## 4 Results and Discussion
### Evaluation of All Investigated Dimensionality Reduction Methods for Clustering Based on MoD Data
The outlier samples in this case have a low probability of being taken into account for fitting through the learning process. Thus, their impact on non-linear function approximation for spatial features of a particular cluster is minimized. This improves the generalization of spatial features for a particular cluster without causing _overfitting_. Furthermore, the slower learning convergence at the start of the process for morning and afternoon clusters is due to their lower number of hourly subclusters. This reduces the total number of learning samples  
Figure 8: Convergence of learning error in the case of the model based on 2D-dimensional convolution layers. The initial training dataset is generated by real-world MoD data. The augmented training datasets represent combined initial datasets with different percentages of samples from three clusters (morning, afternoon, and evening) generated by the proposed Conv2D VAEs framework. for those clusters. Consequently, based on less accurately learned spatial features of those clusters, this induces artefacts in generated synthetic samples for them. Those spatial artefacts can reduce the speed of learning convergence at the start of the process. It is possible to conclude that even with the presence of artefacts in synthetic samples the learning convergence is stabilised quickly and produces learning errors similar to the initial training dataset. Thus, synthetic samples can be fitted into the overall non-linear function without causing _overfitting_. The comparison of average values for all image-alike real-world samples in each of the three investigated clusters compared to the average values of all synthetic samples generated for those clusters can be seen in Figure 9.  
It is possible to conclude that the scale of average values in synthetic samples is in line with the averages of the real-world samples except for the evening cluster. This has been the case since evening synthetic samples are affected by more artefacts than the other clusters. Additionally, one can notice that the decoder of the proposed VAE  
Figure 9: The first column of graphs represents the average values for all image-alike real-world samples in each of the three investigated clusters while the second row represents the average values of all synthetic samples generated for those three clusters. framework has successfully captured the key features of all investigated clusters. The second analysis evaluates the classification performance of both investigated ANN models. They are trained based on different configurations of training datasets used in previous analyses. All trained models are evaluated using the same validation datasets generated by real-world MoD-based data. This provides an analytical setup which assesses the impact of various percentages of synthetic samples in training datasets on MoD-based classification performance based on real-world validation dataset. The two groups of metrics are used to achieve a deeper analysis of classification performance. Thus, the first group involves RMSE and MAE as the commonly used regression metrics. They are used since they directly evaluate the accuracy of trained models by computing prediction errors. This group of metrics enable classification tasks described as regression problems where three discredited values are possible (morning, afternoon and evening cluster). The second group includes metrics such as Recall, Precision and F1 Score. Furthermore, the Precision is computed using Equation (5):  
\[Precision=\frac{TP}{TP+FP}, \tag{5}\]  
where _TP_ denotes true positive predictions. They represent the number of samples in the training dataset correctly predicted for morning, afternoon, and evening clusters. The _FP_ denotes false positives as the number of samples positively categorised for a particular cluster while they do not belong to this cluster. The Recall is computed using Equation (6):  
\[Recall=\frac{TP}{TP+FN}, \tag{6}\]  
where _FN_ denotes false negative predictions.