Towards Synthetic Augmentation of Training Datasets Generated by Mobility-on-Demand Service Using Deep Variational Autoencoders

Abstract

The machine learning-based approaches for analysing the mobility needs of users are currently the most prevalent approach in the mobility-on-demand (MoD) analysis. Their efficiency relies on the comprehensiveness and consistency of training datasets. However, this is also the biggest challenge, as high-quality training data are often difficult to obtain. Thus, the Variational Autoencoders (VAE) are investigated as potential generators of synthetic samples for the augmentation of MoD-based datasets. This MoD-based dataset is created using real-world taxi trip data recorded in the Manhattan district of New York City, USA. This augmentation by synthetic samples can potentially enable larger, balanced, and more consistent datasets for machine learning analysis of MoD-based data. The proposed VAE approaches are compared with common dimensionality reduction techniques and standard autoencoders concerning their efficiency in 2-dimensional clustering based on collected MoD-based data. The proposed 2-dimensional convolution VAE framework has achieved clustering results comparable with the other analysed approaches. Thus, it generates synthetic samples, known as “deepfakes”. They are added in different percentages to the initial dataset based on real-world MoD-based data. Thus, this creates augmented datasets of the initial one. The models for predicting the cluster of each sample are used to evaluate the impact of those augmented datasets on their accuracy and learning convergence compared to the initial dataset. Results have shown that the accuracy and learning convergence are improved if those predictive models are trained on an augmented dataset which includes up to 10% of synthetic samples for each cluster.

1. Introduction

Mobility-on-demand (MoD) is one of the most used approaches for enabling personalised commuting services in dense urban regions. The backbone of this mobility approach is a ride-hailing system enabled by a central call centre that serves as a humanly controlled dispatching service for taxi or privately operated rides. Currently, these dispatching processes are completely or partially automated by various web-oriented platforms easily accessible by end-users which are travellers. Automated dispatching of taxi or private car services through web platforms for end-users reduces the cost of owning and buying a personal vehicle or using overcrowded public transport systems. This can be even more prominent in dense urban regions heavily affected by congestion during peak hours. Simultaneously, it enables a personalised selection of destinations at the desired trip time window which depends upon their current location. This trip time window is in a temporal context defined by the moment of online-based ordering or hailing a taxi service and the end of each trip defined by arriving at the desired destination. Their current location is considered as pick-up place while their destination is denoted by drop-off location. Thus, those services have become very popular, especially in dense urban regions such as New York City. It is found that MoD-oriented companies have increased their ride numbers by over $1000\%$ between 2012 and 2019 [1].

The need to develop more comprehensive data-driven dispatching systems for taxi fleets is caused by increased demand for personalised MoD-based services. More comprehensive dispatching decisions for the MoD enabling services are based on a concept known as Demand Responsive Transit (DRT) [2,3]. This concept is based on proactive-oriented approaches such as travelling demand predictions, optimised routing and accurate traffic anomaly detection (incidents, congestions, etc.) in mobility patterns. Nowadays, numerous studies tackle those problems for different MoD-based services. Most of them are based on various machine learning approaches [4,5,6]. Machine learning is the most used data-driven approach for the non-linear approximation of behavioural patterns in stochastic systems such as traffic systems [7,8]. Thus, sufficiently large, diverse, comprehensive, and consistent training datasets are essential for stable learning convergence with a low probability of early overfitting. The real-life datasets gathered from complex stochastic systems such as demand for MoD-based services can induce difficulties in achieving a satisfied diversity and number of use cases for training datasets. Thus, this paper proposes a framework which creates and introduces synthetic samples to the existing training datasets based on real-world MoD-based data. This should be performed without reducing training dataset consistency. Reduced consistency of training dataset leads to lower accuracy of the models based on which they are trained [9,10].

The MoD-based data are presented as the Origin–Destination (OD) matrices. Thus, the pick-up locations denote origins while destinations of passengers represent their drop-off locations (zones). Autoencoders (AE) in this study are used as the dimensionality reduction method, which encodes each OD-matrix in 2-dimensional latent space. This number of dimensions for latent space representation is chosen for the convenient visualisation of results in a Cartesian coordinated system. Furthermore, the decoder part of the AE framework can be used to reconstruct a multi-dimensional OD matrix from a 2-dimensional latent space. The drawback of classical AE is poor performance in generating OD matrices which are not present in the existing training dataset. Thus, they are not convenient for generating additional samples in the training dataset which differ from existing ones. This drawback is tackled by introducing the Variational Autoencoders (VAE). They use a probabilistic field instead of a regularized one to represent the input data in the latent space [11]. The probabilistic field is described by the statistical distribution of the mean and variance for each input sample instead of points in latent space. Consequentially, this enables the differentiation of newly generated samples by VAE framework compared to existing ones in the training dataset.

The VAE approach has shown promising results in the study [12] for reconstructing missing data in existing samples within the dataset with road traffic demand. This dataset is generated based on the data from the fixed road sensors implemented on a simple road network. Thus, this study using the VAE-based approach only for reconstructing missing data in existing samples within the dataset dedicated to road traffic demand. Thus, they do not create entirely new samples for augmenting the entire training dataset. The proposed study in this paper extends the previously discussed research by augmenting initial training datasets based on real-world MoD-based data with synthetic samples generated by the proposed VAE framework. Furthermore, augmented training datasets with different percentages of synthetic samples are used for training the various architectures of predictive models based on Artificial Neural Networks (ANNs). Those trained predictive models are evaluated concerning their classification accuracy and learning convergence compared to the model which is trained on the initial dataset generated exclusively by real-world MoD-based data. Current studies do not provide such an analytical comparison.

