## 4 Results and Discussion
### Evaluation of All Investigated Dimensionality Reduction Methods for Clustering Based on MoD Data
This also can be concluded by comparing the spatial distribution of subclusters and their combined structures for forming morning, afternoon, and evening clusters in Figure 4.  
Furthermore, the average values for all investigated metrics for interpretation and validation of consistency within data clusters computed for all investigated dimensionality reduction approaches are presented in Figure 5. The analysis is conducted based on aggregated data points across all days during the week. It is possible to conclude that all investigated dimensionality reduction approaches can achieve comparable results. Both VAE frameworks produce the most consistent results for all investigated metrics. Those are important findings since they confirm the robust dimensionality reduction accuracy of the chosen Conv2D VAE framework. Moreover, the comparable dimensionality reduction accuracy with other investigated approaches is the basis for the generation of new learning samples with introduced probabilistic sampling conducted by the proposed VAE framework. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & \\ \hline
**Day in Week** & **t-SNE** & **tSVD** & **PCA** & **FC AE** & **Conv2D AE** & **FC VAE** & **Conv2D VAE** \\ \hline Monday & \(-\)0.027 & 0.032 & 0.023 & 0.044 & \(-\)0.073 & 0.013 & 0.037 \\ \hline Tuesday & 0.017 & 0.052 & 0.053 & 0.094 & \(-\)0.044 & 0.051 & 0.059 \\ \hline Wednesday & 0.017 & 0.022 & 0.031 & 0.071 & \(-\)0.046 & 0.041 & 0.053 \\ \hline Thursday & \(-\)0.029 & \(-\)0.022 & \(-\)0.026 & 0.038 & \(-\)0.108 & 0.005 & 0.009 \\ \hline Friday & \(-\)0.029 & 0.022 & \(-\)0.008 & 0.051 & \(-\)0.066 & 0.043 & 0.030 \\ \hline Saturday & \(-\)0.028 & 0.036 & 0.015 & 0.019 & \(-\)0.062 & 0.056 & 0.020 \\ \hline Sunday & \(-\)0.037 & \(-\)0.021 & \(-\)0.049 & \(-\)0.005 & \(-\)0.089 & \(-\)0.005 & \(-\)0.012 \\ \hline  & & & & & & & \\ \hline Monday & 164.311 & 79.789 & 98.919 & 166.538 & 50.631 & 100.631 & 116.385 \\ \hline Tuesday & 227.420 & 126.133 & 154.008 & 226.726 & 135.298 & 169.694 & 189.848 \\ \hline Wednesday & 214.581 & 108.218 & 126.760 & 187.213 & 167.230 & 144.026 & 148.707 \\ \hline Thursday & 175.834 & 89.941 & 97.654 & 157.528 & 103.168 & 116.444 & 105.123 \\ \hline Friday & 196.488 & 107.494 & 120.546 & 168.360 & 122.636 & 135.600 & 167.400 \\ \hline Saturday & 92.709 & 122.497 & 118.645 & 163.305 & 57.210 & 151.381 & 118 Analysis of Clustering Based on a Combined Dataset with Synthetic and Real-World MoD-Based Data Samples  
The next step is to generate synthetic samples for morning, afternoon, and evening clusters. Those synthetic samples are generated using the Conv2D VAE framework. This VAE framework is selected since it achieves improved performance in dimensionality reduction compared to the FC VAE framework. These synthetic samples are combined with a real-world dataset based on MoD samples in a single dataset. The 100 synthetic samples for each of the three clusters are generated at the current stage of this study. The lower number of synthetic samples is chosen for easier graphical visualisation and as a potential proof of dimensionality reduction robustness with synthetic samples. Furthermore, this combined dataset is presented to all investigated and commonly used dimensionality reduction methods. The main goal is to use those methods to correctly assign synthetic samples to correspond to hourly subclusters created using real-world MoD data. They should remain grouped into morning, afternoon, and evening clusters. Essentially, the idea is to try to \"trick\" the commonly used dimensionality reduction methods with _\"deep fakes\"_ which are imposed in real-world datasets based on MoD data.