## 4 Results and Discussion
### Evaluation of All Investigated Dimensionality Reduction Methods for Clustering Based on MoD Data
The 2-dimensional visualisation of synthetic samples generated by the proposed Conv2D VAE framework for each of the morning, afternoon, and evening clustered by commonly used dimensionality reduction methods with datasets generated by real-world MoD data is presented in Figure 6.  
It is possible to conclude that the spatial distribution of morning, afternoon, and evening subclusters remained the same with imposed synthetic samples. This means that all investigated dimensionality reduction methods can correctly localize (cluster) synthetic samples without deformation in the distribution of morning, afternoon, and evening subclusters. Thus, the Conv2D VAE framework has successfully extracted the features of subclusters for the corresponding morning, afternoon, and evening clusters. Moreover, the probabilistic sampling within the VAE framework did not cause drastic changes in synthetic samples to such an extent that they are located in totally non-related clusters (e.g., morning synthetic samples localised in evening-related hourly subclusters, etc.). However, it is possible to conclude that several samples are localised in \"border regions\" between two close subclusters respecting their temporal context. The most prominent example is when some morning synthetic samples are localised in subcluster \"Hour-14\" which is closest (in temporal context) to the subcluster \"Hour-9\" as the representative of the correct morning cluster. This behaviour can be explained by probabilistic sampling embedded into the VAE framework for generating new samples. Figure 5: Average values of _Silhouette, Calinski–Harabasz_, and _Davies–Bouldin_ metrics for interpretation and validation of consistency within data clusters computed for all investigated dimensionality reduction methods. The analysis is performed based on aggregated data for all days during the week. Evaluation of Learning Performance Using a Combined Dataset with Synthetic and Real-World MoD-Based Data Samples  
The final analysis investigates the performance of two different architectural types of ANN models in learning performance. They are designed as classification models based on a supervised learning approach. Thus, all used samples in the training dataset are categorised using labels. Those labels correspond to three previously analysed clusters: morning, afternoon and evening. Thus, the samples are labelled with three possible classes using _one-hot_ encoding. Firstly, it is necessary to test the simple architecture of the shallow feedforward ANN model based on FC layers. Additionally, this architecture is interesting since it requires vectorised inputs. Each element of this vectorised input is considered an individual feature. It is possible to see the architectural structure of the used shallow ANN model in Table 4. The second ANN model is based on convolution layers which extract features from image-alike or matrix-wise inputs. Furthermore, extracted feature maps are flattened to form a vectorised format and passed to a shallow feedforward ANN model based on FC layers. This is a more comprehensive ANN model since it can detect and extract more complex spatial features for cluster classification. The 2-dimensional convolution ANN model structure for cluster classification based on MoD data can be seen in Table 5.  
Figure 6: The 2-dimensional visualisation of synthetic samples generated by the proposed Conv2D VAE framework for each of the morning, afternoon, and evening clusters. They are combined with the real-world MoD-based datasets. Three commonly used dimensionality reduction methods have clustered synthetic samples into real-world MoD-based data subclusters which correspond to clusters for which they are generated. Furthermore, the learning is performed by using different configurations of training datasets. The initial training dataset contains only real-world data generated by the MoD service. It has 12,600 training samples.