The novel contribution of the proposed VAE approach is in generating new traffic states represented as samples of OD matrices based on learned patterns from real-world data. Additionally, the proposed approach enables to extension initial dataset based on real-world data with any percentage of synthetic samples per each of the three clusters. Thus, it is possible to conduct comprehensive analysis regarding the optimal number of synthetic samples in the initial dataset based on real-world data which improves learning convergence and prediction accuracy. The limitations of the proposed approach are related to the inability to change specific elements or segments of one synthetic sample coded as the OD matrices. Thus, there is no ability to generate specific disturbances in OD matrices to track their effect on training performance. The proposed study uses traditional VAE architectures with embedded attention mechanisms in the encoder model. Furthermore, the domain regarding the latent space of the specific cluster is determined by using a priori dimensionality reduction with an encoder model in trained VAE architecture. The analysis regarding the impact of weekdays and seasonality is not conducted in this study since its primary goal is to provide preliminary investigation of the proposed concept for the specific stochastic dataset such as MoD records. Therefore, the generalizability and robustness of the proposed concept should be verified and investigated by using other use-cases in future research.

The paper is organised as follows. Section 2 offers an overview of previous research concerning the methodologies for synthetic argumentation of training datasets in mobility analysis. The following Section 3 describes the proposed methodologies used in this study. It tackles the techniques used for data preparation, VAE framework design, and approach for generating inputs for the VAE decoder from learned latent space. Section 4 presents the results and findings of the proposed study. This section also provides a comprehensive discussion about possible causes that led to the achieved results. The paper ends with a conclusion in its final section.

2. Related Work

Numerous studies are investigating generative models based on machine learning approaches in improving data analysis generated by MoD services. One of the most used generative models for generating synthetic or augmenting existing MoD-based data samples is based on the VAE framework. The study [13] uses a VAE-based framework to generate trajectories of taxi trips and compare them with the dataset generated by Floating Car Data (FCD). The resulting reconstructed synthetic data are employed to compute the traffic flows and geographic distribution of parked cars. Additionally, this study investigates the impact of synthetic data on learning performance by changing the number of latent space variables. It does not introduce mixed datasets with generated synthetic and real-world data. The more advanced VAE framework for generating OD matrices of crowd flows is investigated in study [14]. It introduces a Variational Multi-modal Recurrent Graph Auto-Encoder (VMR-GAE) which models the uncertainty–awareness for OD matrix interpolation by formulating the problem as semi-supervised learning on directed graphs. The aforementioned study proves that it is possible to generate an OD matrix that models mobility-based traffic flows using the VAE-inspired framework. Furthermore, the additional modification of standard AEs in the form of the Context Augmented Graph Autoencoder (Con-GAE) model is used in study [15]. The proposed model enables leveraging the graph embedding and context embedding techniques to capture the spatial and temporal patterns in sparse and high-dimensional various MoD data and to capture anomalies. Thus, it provides additional proof that it is possible to capture spatiotemporal patterns in MoD flows formatted as the OD matrices.

In the study [16], the VAE is used for data augmentation to reproduce crash data in highly imbalanced datasets. Thus, this approach is used to increase the sample number of crash data compared to non-crash data. This augmentation of the training dataset has improved the separation process between crash and non-crash data.

The Generative Adversarial Networks (GAN) represent another generative framework based on the machine learning approach. The GANs are based on the generator which creates new outputs and the discriminator which asses them. Thus, the aforementioned generative framework is based on a supervised learning approach that uses two loss functions for each of their counterparts. The VAE-based frameworks are based only on one loss function implemented for an unsupervised learning approach. Thus, they are easier to train than GANs. In study [17], the GAN approach predicts mobility demand for taxi-based services. The learning dataset is based on higher resolution since it combines spatiotemporal taxi-GPS data of pick-up and drop-off locations with taximeter records. Thus, the GAN approach provides better accuracy in capturing mobility patterns with high-resolution data when its learning framework is based on a Long-Short Term Memory (LSTM) neural network. A similar GAN-based approach for taxi service prediction is used in study [18], where the previous study is augmented by using multi-source data such as weather forecasting and location point-of-interest.

In summary, the current approaches that are used for the augmentation of datasets based on traffic demand investigate only synthetic data generated by VAE. The second set of studies uses the generative model to detect anomalies in real-world datasets or reconstruct missing elements of existing samples based on traffic demand. The study which is not related to the domain of traffic demand investigates the improvement of crash prediction by using the combination of synthetic and real-world samples in the highly imbalanced dataset. Thus, it only adds the synthetic samples to the category with fewer samples. The proposed research uses a similar approach to a balanced dataset based on traffic demand with different percentages of synthetic samples in each category.

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.

3.1. 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 hail a taxi ride by using a mobile application. Thus, the mentioned datasets can be used for MoD demand analysis. The aforementioned taxi-based 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.

3.2. The Proposed VAE Framework

This study introduces two standard architectures for AE frameworks according to the two possible input formats. Thus, the AE architecture based on a fully connected layer is used for vector-alike inputs while 2-dimensional convolution layers are the basis for the used AE architecture which uses image-alike inputs. The mentioned AE frameworks are analysed prior to their modification into the VAE version since evaluating their efficiency in dimensionality reduction is needed. It is needed since the kernel of VAE architecture is based on the standard AE framework [22].

Furthermore, Keras as the high-level API for the TensorFlow, and scikit-learn package within the Python 3.8 environment are used to design and train all investigated models. Furthermore, the Adaptive Moment Estimation (ADAM) learning algorithm is used for training all investigated models. The learning rate is set to $0.001$. This value is chosen since it is recommended for the used learning algorithm [23]. The hyperparameters for all investigated AE-based models can be seen in

Table 1. Hyperparameters for all investigated AE-based models.

Hyperparameter	Batch size	Learning rate	Regularization	Learning algorithm	Epoch	Learning/ Validation dataset split
Value	128	0.001	Batch Normalization	ADAM	50	80:20

.

The architecture of the AE model is based on four fully connected layers for the encoder and decoder part. Those layers are arranged in a symmetrical structure with 64, 32, 32, and 16 nodes, respectively. The ReLU activation function is used for all nodes except for the layers which encode latent space and output of decoder where the sigmoid activation function is used.

