## 3 Results
### Experiments to Diagnose Each MetS Type without a Blood Test
#### 3.3.1 Approach 1: Diagnosis of Each MetS Type Using the Original Dataset and ANN  
We did the following to diagnose each MetS type without a blood test. We first selected the necessary features to achieve the maximum discrimination in the classification algorithms using a sequential feature selection algorithm in Matlab [58,59] using 17 variables. We obtained the set of variables detailed in Table 10. To compare the traditional or general MetS (MetS) with the MetS types, we also show the features selected to build a model to diagnose it without a blood sample.  
Table 10 shows the predictor variables for the MetS types. It is important to highlight the BFP variable's relationship with the MetS types WPH, WGH, and WTH. This situation occurs due to the risk factor H (dichotomous HDL-C) dependence on gender. The MetS types related to P (dichotomous Blood Pressure) such as WPT, WPH, WPG, PGH, PGT, and PTH, according to the selection algorithm, have an evident relationship with the variables SBP and DBP. On the other hand, the MetS types WGT and GHT have the predictor variables WC and WSR, respectively, presenting a great challenge to discriminate them.  
Figure 6: Prevalence rate of the MetS types.  
We then designed each classification model for the MetS, taking into account which variables would be treated. These selected features were used as inputs of the ANN with several hidden neurons calculated using Equation (9) as shown in Table 11 and with the same configuration parameter recommended by [PERSON] [33] to diagnose the following MetS types: WPG, WPH, WPT, WGT, WGH, WTH, PGT, PGH, PTH, and GHT according to the HMS criterion.  
We validated each ANN using random subsampling, which we explained previously, obtaining the average performance indicators as shown Figure 7. The classification algorithms' performance indicators for diagnosing the MetS type WPT show an outstanding ability to discriminate (AROC = 90.58%). Also, the diagnosis of the MetS type WPH has the same level of outstanding discrimination ability (AROC = 92.85%). The MetS type WPG diagnosis shows an excellent level to discriminate (AROC = 85.28%). The PGT and the PTH types also show an excellent level due to (AROC = 81.06%) and (AROC = 88.84%), respectively. The MetS type WGH, WTH, and PGH show an acceptable level (AROC = 71.93%), (AROC = 70.60%), and (AROC = 73.03%) respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Types** & \multicolumn{4}{c}{**Predicting Variables**} \\ \hline WPT & WC & SBP & DBP & POD \\ \hline WPH & BMI & BFP & HC & SBP & DBP \\ \hline WPG & AGE & HC & SBP \\ \hline WGT & \multicolumn{4}{c}{WC} \\ \hline WGH & BFP & HC \\ \hline WTH & BFP & WC \\ \hline PGH & SBP & POD \\ \hline PGT & AGE & WG & SBP \\ \hline PTH & HC & SBP & DBP \\ \hline GHT & \multicolumn{4}{c}{WSR} \\ \hline MetSG & AGE & WC & WHR & SBP \\ \hline \hline \end{tabular}
\end{table}
Table 10: Selection of predicting variables for each MetS type from original dataset.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**WPT** & **WPH** & **WPG** & **WGT** & **WGH** & **WTH** & **PGH** & **PGT** & **PTH** & **GHT** & **MetSG** \\ \hline
4 & 4 & 3 & 2 & 2 & 2 & 2 & 3 & 3 & 2 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Numbers of hidden neurons from each ANN of the MetS types.  
Figure 7: Performance indicators of the ANN for the MetS types using the original dataset.  
In contrast, for the diagnosis of the MetS types WGT, GHT, results show a substandard level of ability to discriminate (AROC = 60.13%), and (AROC = 54.13%) respectively. This situation is due to the low levels of sensitivity. A reason for this could be that there are so few predictive variables or low prevalence rates for each type, as shown in Figure 6. The figure shows that most of the MetS types have a prevalence rate of less than 10% and are affected or generated by the less prevalence rate of fasting plasma glucose of 13.33% compared to the other risk factors.