## 2 Methodology
### Model
#### 2.3.3 Framework to Diagnose the MetS Types
Each ANN is formed by neurons whose elements are a set of inputs that can come from other neurons or the outside, as shown in Figure 3 the basic structure of an ANN. Each structure of ANN should be initialized according to the propagation rule to the starting and each node has synaptic weights, which are the degree of communication between neurons, as shown Equations (7) and (8). Then, the data used to train the network is introduced into the network after the propagation algorithm is employed to obtain the final parameters in the network. In practice, the algorithm is divided into two parts: network training and network testing. The steps of propagation algorithm are described as follows [43]: \[net^{k}=\sum_{i=1}^{n}(\omega_{i}^{k}\dot{x}_{i}^{k}-\dot{a}_{i}^{k})\] (7) \[y^{k}=\theta(net^{k})\] (8)where \(x_{i}^{k}\) are inputs, \(\omega_{i}^{k}\) are synaptic weights, \(\alpha\) are bias in the input layer, k is the iteration and n is the number of inputs resulting in a net output that is determined by a activation function \(\theta(net^{k})\) with output \(y^{k}\)[44; 45]. This information flows in one direction only from the inputs to the hidden layer and after to the output layer, i.e., the information that comes from different activation function neurons, which is responsible for determining the current state and finally converges all the data to the output [33]. Each ANN has several hidden neurons that have functions, such as the hyperbolic tangent sigmoid function and an output layer with a neuron. The neuron has a function that can be a log-sigmoid function [44; 46]. It should be noted that there are no hard and fast rules for the number of hidden neurons. These hidden neurons can be calculated or found empirically and are highly dependent on the problem and the dataset [47]. However, we used the methodology mentioned by [48; 49; 50] and described in Equation (9), where the number of hidden neurons (_NHN_) can be 2/3 of the input variables plus an output variable. \[NHN=\frac{2(Input\ variables)}{3}+Output\ variables \tag{9}\]  
We used Equation (9), to estimate the number of hidden neurons to contribute to research in the area of machine learning for the diagnosis of MetS without using biochemical variables and in a way, describe every detail of the process for experimentation by other researchers can continue investigating these models as well as [PERSON] [32] that used other equation to calculate the hidden neurons. Another machine learning technique used to diagnose the MetS types was the ensemble Random undersampling Boosted tree (RusBoost) because the data from the MetS study is imbalanced [51]. This technique improves the performance indicators of models using imbalanced data by applying a random undersampling technique. The technique randomly removes samples from the majority class [52], as shown in the algorithm detailed in Appendix B with the configuration showed in Table 5.  
In summary, we used two machine learning techniques ANN and RusBoost to design the models and validating with the performance indicators using random subsampling described in the next subsection. \begin{table}
\begin{tabular}{l l} \hline \hline
**Learned Type** & **Decision Tree** \\ \hline Maximum number of splits & 20 \\ \hline Number of learners & 30 \\ \hline Learning rate & 0,1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: RusBoost Configuration.