The second investigated AE model architecture is based on four 2-dimensional convolution layers. Those layers are arranged in a symmetrical structure. This structure is defined by the distribution of filter numbers for each layer of 2-dimensional convolution layers. Following the distribution of filter numbers 32, 48, 48, and 64 for each of the layers in the encoder and decoder is used. The strides values for all directions is 1, except for the first and third convolution layers where it is set to 3. The convolution layers with increased stride values enable the reduction of the feature maps on the encoder side and feature reconstruction on the decoder side. Additionally, the kernel has a rectangular shape where each edge has a size 17, 4, 10, and 3 for each of the four convolution layers. Those setups of AE models are chosen based on experimental analysis under different architectural parameters.

The two investigated VAE model architectures are based on the ones used in the aforementioned AE models. Thus, the fully connected and convolution layers are used in the described symmetrical architectures for the encoder and decoder in both investigated VAE models. These same architectures of AE and VAE models enable their comparison concerning their efficiency in dimensionality reduction. The VAE models introduce regularisation in the latent space by encoding it as a probability distribution over the latent space. Thus, the regularization prevents the decoder model from reconstructing the input data without variations. The regularization prevents overfitting and too large variance while simultaneously enabling the increased generalization of data representation. This improves the VAE’s ability to add moderated variances based on generalised dataset patterns for generating diverse data samples. The regularization is performed by introducing a Kullback–Leibler (KL) divergence term into the loss function. Thus, the encoder outputs the mean and log-variance of a Gaussian distribution for sampling the values from latent space. The VAE loss function is based on the calculated KL divergence between the distribution of the learned latent variables and a prior distribution. Thus, the KL divergence term enables latent variables to exhibit distributions similar to the prior distribution. This enables the structure and continuity within the latent space, consequently ensuring stability in generative objectives.

Thus, the VAE has a goal to optimize two loss functions. The first of them is the ‘reconstruction’ loss function. It is the same as it is the case with standard AEs. Thus, it uses Mean Squared Error (MSE) metrics to reduce the difference between the original and reconstructed inputs by decoder as it is possible to see in Equation (1):

$$L_{MSE}(\theta ,\varphi )={\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left(x_i-f_{\theta }\left(g_{\varphi }\left(x_i\right)\right)\right)}^2,$$

(1)

where $\theta$ and $\varphi$ are the trainable parameters of the decoder and encoder parts of VAEs, respectively. The variable N denotes the number of samples in the learning dataset, $x_i$ is the original input sequence, while $f_{\theta }$ and $g_{\varphi }$ are decoder and encoder functions, respectively. Thus, Equation (1) is used to compute mean squared differences between each original input sequence $x_i$ and corresponding reconstructions $f_{\theta }\left(g_{\varphi }\left(x_i\right)\right)$ over N samples.

The second loss that must be optimized with the VAE framework is the KL divergence term. Its main goal is to reduce the difference between values within latent space and learned standard normal distribution as the described regularisation approach. The KL divergence loss can be seen in Equation (2):

$$L_{KL}\left[G\left(Z_{\mu },Z_{\sigma }\right)|\mathcal{N}\left(0,1\right)\right]=-0.5\sum _{i=1}^{N}1+log\left(Z_{{\sigma }_i^2}\right)-Z_{{\mu }_i}^2-Z_{{\sigma }_i}^2,$$

(2)

where $G\left(Z_{\mu },Z_{\sigma }\right)$ is the Gaussian distribution generated by the encoder’s outputs $Z_{\mu }$ as the mean and $Z_{\sigma }$ as standard deviation. The $\mathcal{N}\left(0,1\right)$ denoted the standard normal distribution. Thus, the final VAE loss is computed as the weighted sum of KL divergence and reconstruction loss as can be seen in Equation (3):

$${\mathcal{L}}_{VAE}=L_{MSE}(\theta ,\varphi )+L_{KL}\left[G\left(Z_{\mu },Z_{\sigma }\right)|\mathcal{N}\left(0,1\right)\right].$$

(3)

Furthermore, the sampling operation from probabilistic distributions generates stochasticity in encoder outputs. Hence, introduced stochasticity destabilises the learning process since training algorithms use gradients of deterministic operations to minimise back-propagation learning error. The reparameterization approach is used in VAE frameworks to split the sampling operation into two parts. The first part is deterministic while the other is stochastic. Hence, a random variable $ϵ$ is sampled from a simple probabilistic distribution outside the learning loop. In this study, the sampling is performed by standard normal distribution $N(0,1)$. The outputs of the encoder model in the form of latent space variables $z\left[0\right]$ and $z\left[1\right]$ in function z are computed based on the deterministic and differentiable Equation (4):

$$z=\eta +\sigma ·ϵ.$$

(4)

This approach prevents direct sampling from the parameterised distribution $N\left(\eta ,{\sigma }^2\right)$ learned by the encoder model. Thus, a learning algorithm based on the back-propagation approach can be implemented through it.

3.3. Generating Input Variables for VAEs Decoder from Learned Latent Space

The next step is to define inputs for the VAE decoder which generates new samples. Those inputs represent queries for the VAE decoder which generates new samples that reassemble features of specific clusters (morning, afternoon and evening). They must be sampled from the latent space that spatially defines those clusters. Furthermore, those clusters must be defined in a 2-dimensional latent space by the corresponding VAE encoder. This is possible since the VAE encoder uses a 2-dimensional representation of latent space. Based on centroids of 2D morning, evening and afternoon clusters, it is possible to determine the two latent inputs (latent variables $z\left[0\right]$ and $z\left[1\right]$ ) for the encoder part of VAE.

The first step in this process is to use subclustering results computed using the Conv2D VAEs framework. Those hourly subclusters are aggregated into three aforementioned clusters. The next step is to compute the centroid of each of those clusters by the k-means algorithm. Naturally, the k value represents the number of clusters. A centroid is a data point that denotes the centre of cluster mass and it does not have to be one of its members. Thus, the potential new points of latent space need to be in spatial proximity to those centroids. This approach generates points in latent space which correspond to the adjacent clusters. Thus, new samples generated by the VAE decoder should resemble features of their corresponding clusters. This approach enables the augmentation of learning samples for specific clusters.

