## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Anthropometric Parameter**} & \multicolumn{2}{c}{**Group 1**} & \multicolumn{2}{c}{**Group 2**} \\ \cline{2-5}  & **Female 2** & **Male** & **Female 2** & **Male** \\ \hline Body mass (kg) & 91.3 \(\pm\) 18.2 * & 108.4 \(\pm\) 20.8 & 78.6 \(\pm\) 17.2 * & 103.3 \(\pm\) 25.3 \\ Body height (m) & 165.1 \(\pm\) 5.8 & 173.9 \(\pm\) 8.2 & 163.8 \(\pm\) 7.2 & 175.8 \(\pm\) 7.4 \\ BMI (kg/m\({}^{2}\)) & 32.8 \(\pm\) 6.7 & 35 \(\pm\) 6.1 & 32.9 \(\pm\) 8.5 & 38.3 \(\pm\) 8 \\ Chest circumference (cm) & 88.8 \(\pm\) 12 & 99.7 \(\pm\) 10.9 & 88.4 \(\pm\) 11.7 & 99.8 \(\pm\) 14 \\ Waist circumference (cm) 1 & 101.2 \(\pm\) 12.9 & 105.4 \(\pm\) 11.5 & 100.9 \(\pm\) 13.5 & 110.7 \(\pm\) 15.8 \\ Hips circumference (cm) & 108.9 \(\pm\) 13.2 & 113.8 \(\pm\) 14.1 & 106.7 \(\pm\) 13.2 & 114.9 \(\pm\) 16.2 \\ Biceps circumference (cm) & 33.8 \(\pm\) 4.5 & 37.2 \(\pm\) 4.7 & 33.8 \(\pm\) 5.8 & 37.1 \(\pm\) 4.1 \\ Thighs circumference (cm) & 66.2 \(\pm\) 6.6 & 67 \(\pm\) 7.1 & 64.9 \(\pm\) 9.1 & 68.5 \(\pm\) 7.6 \\ \hline \hline \end{tabular}  
* Circumference at the level,* Statistically significant difference (\(p<\) 0.05) comparing same gender in two groups; SD: standard deviation; BMI: body mass index. 2 Share of the females in group 1 is 70% and in group 2 is 58%.  
\end{table} 
Table 1: Anthropometric measures of the participants (72 males and 128 females) during the first medical exam, presented as mean value and its standard deviation (Mean \(\pm\) SD). (less than 5.2 mmol/L) and for glucose is between 70 mg/dL and 100 mg/dL (3.9 to 5.6 mmol/L) [23; 24; 25]. A normal level of ALT (alanine aminotransferase) for adults, which measures the level of an enzyme in liver, is between 7 and 55 units per liter (U/L) [24; 25; 26]. For triglycerides, which measure the amount of fat in the blood, a normal level for adults is less than 150 mg/dL or 1.7 mmol/L [24; 25; 26]. For TSH (thyroid-stimulating hormone), which measures the level of a hormone that stimulates thyroid gland [23; 24; 25], a normal level for adults is between 0.4 and 4.0 milliunits per liter (mU/L). Normal magnesium level is typically between 1.5 and 2.4 mg/dL. Neural networks are algorithms that take an input (x) and compute an output (y). For calculation, the 13 features mentioned above are taken. The output is often represented as a set of probabilities, where each probability corresponds to a different class or category; in our case, y has two classes: 0--healthy person or 1--overweigh/health problem. Mathematically [27], a neural network defines a function represented by the weights (w) of its neurons  
\[y=f_{w}(x) \tag{1}\]  
Calculation of the function goes through a sequence of several stages, with each stage performing elementary calculations such as additions, multiplications, and applying activation functions. These calculations are performed based on the weights of the neurons. Before using a neural network, the weights of the neurons need to be adjusted or \"trained\" so that the network can perform well on the given task. During the training procedure of a neural network, the goal is to adjust the weights (w) in such a way that the network, denoted as \(f_{w}\), accurately predicts the associated output y for each input x. In other words, we aim to achieve \(\overline{y}\approx f_{w}(x)\) after training. One common approach is to minimize the sum E(w) of squared errors, mathematically represented as  
\[minE_{(w)}=\sum_{(x,y)}\left(f_{w}(x)-\overline{y}\right)^{2} \tag{2}\]  
This formulation represents an optimization problem, where it is required to find a set of parameters (weights) that optimize a specific quantity of interest. However, this is a challenging problem due to the large number of parameters involved, especially in the hidden layers, which have a complex influence on the network's performance.