## 4 Results and Discussion
### Evaluation of All Investigated Dimensionality Reduction Methods for Clustering Based on MoD Data  
The next step is to evaluate the accuracy of all investigated commonly used AE and VAE frameworks for dimensionality reduction of high-dimension MoD data samples. Thus, each high-dimensional MoD data sample is reduced at a single point in 2-dimensional space. The samples with highly correlated features defined by shared patterns are positioned closely to each other in the same 2-dimensional space. Thus, all investigated methods for dimensionality reduction on the larger dataset of samples can be considered as clustering methods for which purpose they are mainly used [24]. The selected representative hourly subclusters of MoD-based samples are used for deeper insight into their distribution, respecting corresponding larger morning, afternoon and evening clusters within which they can be grouped. The clustering (or super-clustering) based on hourly subclustering is conducted since it is imperative to observe whether all investigated methods can group selected hourly subclusters into the corresponding larger morning, afternoon and evening clusters. Moreover, such clustering analysis needs to be conducted for each weekday. This is needed to analyse cluster structure and distribution over weekdays. It is noticed that cluster structure and distribution in 2-dimensional space over weekdays are similar. Thus, it is possible to conduct the generalization of MoD demand patterns with the VAE framework at the scale of one characteristic day. Additionally, the comparative aspect of this analysis should provide insights which confirm that the accuracy of latent space clustering conducted by AE and VAE approaches is comparable with the commonly used clustering methods such as t-distributed Stochastic Neighbour Embedding (t-SNE), truncated Singular Value Decomposition (tSVD), and Principal Component Analysis (PCA). These clustering methods are chosen since they are the most prominent representatives of two groups of approaches for dimensionality reduction. The t-SNE represents the group which preserves only local similarities between clusters, while PCA preserves large pairwise distances of the global data structure of by maintaining the overall variance and relationships between data points. Since the t-SNE is better in clustering data with complex, non-linear structures, such as OD matrices based on MoD records it produce overall better results. The tSVD is chosen because it preserves the variance in the dataset, while the t-SNE preserves the relationships between data points in a lower-dimensional space. Thus, the tSVD is chosen as a representative of the methods which perform better in sparse datasets. Those methods conduct dimensionality reduction of high-dimensional non-labelled samples into lower dimensional space based on a non-parametric unsupervised approach. Usually, the 2-dimensional space is used for projection of dimensionality reduction due to more convenient visualisation. The t-SNE calculates the pairwise conditional probability for each point in a non-linear fashion. It converts similarities between data points to joint probabilities and minimises the KB divergence between the joint probabilities. Furthermore, the tSVD and PCA are linearly oriented approaches. They compute eigenvectors and eigenvalues of the covariance matrix. The tSVD does not centre the data before computing the truncated Singular Value Decomposition. Thus, this method can efficiently use sparse \begin{table}
\begin{tabular}{l l l l} \hline  & **RMSE** & **MAE** & **MAPE** \\ \hline FC AE & 0.00138 & 0.0208 & 27.200 \\ \hline Conv2D AE & 0.00134 & 0.0203 & 26.283 \\ \hline \end{tabular}
\end{table} 
Table 2: Evaluation results of both investigated AE architectures. matrices compared to PCA which needs to conduct _prior_ data centring. It is possible to conclude that all investigated commonly used dimensionality reduction approaches used different models for the same goal. Thus, this introduces additional robustness to the analysis.