Using the normal random distribution, it is possible to generate an arbitrary number of latent points in quadratic patches with its centre represented by one of the three cluster’s centroids. The length and the width of those patches are set to $25\%$ of $z\left[0\right]$ and $z\left[1\right]$ latent axis, respectively. Figure 3 shows the illustration of the concept with 100 latent inputs for the VAEs decoder created in the proximity of each cluster’s centroids.

Those patches can have two different tasks. The first task complements real-world datasets with additional samples within the same cluster boundaries. This can be observed in the case of evening and afternoon clusters. They are compact and have a high level of homogeneity. Thus, this task expands the number of samples for a particular cluster. The second task is related to expanding the surface of the current cluster which is divided into two subclusters. Thus, the position of the synthetic samples in patches between dispersed sections of clusters should improve classification results for that particular cluster using machine learning. It is assumed that reducing the distance between two divided sections of one cluster by imposing the aforementioned patch between them could improve its identification as single through machine learning. This is the case with the morning cluster which is dispersed in two sections even at the level of weekday observations represented in Figure 4 (last row of graphs).

4. Results and Discussion

It is imperative to create and evaluate two distinctive ANN-oriented architectures of AE which serve as the basis for proposed VAE frameworks. Moreover, they differ from each other based on their required input format. The first AE architecture is based on fully connected layers (FC AE). Thus, it requires input in the form of a 1-dimensional vector. The second architecture is based on 2-dimensional convolution layers (Conv2D AE). This implies that their inputs must be formatted as 2-dimensional image-alike matrices. Both AE architectures are evaluated by using hyperparameters presented in Table 1. The evaluation results concerning the RMSE, MAE and MAPE for both investigated AE architectures can be seen in

Table 2. Evaluation results of both investigated AE architectures.

	RMSE	MAE	MAPE
FC AE	0.00138	0.0208	27.200
Conv2D AE	0.00134	0.0203	26.283

.

The results suggest that both proposed AE architectures can produce satisfying results respecting all three performance measures. Additionally, it is possible to notice that Conv2D AE architecture provides slightly better performance. This is the case since the convolution layers can utilise deep spatial features to compress the inputs in latent space. Those results suggest that both AE architectures can be used to design their VAE counterparts.

4.1. 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 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.

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. Evaluation results of all investigated approaches using Silhouette, Calinski–Harabasz, and Davies–Bouldin metrics for evaluation of dimensionality reduction respecting clustering performance on corresponding hourly subclusters. The analysis is conducted for all weekdays.

	Silhouette
Day in Week	t-SNE	tSVD	PCA	FC AE	Conv2D AE	FC VAE	Conv2D VAE
Monday	−0.027	0.032	0.023	0.044	−0.073	0.013	0.037
Tuesday	0.017	0.052	0.053	0.094	−0.044	0.051	0.059
Wednesday	0.017	0.022	0.031	0.071	−0.046	0.041	0.053
Thursday	−0.029	−0.022	−0.026	0.038	−0.108	0.005	0.009
Friday	−0.029	0.022	−0.008	0.051	−0.066	0.043	0.030
Saturday	−0.028	0.036	0.015	0.019	−0.062	0.056	0.020
Sunday	−0.037	−0.021	−0.049	−0.005	−0.089	−0.005	−0.012
	Calinski−Harabasz
Monday	164.311	79.789	98.919	166.538	50.631	100.631	116.385
Tuesday	227.420	126.133	154.008	226.726	135.298	169.694	189.848
Wednesday	214.581	108.218	126.760	187.213	167.230	144.026	148.707
Thursday	175.834	89.941	97.654	157.528	103.168	116.444	105.123
Friday	196.488	107.494	120.546	168.360	122.636	135.600	167.400
Saturday	92.709	122.497	118.645	163.305	57.210	151.381	118.362
Sunday	55.707	56.387	65.554	101.866	25.980	77.698	85.096
	Davies−Bouldin
Monday	5.404	2.713	3.151	2.378	3.300	3.138	4.100
Tuesday	7.961	2.815	2.437	2.499	17.417	2.863	4.011
Wednesday	5.699	2.932	2.851	2.822	10.432	3.375	4.177
Thursday	9.839	4.014	3.604	3.417	8.149	3.662	4.151
Friday	7.101	2.734	2.713	2.389	11.209	2.280	2.892
Saturday	7.352	3.296	4.554	4.333	7.324	3.942	11.073
Sunday	12.706	4.682	5.133	3.821	10.933	5.448	5.931

, 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. 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.

4.2. 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. The 2-dimensional visualisation of synthetic samples generated by the proposed Conv2D VAE framework for each of the morning, afternoon, and evening clustered by commonly used dimensionality reduction methods with datasets generated by real-world MoD data is presented in Figure 6.

It is possible to conclude that the spatial distribution of morning, afternoon, and evening subclusters remained the same with imposed synthetic samples. This means that all investigated dimensionality reduction methods can correctly localize (cluster) synthetic samples without deformation in the distribution of morning, afternoon, and evening subclusters. Thus, the Conv2D VAE framework has successfully extracted the features of subclusters for the corresponding morning, afternoon, and evening clusters. Moreover, the probabilistic sampling within the VAE framework did not cause drastic changes in synthetic samples to such an extent that they are located in totally non-related clusters (e.g., morning synthetic samples localised in evening-related hourly subclusters, etc.). However, it is possible to conclude that several samples are localised in “border regions” between two close subclusters respecting their temporal context. The most prominent example is when some morning synthetic samples are localised in subcluster “Hour-14” which is closest (in temporal context) to the subcluster “Hour-9” as the representative of the correct morning cluster. This behaviour can be explained by probabilistic sampling embedded into the VAE framework for generating new samples.

4.3. Evaluation of Learning Performance Using a Combined Dataset with Synthetic and Real-World MoD-Based Data Samples

The final analysis investigates the performance of two different architectural types of ANN models in learning performance. They are designed as classification models based on a supervised learning approach. Thus, all used samples in the training dataset are categorised using labels. Those labels correspond to three previously analysed clusters: morning, afternoon and evening. Thus, the samples are labelled with three possible classes using one-hot encoding.

