## 3 Methodology  
The main goal of this study is to evaluate the proposed VAE framework for improving learning convergence by augmenting learning datasets with synthetically generated samples. Thus, the first stage of the applied methodology is the evaluation of the proposed AE-based frameworks concerning dimensionality reduction. The 2-dimensional latent space is used for all investigated AE-based frameworks to evaluate their dimensionality reduction capabilities through data clustering efficiency. In the case of MoD trip records, those clusters are spatially defined by time intervals during one day which serves as the expected classes of each sample (e.g., morning, afternoon and evening clusters). Additionally, 2-dimensional space enables a graphical representation of clusters in a _Cartesian_ coordinate system. This stage is mandatory since it is necessary to confirm that the proposed AE-based frameworks can achieve data clustering efficiency comparable with commonly used dimensionality reduction methods. Thus, the 2-dimensional latent space must accurately represent encoded patterns and data relations from original inputs.  
The next step is generating new samples which reassemble patterns with ones provided by MoD services. Furthermore, the main goal of standard AEs is compressing the input data into the latent space using the encoder part. Its decoder counterpart reconstructs the same input entry from encoded latent space. A regularized field of discrete values represents the latent space in a standard AE framework. This eliminates the possibility of using them in generating new samples for learning datasets. The standard AE framework can be extended by replacing the regularised field with a probabilistic one. It models the input data as a probability distribution and learns the parameters of this distribution [19]. This approach extends the standard AE frameworks with variational capabilities of originally encoded inputs. Thus, the VAE framework can generate new samples that resemble the key features of the original input data but also contain the learned probabilistic differences.  
The synthetic samples for specific data clusters are achieved by changing the variables of 2-dimensional latent space for inputs of the VAEs decoder. The next step is to generate synthetic samples by the proposed VAE framework for each of the aforementioned clusters. Those synthetic datasets for each cluster are generated by the proposed VAEs framework and imposed in existing (\"real-world\") datasets. Furthermore, this combined dataset is clustered with the most successful standard method for that purpose. Thus, it is possible to compare the positional definition of synthetic data samples concerning the cluster for which they are generated and compare them with positional areas of \"real-world\" data samples of particular clusters. This analysis compares the synthetic data samples with their \"real-world\" counterparts based on which they are generated.  
The final step is to generate several different learning datasets based on combined real and synthetic samples. Those datasets differ compared to each other regarding the ratio between synthetic and real-world MoD-based data samples. Additionally, their differentiation is defined by the distribution of synthetic samples regarding the morning, afternoon and evening clusters. They are used for the classification of clusters. The classification task is conducted using shallow and convolution ANN models. Thus, the learning convergence of the ANN-based models for each of those combined learning datasets is analysed. The concept of using synthetic samples computed by the VAEs framework for augmenting learning datasets generated by MoD mobility patterns can be seen in Figure 1.