## 3 Results
### Results of the Preliminary Data Analysis
#### 3.2.2 Neural Network Architecture Selection  
Using algorithm [47] (p. 402), we can predefine the neurons number of the desired neural network based on the decisions' root (see, Figure 6). The first hidden layer has 12 neurons, because four input variables are indicated on Set 3 by encoded discrete values {1; 2; 3}. For both convolution matrices from the bottom level of the decisions' roots, there are nine neurons on the second hidden layer, because matrices have nine elements. Matrix M\({}^{\text{L}}\) has four values, M\({}^{\text{R}}\) has three values, so the third hidden layer has seven neurons. The fourth hidden layer has 12 neurons because root matrix M\({}^{\text{L}}\) has 12 elements. The fifth hidden layer has two neurons because root matrix M\({}^{\text{S}}\) has values from set {CON; AD}. Thus, we have obtained a neural network with five hidden layers and 56 neurons on all layers (including one input and one output layer). The neural network architecture is shown in Figure 7, and the parameters of this network are presented in Table 5.  
Figure 6: Decision’s root for diagnosing [PERSON]’s disease. The values in the left matrix at the lower level are the average numbers of the rows of the root matrix, the values in the right matrix are the numbers of the columns of the root matrix, respectively. Figure 7: Neurons of artificial neural network (where: vector of neurons on the Input Layer \(\in\) R\({}^{\text{L}}\), vector of neurons on the Hidden Layer (1) \(\in\) R\({}^{\text{12}}\), vector of neurons on the Hidden Layer (2) \(\in\) R\({}^{\text{18}}\),  
vector of neurons on the Hidden Layer (3) \(\in\mathbb{R}^{7}\), vector of neurons on the Hidden Layer (4) \(\in\mathbb{R}^{12}\), vector of neurons on the Hidden Layer (5) \(\in\mathbb{R}^{2}\), vector of neurons on the Output Layer \(\in\mathbb{R}^{1}\)). The synaptic connections (Figure 8) are determined in full accordance with the elements of convolutional matrices in the decisions' roots (see, Figure 6). The total number of unknown parameters (synaptic coefficients) of the incompletely connected neural network predefined, based on the decision's root is 158. The structure of the predefined neural network model had 12 connections between the input signals and the first hidden layer (each connection generates two parameters of the mathematical model, which means that we have 24 parameters in total). The next layer, in which the neurons correspond to the elements of the matrix, has three parameters each (two inputs from the previous layer and one unknown constant). Since we have two matrices of nine elements each at the bottom level of the criteria tree, this generates 18 neurons on the second layer, which means a total of 54 unknown parameters. The next layer consists of the neurons corresponding to the matrix estimates, and there are exactly as many connections as there were neurons on the previous layer, i.e., in our case, 18, but we need to add seven parameters to them (determined by the number of neurons on the 3 rd layer), which also means we have eighteen and seven parameters (25 parameters on the third layer). Then, there is a matrix containing 12 elements, where each element corresponds to three parameters (two inputs and one unknown constant). It means 36 parameters on the 4 th layer. Figure 8: Incompletely connected artificial neural network identified based on the decision root. Numbers from 1 to 5 designations of serial numbers of hidden layers of the neural network.