## 3 Tree-Based Entropy Structured Self-Organizing Maps--Tessom  
_Self-organizing maps_ are artificial neural networks whose architecture consists of an input layer and an output layer. The input is where an object from a dataset used for training is presented to the network. The output is usually a spatially and globally ordered two-dimensional lattice of neurons. Each neuron has a vector of weights whose dimensions are the same as the object presented in the input. The training algorithm is of the unsupervised type and has characteristics of competitiveness and cooperation. The competitiveness consists of finding the neuron that best represents the input object. The cooperation, in turn, consists of updating the weight vector of the winning neuron to ensure that similar objects have the same neuron as the winner. The weight vector of its neighbors is also updated so that objects with less similarity have neurons adjacent to the winner. This guarantees a topological ordering of the data in the lattice. The weight vector of each of the neurons, after the model is trained, represents a virtual object that may or may not coincide with a real object, and around which the other objects of the neuron are close. This vector will be treated as a prototype. There are works such as [39; 40] that deal with techniques for selecting multiple prototypes in a SOM model. The topological ordering and also the vector quantization, given that each neuron can represent a set of similar objects, brings positive aspects, such as the analysis of data characteristics through cluster analysis and the visualization of the results using different types of graphs that allow bidimensional manipulations of the objects in a neuron (or the weight vector) for analysis and formation of groups. Another advantage to using SOM relates to data. As presented in [39; 41; 42], the fact that the training is unsupervised allows ignoring class imbalance. However, an aspect that generates uncertainty in the use of SOM has to do with defining the optimal dimensions for the map. Thus, some authors define heuristics that help with finding the best lattice dimensions [40]. However, according to [43], the size of the map to be generated directly impacts the training, so an effective approach to defining the size can be based on starting with smaller maps and then adding intermediate neurons up to the maximum size. Other authors propose structuring the SOM in a tree so that the lattice is hierarchically composed until reaching a level defined a priori. There are two types of tree SOM structures in the literature: hierarchical and pyramidal. Hierarchical, as the name suggests, defines a tree structure with different hierarchies, where the evaluation of the values in the initial node generates a division of the objects for the secondary nodes according to their neighborhood, and so on. The pyramid organizes the dimensions of the map in a pyramidal shape, so that the top of the pyramid is the most representative node, and the other dimensions follow according to their weights. Examples of hierarchical orderings are as follows: **BTASOM** (_binary tree TASON_) [44], where a binary tree is created, each node being a model of type **TASOM** (time adaptive self-organizing map), which is a SOM-derived algorithm that has variable learning rates and neighborhood size, and can reflect changes in the environment as per the latest input during model training [45; 46]. **SOTA** (self-organizing map tree map) [47; 48] has its neurons internally distributed similarly to a binary tree, with one node being considered the most important according to defined criteria, and the others organized below. **GHTSOM** (growing hierarchical tree SOM) [49] performs hierarchical model growth according to the variation of the weights in the neurons. **TTO-SOM** (tree-based topology-oriented SOM) [50] organizes neurons in a predefined tree structure, with free growth defined by the relationships between neurons and their neighborhoods.