## 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
By bringing 157 available vectors to the input layer of the network, the same number of modified copies is obtained at the output as the interpretation of the input. Therefore, with one described iteration, the input dataset is doubled. In each subsequent iteration, the sum of the input number of vectors and the corresponding number of reconstructed vectors from the previous iteration is added to the input layer of the autoencoder network, which is shown graphically in Figure 8.  
Figure 8: Four iterations of dataset augmentation using the autoencoder network. Figure 7: Architecture of the used autoencoder neural network. Figure 8 shows that in the fourth iteration, the total number of vectors increased to 2512. After each iteration, training and testing of several models was performed, and the prediction results for each of the three most accurate predictive models are shown in the diagram in Figure 9.  
From Figure 9, it can be concluded that the value of the relative prediction error decreases with the expansion of the training and testing dataset, while at the same time the correlation coefficients increase, which is the case for all created models. The predictive model that shows the best performance of all presented is the model based on C&R trees. According to Figure 9, the RE prediction of this model is 0.274, while the correlation coefficient is equal to 0.853 in the fourth iteration. If the scale of Pearson's coefficients shown in Table 5 is taken into account, it can be concluded that the \(QoE_{i}\) values from the set for testing the model and the values obtained as a result of prediction have a very high level of correlation. In total, 2512 input-output vectors were used for training and testing the tree model, out of which 2260 were used for training and 252 for testing. The trend of decreasing relative error of all the models shown in Figure 9 can be represented by the following linear equation:  
\[RE=-0.042\cdot m+0.788 \tag{8}\]  
where \(m\) represents the serial number of the model starting from the generalized linear model from the first iteration, which has serial number 1. Figure 10 shows the layered structure of the created tree with a depth equal to five (tree depth = 5). Figure 9: Results of testing predictive models of \(QoE_{i}\) in four iterations of increasing the dataset using the DA method. The C&R tree algorithm starts by examining the input nodes to find the best split, which is defined by the minimum _impurity index_ as the result of the split. The _Gini index_ is most often used to define impurity, which is related to the probability of random sample misclassification. In the IBM SPSS Modeler software, a minimum impurity change of \(10^{-4}\) is defined by default to create a new split in the tree. All divisions are binary, which means that each division generates two subgroups, each of which is then divided into another two and so on until one of the stopping criteria is reached. The following were set as stopping criteria in the created C&R tree model:  
* _Minimum records in parent branch_--prevents splitting if the number of records in a node to be split (parent) is less than the set value--2% of the total dataset. * _Minimum records in child branch_--prevents the split if the number of records in any branch created by the split (child node) would be less than the set value--1% of the total dataset. In order to further improve the accuracy of the C&R tree model in the IBM SPSS Modeler software, the _boosting_ method was applied. This method is based on creating several models (components) in sequence, i.e., creating _ensemble models_. Increasing prediction accuracy is achieved by creating each subsequent model in the ensemble in such a way that it focuses on inputs for which the previous model made poor predictions. Finally, prediction is made by applying a whole series of models, using a _weighted voting_ procedure. In this way, separate predictions are combined into one resultant.