Firstly, it is necessary to test the simple architecture of the shallow feedforward ANN model based on FC layers. Additionally, this architecture is interesting since it requires vectorised inputs. Each element of this vectorised input is considered an individual feature. It is possible to see the architectural structure of the used shallow ANN model in

Table 4. The architecture of the shallow ANN model based on FC layers which uses vector-alike inputs for the classification of MoD-based data samples in three distinctive clusters.

Shallow FC Layers Based ANN Model
Layer Number	Type of Layer	Activation Function	Nodes	Dropout Rate
1	Dense (FC)	ReLu	256
2	Dropout			0.3
3	Dense (FC)	ReLu	64
4	Dropout			0.3
5	Dense (FC)	ReLu	32
6	Dropout			0.3
7	Dense (FC)	Softmax	3

. The second ANN model is based on convolution layers which extract features from image-alike or matrix-wise inputs. Furthermore, extracted feature maps are flattened to form a vectorised format and passed to a shallow feedforward ANN model based on FC layers. This is a more comprehensive ANN model since it can detect and extract more complex spatial features for cluster classification. The 2-dimensional convolution ANN model structure for cluster classification based on MoD data can be seen in

Table 5. The 2-dimensional convolution ANN model architecture which uses image-alike inputs for classification of MoD data samples in three distinctive clusters.

2-D Convolution Based ANN Model
Layer Number	Type of Layer	Filter Number	Kernel Size	Strides	Activation Function	Nodes
1	Conv2D	128	(12,12)	(2,2)	ReLu
2	Batch Normalization
3	MaxPooling		(5,5)	(1,1)
4	Conv2D	64	(8,8)	(1,1)	ReLu
5	Batch Normalization
6	MaxPooling		(3,3)	(1,1)
7	Conv2D	32	(3,3)	(2,2)	ReLu
8	Batch Normalization
9	MaxPooling		(3,3)	(1,1)
10	Flatten
11	Dense (FC)				ReLu	32
12	Dense (FC)				Softmax	3

.

Furthermore, the learning is performed by using different configurations of training datasets. The initial training dataset contains only real-world data generated by the MoD service. It has 12,600 training samples. Thus, there are 4200 training samples assigned to each group of hourly subclusters which correspond to morning, afternoon and evening clusters. All other configurations of training datasets include the initial training dataset combined with synthetic samples generated by the proposed Conv2D VAE framework. The first group of combined datasets configuration augments each of the morning, afternoon and evening clusters by 3%, 5%, and 10% synthetic samples. Those percentages are computed based on the initial training dataset. This gradual increase in added synthetic samples for initial data clusters was chosen since it is necessary to examine at which percentage the improvements in the learning process are noticeable. Moreover, a percentage of synthetic samples that are too large can distort learning goals. The second group of training dataset configurations is based on synthetic samples which augment only one of the three initial data clusters with $10\%$ of synthetic samples. This group of training dataset configurations is investigated since it is needed to evaluate whether the targeted augmentation of individual initial data clusters can improve overall learning performance.

The convergence of learning error for shallow ANN model based on FC layers can be seen in Figure 7. In all training datasets, augmentations with synthetic samples induce faster learning convergence compared to the initial real-world dataset. Thus, augmentation of the initial dataset with any percentage of synthetic samples can speed up the learning of shallow ANN models for classification. Moreover, those results are achieved without overfitting or reducing final learning errors. Those results suggest that synthetic samples created by the proposed Conv2D VAE framework are consistent with the features of a shared cluster for which they are generated. Those results are expected for a shallow ANN-based model since it does not utilise complex mechanisms for deeper feature extraction.

The convergence of learning error for the ANN model based on 2D-dimensional convolution layers can be seen in Figure 8. The initial training dataset augmented with synthetic samples by $3\%$ for each cluster and $10\%$ for the afternoon cluster can improve the convergence of the learning curve. Improvement in learning convergence for the ANN model based on 2-dimensional convolutions is only noticeable with the initial training dataset augmented with a lower percentage of synthetic samples. This suggests that artefacts generated within synthetic samples are not consistent with outlier regions in samples generated by real-world MoD-based data. Thus, this slows down the learning convergence since convolution layers had to learn more features for the outlier regions based on real-world MoD data and ones caused by artefacts in synthetic samples. The hidden abnormalities and artefacts in spatial features within synthetic samples slow down the learning convergence only if they are present in a higher percentage for each cluster. Thus, a higher synthetic sample percentage for each cluster requires more time to fit artefacts in their spatial features with samples generated by real-world MoD-based data. This increase in synthetic samples for each cluster combined with the initial training dataset reduces the speed of learning convergence over the entire learning process but still avoids overfitting.

The augmentation of the largest afternoon clusters with synthetic samples improves the speed of learning convergence. It is possible to conclude that the proposed Conv2D VAE framework accurately learns the spatial features of this cluster. This largest afternoon cluster contains four hourly subclusters while all other clusters contain only two hourly subclusters. This suggests that the Conv2D VAE framework had more samples to learn from for the afternoon cluster. Thus, the proposed framework has produced high accuracy in generating spatial features for synthetic samples in the afternoon cluster. It is possible to notice that all other augmentations of specific clusters with higher percentages of synthetic samples have produced satisfying learning convergence results without causing overfitting. This proves that the proposed Conv2D VAE framework has learned a sufficiently accurate representation of spatial features for particular clusters based on which synthetic samples are generated. The augmentation of specific clusters with synthetic samples increases the differentiation between other clusters generated only using real-world MoD-based data. Simultaneously, all training datasets with synthetic samples for a particular cluster induce similar final learning errors.

