms are sensible to class imbalance, which we knew could be a disadvantage in the context of this work. For this reason, techniques to obtain balance between classes were used to introduce artificial data, generated specifically for this purpose, that did not come from actual patients. Therefore, this work presents a SOM network tree whose growth is controlled by entropy. Thus, the TESSOM (_tree-based entropy structured self-organizing maps_) algorithm is based on a semi-supervised training; that is, SOM training is the unsupervised portion, which is not influenced by class imbalance, and the entropy calculation for each neuron that needs labeling information is the supervised part. The outcome of this training process is the selection of neurons that should generate a new SOM network. Thus, data subsets with large overlaps, measured by entropy, form a new network in order to reorganize the data, as we seek better separation. In addition to the proposed algorithm, another contribution is the possibility of better interpreting results manually--for example, by allowing one to identify the probability of association with COVID-19 diagnosis for each range of values of each blood test factor.