## 4 Results and Discussion
### Evaluation of All Investigated Dimensionality Reduction Methods for Clustering Based on MoD Data
Their mutual goal is to find patterns in the dataset and use individual sample clustering represented as single points in 2-dimensional space. Thus, their clustering results provide a reference frame for accuracy in dimensionality reduction based on MoD data samples. The number of components to keep in clustering for all investigated commonly used dimensionality reduction methods is set to eight. This number corresponds to the total number of hourly subclusters. Furthermore, the AE and VAE frameworks based on non-supervised learning have the same goals as the commonly used dimensionality reduction methods. The only difference is that the 2-dimensional space represents the corresponding 2-dimensional latent space learned by their encoders. Thus, the spatial relationships between subclusters distributed in corresponding clusters conducted by VAE and AE frameworks must be comparable with clustering results derived by commonly used methods for dimensionality reduction. Adequate results in dimensionality reduction by AE and VAE framework provide a basis for the generation of synthetic samples based on MoD data using the VAE framework. The graphical representation of hourly subclusters respecting their spatial positioning conducted by all analysed approaches can be seen in Figure 4.  
It is possible to conclude that all investigated dimensionality reduction methods accurately group hourly subclusters into the corresponding morning, afternoon, and evening clusters. The individual weekday analysis shows consistency in clustering afternoon and evening hours subclusters. However, AE and VAE frameworks disperse morning subclusters into two subgroups. One smaller and one larger. This behaviour is present on all weekdays but is more prominent during weekends. The further analysis includes _Silhouette, Calinski-Harabasz_, and _Davies-Bouldin_ evaluation metrics for interpretation and validation of consistency within data clusters. All investigated clustering metrics are based on the computation of similarities between objects (points) compared to their cluster (cohesion evaluation), and compare them to other clusters (separation evaluation). Thus, the _Silhouette_ metrics evaluate the optimal number of clusters by computing the difference between the average distance within the points in the cluster and the minimum distance between the clusters. The _Calinski-Harabasz_ is an evaluation index representing the sum of the dispersion from cluster to cluster to the inter-cluster dispersion for all clusters [25]. Thus, large values of this metric indicate low variability within clusters and large variability between clusters. Finally, the _Davies-Bouldin_ metric is computed as the average similarity between each cluster with its most similar cluster. The similarity is computed as the ratio concerning within-cluster distances to between-cluster distances [26]. Thus, the clusters which are farther apart and less dispersed result in a better score for this metric. In Table 3, it is possible to see the results of all used evaluation metrics for validation of consistency within data clusters for all investigated methods during all weekdays. The results have shown that all investigated approaches show lower values of the aforementioned metrics for Monday and the weekend. Such results are expected. The proposed VAE framework produces the most consistent results during all days of the week with few outliers during some days in weekends (e.g., low _Silhouette_ values during Sunday, or increased value of _Davies-Bouldin_ during Saturday). The reason is the sampling nature of VAE frameworks where randomness is added during the learning process. Additionally, the obtained results suggest that it is possible to aggregate all days during the week for morning, afternoon, and evening clusters to simplify further analysis. It is also possible to conclude that data points for all days during the week do not significantly disrupt the spatial distribution of clusters achieved through dimensionality reduction conducted by investigated VAE frameworks.