The augmentation of the initial training dataset for a particular cluster with synthetic samples containing features, which accurately approximate their real-world counterparts, tackles the negative effects of outlier samples on learning convergence. The 2-dimensional convolution layers use those outlier samples for a non-linear function approximation of all samples for classification tasks through the learning process. This attempt to fit the outlier samples consequently results in a longer and fluctuating learning convergence. The augmentation of particular clusters with synthetic samples with an accurate representation of these cluster spatial features can reduce the impact of those outlier samples on the learning process. This is especially noticeable in the case of clusters with a larger number of samples, e.g., afternoon cluster, and batch-oriented learning approaches. The outlier samples in this case have a low probability of being taken into account for fitting through the learning process. Thus, their impact on non-linear function approximation for spatial features of a particular cluster is minimized. This improves the generalization of spatial features for a particular cluster without causing overfitting. Furthermore, the slower learning convergence at the start of the process for morning and afternoon clusters is due to their lower number of hourly subclusters. This reduces the total number of learning samples for those clusters. Consequently, based on less accurately learned spatial features of those clusters, this induces artefacts in generated synthetic samples for them. Those spatial artefacts can reduce the speed of learning convergence at the start of the process. It is possible to conclude that even with the presence of artefacts in synthetic samples the learning convergence is stabilised quickly and produces learning errors similar to the initial training dataset. Thus, synthetic samples can be fitted into the overall non-linear function without causing overfitting.

The comparison of average values for all image-alike real-world samples in each of the three investigated clusters compared to the average values of all synthetic samples generated for those clusters can be seen in Figure 9.

It is possible to conclude that the scale of average values in synthetic samples is in line with the averages of the real-world samples except for the evening cluster. This has been the case since evening synthetic samples are affected by more artefacts than the other clusters. Additionally, one can notice that the decoder of the proposed VAE framework has successfully captured the key features of all investigated clusters. The second analysis evaluates the classification performance of both investigated ANN models. They are trained based on different configurations of training datasets used in previous analyses. All trained models are evaluated using the same validation datasets generated by real-world MoD-based data. This provides an analytical setup which assesses the impact of various percentages of synthetic samples in training datasets on MoD-based classification performance based on real-world validation dataset. The two groups of metrics are used to achieve a deeper analysis of classification performance. Thus, the first group involves RMSE and MAE as the commonly used regression metrics. They are used since they directly evaluate the accuracy of trained models by computing prediction errors. This group of metrics enable classification tasks described as regression problems where three discredited values are possible (morning, afternoon and evening cluster). The second group includes metrics such as Recall, Precision and F1 Score. Furthermore, the Precision is computed using Equation (5):

$$Precision={\displaystyle \frac{TP}{TP+FP}},$$

(5)

where TP denotes true positive predictions. They represent the number of samples in the training dataset correctly predicted for morning, afternoon, and evening clusters. The FP denotes false positives as the number of samples positively categorised for a particular cluster while they do not belong to this cluster. The Recall is computed using Equation (6):

$$Recall={\displaystyle \frac{TP}{TP+FN}},$$

(6)

where FN denotes false negative predictions. It is the number of samples in the training dataset wrongly classified that they do not belong to a particular cluster when they should be classified as positive for that cluster. The F1 Score is computed using Equation (7):

$$F1score={\displaystyle \frac{2\times Precision\times Recall}{Precision+Recall}}.$$

(7)

The F1 Score is computed as the harmonic mean of the Precision and Recall values. Thus, it favours smaller differences in values between Precision and Recall. It is possible to conclude that the larger differences between Precision and Recall values induce a smaller harmonic mean. The reduction of the harmonic mean has a negative effect on the investigated model classification accuracy. All explained metrics are commonly used for standard classification problems.

Table 6. Classification performance using trained shallow ANN models based on FC layers. The individual training of each model is performed using different configurations of training datasets augmented by the proposed VAE model. All models are tested with the same validation datasets generated by real-world MoD-based data.

	Training Dataset Configuration	Prediction Performance Metrics
		RMSE	MAE	Recall	Precision	F1 Score
	Initial Training Dataset	0.142	0.027	0.962	0.963	0.963
Initial training dataset augmented by VAEs decoder	+12% synthetic samples for each cluster	0.151	0.026	0.962	0.962	0.962
	+11% synthetic samples for each cluster	0.145	0.023	0.964	0.964	0.964
	+10% synthetic samples for each cluster	0.136	0.022	0.968	0.968	0.967
	+9% synthetic samples for each cluster	0.135	0.024	0.968	0.968	0.967
	+8% synthetic samples for each cluster	0.132	0.020	0.970	0.970	0.970
	+7% synthetic samples for each cluster	0.137	0.021	0.968	0.961	0.968
	+5% synthetic samples for each cluster	0.133	0.023	0.967	0.967	0.967
	+3% synthetic samples for each cluster	0.135	0.022	0.970	0.970	0.970
	+10% synthetic samples only for morning cluster	0.139	0.024	0.965	0.966	0.966
	+10% synthetic samples only for afternoon cluster	0.134	0.022	0.970	0.970	0.970
	+10% synthetic samples only for evening cluster	0.148	0.031	0.962	0.963	0.963

presents the classification performance results achieved by a trained shallow ANN model based on FC layers. The trained models based on training dataset configurations with synthetic samples improve accuracy over the model trained with the initial training dataset in almost all cases. It is possible to conclude that if the number of augmentations of the initial real-world training dataset are more than $11\%$ of synthetic samples for each cluster, it can reduce prediction accuracy. This larger augmentation of the initial training dataset with synthetic samples for each cluster introduces too many synthetic artefacts in the combined dataset. This consequently reduces the accuracy of predictive models trained by over-augmented configurations of the training dataset. In general, it is possible to notice that shallow ANNs based on FC layers respond minimally to synthetic augmentation of MoD-based datasets. Those results can be explained by the limitations in their architecture, which cannot accurately capture spatial patterns between drop-off, and pick-up zones.

