# Application of Artificial Neural Network to Somatotype Determination
## 3 Results
After taking into account the results of sensitivity analysis of ANNs (reducing the number of input data) and applying linear activation functions in the output layer, the following straight neural networks were obtained for somatotype determination (Figure 1). Comparing the obtained ANN: MLP 4-4-1 for Endo and Meso with MLP 6-5-1, it can be seen those correlation coefficients are slightly worse (R of 0.87 and 0.83 for Endo and Meso, respectively). The correlation coefficient for MLP 2-4-3 is also not much worse than for MLP 6-5-3 and it is 0.88. The Endo somatotype can be calculated from the ANN (MLP 4-4-1):  
\[\text{Endo}=\frac{5\bigg{(}\bigg{(}\sum\limits_{i=1}^{4}W_{i}F_{i}+W_{b} \bigg{)}+1\bigg{)}}{2}+2, \tag{6}\]  
where \(F_{(i=1,2,3,4)}\) can be calculated using:  
\[F_{\text{i}}=\frac{2}{1+\exp^{-(D_{1i^{\prime}}(\frac{\text{BMI}-16.4}{3.7}-1) +D_{2i^{\prime}}(\frac{\text{Rose}-30.1}{37.7}-1)+D_{3i^{\prime}}(\frac{\text {Rose}-194}{34.33}-1)+D_{4i^{\prime}}(\frac{\text{Rose}-194}{17.3}-1)+D_{5i^{ \prime}}})}-1, \tag{7}\]  
and weights (\(D_{1i^{\prime}}-D_{4i}\) and \(W_{i}\)) and biases (\(D_{5i}\) and \(W_{b}\)) are in Table 3.  
Figure 1: Three layer neural networks: (**a**) MLP 4-4-1 for Endo somatotype, (**b**) MLP 4-4-1 for Meso somatotype and (**c**) MLP 2-4-3 for Endo, Ecto and Meso somatotypes; transfer functions: hidden and output layers: tangent sigmoid and linear, respectively. The Meso somatotype can be calculated from the ANN (MLP 4-4-1):  
\[\text{Meso}=\frac{5\bigg{(}\bigg{(}\sum\limits_{i=1}^{4}W_{i}F_{i}+W_{b}\bigg{)}+ 1\bigg{)}}{2}+1 \tag{8}\]  
where \(F_{(i=1,2,3,4)}\) can be calculated using:  
\[F_{i}=\frac{2}{1+\exp^{-(D_{ii}\cdot(\frac{\text{BM}-16A}{3}-1)+D_{2i}\cdot( \frac{\text{EM}-92.33}{16.760}-1)+D_{3i}\cdot(\frac{\text{Reg}-194}{34.32}-1)+D _{4i}\cdot(\frac{\text{IBW}-4.15}{14.750}-1)+D_{5i})}}-1 \tag{9}\]  
The Endo, Eto and Meso somatotypes can be calculated from the ANN (MLP 2-4-3):  
\[\text{Endo}=\frac{5\bigg{(}\bigg{(}\sum\limits_{i=1}^{4}W_{\text{Endo}\ i}F_{ \text{Endo}\ i}+W_{b\ \text{Endo}}\bigg{)}+1\bigg{)}}{2}+2 \tag{10}\]  
\[\text{Eto}=\frac{5\bigg{(}\bigg{(}\sum\limits_{i=1}^{4}W_{\text{Eto}\ i}F_{ \text{Eto}\ i}+W_{b\ \text{Eto}}\bigg{)}+1\bigg{)}}{2}+1 \tag{11}\]  
Table 2.0  
where \(F_{\text{Endo}\ i}\), \(F_{\text{Endo}\ i}\) and \(F_{\text{Endo}\ i}\) can be calculated according to:  
Table 2.1  
weights (\(D_{1i}\), \(D_{2i}\) and \(W_{i}\)) and biases (\(D_{3i}\), \(W_{b}\)) of the ANN are in Table 2.2  
The results of statistical analysis (Table 2) shown that calculation of somatotypes from simpler ANNs: Endo--using MLP 4-4-1 (RMSE = 0.66, greater by 0.21 than for MLP 6-5-1) and Meso--using MLP 4-4-1 (RMSE = 0.76, by 0.15 more than for MLP 6-5-1) is possible. However, considering the fact that the values of all somatotypes are usually needed at the same time, the proposed ANN (MLP 2-4-3) is the easiest to use. Although R is 0.88, comparing its statistics for each of somatotypes with the other proposed, more complex ANNs, the Endo somatotype is calculated more accurately (RMSE = 0.61) than with MLP 4-4-1 (RMSE smaller by 0.05) and not much worse than with MLP 6-4-3 (RMSE greater by