# Application of Artificial Neural Network to Somatotype Determination
## 2 Materials and Methods
### Somatotypes Modelling--Artificial Neural Network (ANN)  
ANN modelling was carried out with Matlab R2018a. The somatotypes Endo, Meso and Eto were predicted with feedforward multilayer perceptron ANN. In this study, 173 cases were randomly divided into the following sets: for training 121 sample (70% cases), for validation 26 samples (15% cases) and for testing 26 samples (15% cases) [42; 43]. Data were normalized using a function (mapminmax):  
\[y=\frac{(y_{\text{max}}-y_{\text{min}})(x-x_{\text{min}})}{(x_{\text{max}}-x_{ \text{min}})}+y_{\text{min}} \tag{5}\]  
where \(x\) is the value before normalized (range \(x_{\text{min}}\) and \(x_{\text{max}}\) in Table 1) and \(y\) is the value after normalized.  
The Levenberg-Marquardt training function was used in study. Detailed information on the selection of the ANN architecture and the ANN learning process can be found in [42; 44].  
The goodness of fit of the tested ANNs to the experimental data was evaluated with the correlation coefficient (R), the reduced chi-square (\(\chi^{2}\)), and the root mean square error (RMSE) [45; 46]. The higher the R-value, and lower the RMSE and \(\chi^{2}\) values confirm better goodness of fit.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Unit**} & \multicolumn{3}{c}{**Statistical Parameters**} \\ \cline{3-4}  & & **Mean \(\pm\) SD (Range)** & **Coefficient of** & **Skewness Coefficient** \\ \hline Age & year & 22.9 \(\pm\) 1.70 (19–29) & 0.07 & 0.45 \\  & \multicolumn{3}{c}{Anthropometric measurement} \\ Body weight & kg & 59.57 \(\pm\) 7.80 (40–78) & 0.13 & 0.09 \\ Body height & cm & 166.97 \(\pm\) 5.91 (151–179) & 0.04 & \(-\)0.59 \\ Triceps skinfeld & mm & 13.09 \(\pm\) 4.82 (6–28) & 0.37 & 0.96 \\ Subscapular skinfold & mm & 11.80 \(\pm\) 4.77 (5–29) & 0.40 & 1.59 \\ Supraspanale skinfold & mm & 10.64 \(\pm\) 4.62 (4.5–23) & 0.43 & 0.91 \\ Medial calf skinfold & mm & 11.87 \(\pm\) 6.14 (1–35.5) & 0.52 & 1.11 \\ Biepicondylar breadth of the humerus & cm & 6.19 \(\pm\) 0.39 (5.5–7) & 0.06 & 1.08 \\ Biepicondylar breadth of the femur & cm & 7.64 \(\pm\) 0.99 (4–9) & 0.13 & \(-\)0.81 \\ Upper arm girth & cm & 26.39 \(\pm\) 2.56 (20–33) & 0.10 & 0.10 \\ Calf girth & cm & 35.91 \(\pm\) 2.67 (30–41) & 0.07 & 0.19 \\ \multicolumn{3}{c}{Body composition (BIA)} \\ FFM & \% & 74.12 \(\pm\) 7.10 (57.5–91) & 0.10 & \(-\)0.36 \\ FM & \% & 25.88 \(\pm\) 7.10 (8.9–42.5) & 0.28 & 0.36 \\ TBW & \% & 53.01 \(\pm\) 5.17 (43–73) & 0.10 & 1.11 \\ Reac & \(\Omega\) & 157.56 \(\pm\) 43.93 (86–282) & 0.28 & 0.88 \\ Res & \(\Omega\) & 620.64 \(\pm\) 116.45 & 0.19 & \(-\)1.47 \\  & & (194–881) & 0.04 & \(-\)0.16 \\ RMR & kcal & 1546.64 \(\pm\) 61.35 & 0.04 & \(-\)0.16 \\  & & (1373–1719) & & \\  & & Indices in used formulas & & \\ BMI & kg/m\({}^{2}\) & 21.32 \(\pm\) 2.70 (16–28) & 0.13 & 0.45 \\ FMi & kg/m\({}^{2}\) & 9.33 \(\pm\) 2.73 (3.5–16.0) & 0.30 & 0.47 \\ FFMi & \(\text{=}\) FFM/H\({}^{2}\) & kg/m\({}^{2}\) & 16.77 \(\pm\) 2.26 & 0.14 & 1.72 \\  & & (14.17–25.0) & 0.14 & 1.72 \\ \hline \hline \end{tabular} BIA—Bioelectrical Impedance Analysis, BMI—Body Mass Index, FFM—Fat Free Mass, FM—Fat Mass, TBW—Total Body Water, Reac—Reacitance, Res—Resistance, RMR-Resting Metabolic Rate, H—Body height, FMi—Fat Mass Index, FFMi—Free Fat Mass Index.  
\end{table}
Table 1: Group characteristic and statistical parameters of the used data.