The second trained model, which performs slightly less accurately compared to the model trained by the initial training dataset, uses an augmentation of the initial training dataset with $10\%$ of synthetic samples for the evening cluster. Those results can be explained by less accurately learned features of the evening cluster, since it contains only two hourly subclusters. To increase the prediction accuracy of the model which is trained on a dataset exclusively augmented by synthetic samples which correspond to the evening cluster, it is necessary to conduct several techniques to improve the learning of its general behaviour patterns. Thus, it is necessary to additionally extend the sub-dataset of the evening cluster with real-world samples which correspond to that cluster. This approach can improve the generalisation of the VAE model for the evening cluster. Thus, the VAE can generate synthetic samples which reassemble more generalised evening behavioural patterns. Consequently, this can reduce the number of artefacts in those synthetic samples that are caused due to frequent outliers in smaller datasets, such as evening clusters. Based on current results on the other two clusters with a lower number of outliers, it is recommended that the percentage of synthetic samples for evening clusters remains at $10\%$.

In general, it is possible to conclude that the shallow architecture of ANN models is less reactive to the augmentation of the initial training dataset with synthetic samples since it does not have advanced abilities to capture deeper structures of features within samples. Those models consider samples as highly dimensional inputs. Thus, the high dimensionality of input samples can reduce sensitivity for artefacts represented by individual features introduced by some parts of synthetic samples. They can slightly improve the fitting process during learning only if they are present in a smaller percentage for each cluster.

Furthermore, augmentation of the particular cluster with a higher percentage of the synthetic sample can increase classification performance only if this cluster has a larger number of hourly subclusters, such as the afternoon cluster. In the case of larger clusters, the synthetic artefacts are less prominent and less present since the VAE framework had more training samples from which to learn their baseline features. The high accuracy in learning baseline features within a particular cluster is essential for generating valid synthetic samples.

Table 7. Classification performance using trained ANN model based on 2-dimensional convolution layers. The individual training of each model is performed using different configurations of training datasets augmented by the proposed VAE model. All models are tested with the same validation datasets generated by real-world MoD-based data.

	Training Dataset Configuration	Prediction Performance Metrics
		RMSE	MAE	Recall	Precision	F1 Score
	Initial Training Dataset	0.179	0.042	0.939	0.941	0.943
Initial training dataset augmented by VAEs decoder	+12% synthetic samples for each cluster	0.339	0.168	0.789	0.776	0.783
	+11% synthetic samples for each cluster	0.309	0.105	0.845	0.845	0.845
	+10% synthetic samples for each cluster	0.162	0.028	0.957	0.608	0.958
	+9% synthetic samples for each cluster	0.147	0.026	0.962	0.962	0.962
	+8% synthetic samples for each cluster	0.148	0.024	0.964	0.964	0.964
	+7% synthetic samples for each cluster	0.156	0.026	0.960	0.960	0.960
	+5% synthetic samples for each cluster	0.152	0.025	0.961	0.961	0.961
	+3% synthetic samples for each cluster	0.149	0.024	0.964	0.964	0.964
	+10% synthetic samples only for morning cluster	0.161	0.03	0.958	0.958	0.958
	+10% synthetic samples only for afternoon cluster	0.163	0.029	0.957	0.957	0.957
	+10% synthetic samples only for evening cluster	0.202	0.054	0.919	0.926	0.922

presents the classification performance results of a trained ANN model based on 2-dimensional convolution layers. It is possible to conclude that an optimal percentage of synthetic samples is below $10\%$ in the initial training dataset. Furthermore, augmentation of the evening cluster with $10\%$ of synthetic samples induces lower prediction results. Those results can be explained by a lower number of training samples within this cluster. The best classification accuracy is achieved with the models trained on an initial training dataset augmented by $8\%$ and $3\%$ with synthetic samples for each cluster. It is necessary to emphasise that in 2-dimensional image-like inputs, artefacts are spatially localised at specific places in synthetic samples. Those spatial artefacts in synthetic samples are generated due to a low number of training samples or an increased number of outliers in that spatial section. Usually, they are defined by pairs of drop-off, and pick-up zones with the highest mobility frequencies where different anomalies can happen for each cluster.

The filters in 2-dimensional convolution layers can more accurately detect spatial features of artefacts in synthetic samples through learning. Those learned features can be fitted into the non-linear functions for clusters without negative effects on final classification results. This effect is most prominent in the case of a smaller percentage of synthetic samples. Thus, this introduces fewer artefacts in the combined training dataset.

Consequentially, learned non-linear functions for each cluster are less prone to distortion caused by fewer artefacts. All other parts of synthetic samples without artefacts improve the fitting process. This improves the classification accuracy of those models. The increased percentage of synthetic samples implies a higher number of spatial artefacts within them in the combined learning dataset. This reduces the stability of the fitting process during the training and consequently classification accuracy. Despite that, all investigated models trained on different configurations of augmentation for each cluster with synthetic samples achieve better classification accuracy than the initial training dataset.

This suggests that the proposed Conv2D VAE framework generates other spatial parts of synthetic samples without prominent artefacts. Results suggest that areas of those parts in synthetic samples are much larger than the ones affected by problematic artefacts caused by the intense fluctuations in mobility demand. Thus, they are the main features of synthetic samples that drive the improvement of classification accuracy over the model trained using an initial real-world MoD-based dataset. This is the case since the spatial filters of the Conv2D VAE framework are less prone to adjustments in areas of synthetic samples which are prone to artefacts. This is the case since at the corresponding places in the real-world MoD-based samples, the outliers (approximated as artefacts by Conv2D VAE) can also occur with high probability.

For the sake of comparative analysis with the proposed VAE approach, the GAN model is used to generate synthetic samples. The GAN model cannot be used directly for dimensionality reduction using latent space, based on which its decoder creates synthetic samples for specific clusters. Thus, three identical GAN models are created. Each of those three GAN models is individually trained on samples from one of the three investigated clusters. Thus, one GAN model is used to create synthetic samples for a specific cluster upon which it is trained. It is possible to conclude that this approach is not feasible for a larger number of clusters with a lower number of samples.

Table 8. Classification performance using trained ANN models based on 2-dimensional convolution layers. The individual training of each model is performed using different configurations of training datasets augmented by the GAN model. All models are tested with the same validation datasets generated by real-world MoD-based data.

