## 3 Methodology
### Use Case and Data Preparation  
The use case for MoD service analysis is conducted by the _NYC Yellow Cab Taxi_ company in the _Manhattan_ district of New York City. It is chosen since it is commonly used in taxi service studies which requires extensive data analysis. Currently, for _NYC Yellow Cab Taxi_ services it is possible to nail a taxi ride by using a mobile application. Thus, the mentioned datasets can be used for MoD demand analysis. The aforementioned taxi-based  
Figure 1: The concept of using synthetic samples computed by the VAEs framework for augmenting learning datasets generated by MoD mobility patterns.  
company provides an open data platform where it is possible to download datasets of taxi-demand tracking over numerous years. This study uses a dataset for the year 2018 as most used in other comparable studies. A detailed explanation of this dataset with statistical descriptive analysis can be found in study [20].  
This _Manhattan_ district is segmented into 54 zones which denotes the origins and destinations. Those zones can represent the possible _pick-up_ and _drop-off_ locations of passengers (or end-users of MoD taxi service). The transitions of passengers between them represent mobility patterns. Each transition between zones represents one entry in the dataset. This study aggregated these samples in 10 min intervals for easier further processing. Thus, there are 52.560 aggregate samples in the investigated dataset for an entire year. The mobility patterns of taxi-based MoD services can be presented as the OD matrices where origins are _pick-up_ zones and destinations are _drop-off_ zones. They can be formatted as 2-dimensional image-alike or 1-dimensional vectorised inputs. In an image-alike structure, rows represent _pick-up_ zones while columns _drop-off_ zones. Furthermore, the image-alike inputs can be converted into vectorised inputs by stacking their rows beside each other in a 1-dimensional structure. All image-alike inputs are normalised to achieve feature transformation on a similar scale. This approach improves the learning performance and stability [21].  
The two mornings (Hour-8 AM and Hour-9 from 8 to 10 AM) hourly intervals, four afternoons (Hour-14, Hour-15, Hour-16 and Hour-17 from 2 to 6 AM) hourly intervals, and finally evening (Hour-21 and Hour-22, from 9 to 11 PM) hourly intervals are taken into consideration. Those hours of the day are considered since they represent subclusters of three larger clusters. They corresponds to daily intervals with distinctive mobility demand characteristics such as morning, afternoon and evening clusters. The clustering approach is used to evaluate the efficiency of dimensionality reduction induced by the proposed approaches. Thus, the first analytic approach in this direction is to assess the possibility of grouping subclusters into corresponding clusters.  
The analysis of average values for each hour-based subcluster for the entire year formatted in an image-alike structure is shown in Figure 2. It proves that the three mentioned clusters are distinctive from each other since their subclusters exhibit similar features. Those features can be observed concerning the ratio between maximal values of _pick-up_ zones and _drop-off_ zones, highest average and maximal maximums of values. The subclusters related to the morning cluster show the highest differences between maximal values of _pick-up_ zones and _drop-off_ zones. Furthermore, the afternoon-related subclusters show the highest averages and maximal values of analysed values with low differences between maximal values of _pick-up_ zones and _drop-off_ zones. Finally, the evening-related subclusters display a tendency for uniform values for all zones and moderate differences between maximal values of _pick-up_ zones and _drop-off_ zones. Thus, this simple descriptive statistical analysis based on average values of hour-based subclusters shows enough distinctive features between them. Those features can be used for grouping them into those three mentioned clusters.