## 5 Results of QoE\({}_{i}\) Modeling and Discussion
### Predictive Models of \(QoE_{i}\)
#### 5.5.3 Predictive Models Created by Using an Automatic Modeling Method  
Table 4 shows the results of testing the three most accurate predictive models created using the _Auto Numeric_ node [36; 37]. It is concluded that the regression model has the smallest relative testing error, which is 1.070. However, a relative prediction error equal to 1 is a characteristic of the _null_ or _intercept_ model, which as a prediction result returns the arithmetic mean of the target variable. Models with relative testing errors less than 1 are considered better than the null, with the smaller the relative error, the better the model. Thus, the created models with the relative testing errors shown in Table 4 can be considered unsatisfactorily accurate [61]. If the obtained correlation coefficients for the three models from Table 4 are compared with the scale of Pearson's correlation coefficients, shown in Table 5, it is concluded that, in the best case, there is only a low correlation between the estimated \(QoE_{i}\) values and the \(QoE_{i}\) values obtained by prediction, and that is for the model based on the k-NN machine learning technique (r = 0.206). The C&R tree model shows the worst prediction performance in terms of both correlation (0.000) and relative error (1.147) [62]. The presented results of model testing are a direct consequence of the insufficiently large training dataset. Therefore, using the data augmentation method, the basic dataset is augmented with \"synthetic\" data, obtained on the basis of 157 existing vectors [41]. The artificial expansion of the dataset was performed with the autoencoder artificial neural network implemented in the MATLAB programming environment, and its architecture is shown in Figure 7[63]. The autoencoder represents a feedforward neural network that sends signals in only one direction, from the input to the output layer, and thus forms a directed acyclic graph, the aim of which is to learn to compress \begin{table}
\begin{tabular}{c c c} \hline \hline
**Created Model** & **Correlation** & **Relative Error** \\ \hline
1. Regression & 0.127 & 1.070 \\
2. k-nearest neighbors (k-NN) & 0.206 & 1.075 \\
3. C\&R tree & 0.000 & 1.147 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ranking list of the best tested models for \(QoE_{i}\) prediction. Figure 6: The importance of the influence of indicators on the prediction of \(QoE_{i}\): (**a**) all indicators; (**b**) satisfaction indicators; (**c**) indicators of dissatisfaction (adapted with permission from Ref. [15]. 2023, International Journal for Quality Research ). \begin{table}
\begin{tabular}{c c} \hline \hline
**Absolute Value of the Correlation Coefficient** & **Qualitative Assessment** \\ \hline
0.00 \(<\)\(|r|\)\(\leq\) 0.19 & Very low correlation \\
0.20 \(\leq\)\(|r|\)\(\leq\) 0.39 & Low correlation \\
0.40 \(\leq\)\(|r|\)\(\leq\) 0.59 & Moderate correlation \\
0.60 \(\leq\)\(|r|\)\(\leq\) 0.79 & High correlation \\
0.80 \(\leq\)\(|r|\)\(\leq\) 1.00 & Very high correlation \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The usual five-point scale of [PERSON]’s correlation coefficients. autoencoder represents data on the input side of the network using fewer nodes in the hidden layer. Based on this performance, its task is to perform a complete reconstruction of the input. Therefore, the hidden layer can be considered as a features detector. The architecture of the autoencoder, shown in Figure 7, consists of an input layer with 11 nodes (ten independent variables X\({}_{1}\)...X\({}_{10}\) and one dependent variable \(QoE_{i}\)), 5 nodes in the hidden layer and 11 nodes in the output layer in which the input vectors (X\({}_{1}\)'...X\({}_{10}\)', \(QoE_{i}\)') are reconstructed. The transfer functions of the neurons of the hidden and output layer have the form of a logistic sigmoid function (logsig):  
\[f(z)=\frac{1}{1+e^{-z}} \tag{7}\]  
where \(z\) is the input to the neuron.