## 3 Tree-Based Entropy Structured Self-Organizing Maps--Tessom
### TESSOM Result Interpretation  
The interpretation of the generated **TESSOM** model results can be done by analyzing the nodes (SOM models), their entropy levels and all the information collected in the process. The proposed sequence for analysis consists of the following steps:  
1. The analysis of the TESSOM tree starts at level 1, which contains the first SOM model. At this point, the database used by SOM is complete, and this model performs the first data classification process. It is possible to analyze the entropy generated and the distribution of objects by neurons, and the contributions of variables. 2. The grouping of objects is based on vector analysis of the set of variables of the objects during training. This type of analysis makes the objects approach by close values, and for each neuron the contributions of the variables is different. When analyzing the contributions of the variables in the definition of the subset of data referring to the neuron, it is possible to perceive differences in how the data are related, and these are hidden when working with the integral base. 3. The selection criteria for the analysis of neurons must be defined. For this example, two neurons were selected, with lower and higher entropies, to deepen the analysis. However, it is possible to expand the analysis to all neurons, as they can all have relevant information. For the analysis of the experiment of this work, the neuron with the highest number of positives per level was selected. 4. With the neurons selected for analysis according to the criteria of the previous step, it is possible to assess which variables contributed to the clustering and which values of each variable were considered (heat map). 5. For the neuron with the highest entropy, if it is above the limit defined in the training, it is possible to analyze the new model, this time with the data already segmented. 6. For the neuron selected for analysis, the contribution of each variable must be evaluated, along with how the object classification process approached objects, evaluating them by their labels (remembering that they were not used in the classification process, but are available for analysis). Through the heat map, it is possible to identify the ranges of values of the variables in each of the neurons. 7. It is possible to analyze each of the neurons whose set of objects derived a new model by selecting it and repeating the sequence from step 3, and at each new level the information contained is more and more specific. The model also provides additional information to support the analysis, such as tables containing segmented data. Next, we exemplify how the process of analyzing the structure information generated by the algorithm **TESSOM** should be carried out using an synthetic database composed of 100 objects, containing three variables identified as: \"_Attribute1_, \" \"_Attribute2_\" and a third variable containing the classes (labels) of each of the objects. The dataset was divided into three classes of 50 objects each (balanced), with overlap between the objects. The parameters used for training were: entropy of 0.5 and minimum number of neurons equal to four. With the first SOM generated, it is possible to analyze the data overlap through the entropy table calculated for the neurons, according to Table 1 of the object mapping graph, according to Figure 4.  
In this model, neurons 1, 2 and 3 have entropies above 0.5, and will generate new models. Neuron 4 contains only objects. We can validate this distribution through a Voronoi graph shown in Figure 4, where all the base points are identified, and the prototypes defined by the SOM model are identified with highlighted crosses. Lines are also printed, delimiting boundaries between objects belonging to each of the neurons. Figure 4 shows how the definition of neurons occurred, showing that the objects were close to their prototypes, and that data overlapping did not occur for one of the neurons.