	Training Dataset Configuration	Prediction Performance Metrics
		RMSE	MAE	Recall	Precision	F1 Score
	Initial Training Dataset	0.179	0.042	0.939	0.941	0.943
Initial training dataset augmented by VAEs decoder	+12% synthetic samples for each cluster	0.327	0.116	0.826	0.827	0.826
	+11% synthetic samples for each cluster	0.288	0.060	0.908	0.913	0.910
	+10% synthetic samples for each cluster	0.242	0.070	0.901	0.904	0.902
	+9% synthetic samples for each cluster	0.431	0.201	0.918	0.925	0.922
	+8% synthetic samples for each cluster	0.328	0.130	0.796	0.799	0.797
	+7% synthetic samples for each cluster	0.271	0.127	0.948	0.947	0.947
	+5% synthetic samples for each cluster	0.157	0.027	0.957	0.951	0.959
	+3% synthetic samples for each cluster	0.157	0.024	0.961	0.965	0.963
	+10% synthetic samples only for morning cluster	0.196	0.049	0.931	0.932	0.932
	+10% synthetic samples only for the afternoon cluster	0.234	0.064	0.905	0.909	0.907
	+10% synthetic samples only for evening cluster	0.441	0.208	0.686	0.688	0.687

presents the classification performance results conducted by a trained 2D-convolution ANN model with synthetic samples generated by GAN models.

It is possible to conclude that trained GAN models can improve the prediction accuracy up to the $7\%$ of synthetic samples in the augmented training dataset. This is a lower percentage of synthetic samples in the augmented training dataset, which can induce prediction improvements compared to the proposed VAE approach. Additionally, the exclusive augmentation of the articular cluster with $10\%$ of synthetic samples also results in lower prediction accuracy compared to the proposed VAE approach. This is the reason for the inability of GAN to optimise data reconstruction within a probabilistic framework. The reconstruction of synthetic data from a probabilistic framework is highly beneficial for stochastic systems, such as modelling traffic demand. Thus, the proposed VAE framework generates more realistic traffic scenarios within generated synthetic samples. This enables a higher percentage of synthetic samples in the augmented training dataset, which can be used in the training process for improved prediction accuracy.

Table 9. Prediction performance for classification of synthetic samples by using trained ANN models.

		Prediction Accuracy%
	Model Which Generated Synthetic Samples	2D- Convolution VAE		2D-Convolution GAN
	Training Dataset Configuration	Shallow ANN Model with FC Layers	2D Convolutional ANN Model	2D Convolutional ANN Model
	Initial Training Dataset	81	83	83
Initial training dataset augmented by VAEs decoder	+12% synthetic samples for each cluster	78	98	85
	+11% synthetic samples for each cluster	78	98	84
	+10% synthetic samples for each cluster	77	82	84
	+9% synthetic samples for each cluster	78	91	83
	+8% synthetic samples for each cluster	78	95	80
	+7% synthetic samples for each cluster	79	94	84
	+5% synthetic samples for each cluster	79	93	85
	+3% synthetic samples for each cluster	78	97	85
	+10% synthetic samples only for morning cluster	79	91	83
	+10% synthetic samples only for afternoon cluster	79	97	84
	+10% synthetic samples only for evening cluster	80	97	84

presents the prediction performance for the classification of synthetic samples by using trained ANN models. The 100 synthetic samples are generated for each of the three investigated clusters for the validation dataset. It is possible to conclude that the ANN model based on 2-dimensional convolution layers produces overall better prediction results for the classification of synthetic samples than the ANN model based on FC layers.

5. Conclusions

The conducted study has shown that the proposed Conv2D VAE can generate synthetic samples for augmentation of the initial training dataset based on real-world MoD-based data. This is proven by analysis which conducts dimensionality reduction based on combined datasets with synthetic and real-world MoD-based samples. The synthetic samples are spatially located in the correct clusters defined by real-world MoD-based samples. The second analysis includes different configurations of training datasets with synthetic and real-world MoD-based samples for the classification of clusters. It is shown that the models trained on the configuration with a lower percentage of synthetic samples combined with the initial training dataset can improve the classification accuracy. Those results are achieved for both investigated architectures of ANN models. Thus, this suggests that the proposed Conv2D VAE framework can produce artefacts defined by the intense fluctuation of mobility demand between pairs of drop-off, and pick-up zones. Consequently, this can reduce the categorisation accuracy of trained models based on these datasets with a higher percentage of synthetic samples affected by artefacts.

Additionally, the study has shown that more training samples within one cluster (afternoon) than others can improve the classification accuracy of the trained model based on exclusive augmentation of this cluster with synthetic samples. This suggests the importance of training dataset size for learning baseline features of a particular cluster. Those learned features represent the foundation based on which the proposed Conv2D VAE framework generates synthetic samples. The final finding of this study is that the investigated ANN model architecture based on 2-dimensional convolution is less prone to localised spatial artefacts within synthetic samples. Those artefacts in the case of MoD-based data are correctly approximated through learning filters within 2-dimensional convolution layers. Thus, if the training dataset is augmented with up to $10\%$ of synthetic samples it is possible to improve the classification accuracy of investigated predictive ANN-based models that are trained on them. Those results imply that augmentation of the training dataset with synthetic samples generated by the proposed Conv2D VAE can improve the accuracy of predictions using learned spatio-temporal patterns for the approximation of stochastic mobility demand processes within dense urban areas. Additionally, in comparison with results achieved by GAN models, it is possible to conclude that reconstruction of synthetic data from a probabilistic framework used by VAE is highly beneficial for stochastic processes such as generating realistic mobility demand. The proposed VAE framework can be used for deeper spatial analysis of commuters’ behaviour for strategic planning of dispatching vehicles within MoD services.

Future research will address the more complex architecture of VAE models. Those more complex VAE models will be investigated regarding their impact on generating artefacts in synthetic samples. This is especially needed for the investigation of smaller datasets with numerous outliers, such as the evening cluster in the presented MoD study.