## 5 Experimental Analysis
### Reference Methods  
The proposed model is compared against the following state-of-the-art methods expressly devised to solve the citywide vehicle flow prediction problem [7]:  
**ST-ResNet [4]**: it is one of the first deep learning approaches to traffic prediction. It predicts the flow of crowds in and out each individual region of activity. ST-ResNet uses three residual networks that model the temporal aspects of _proximity_, _period_, and _trend_ separately. Figure 7: Spatial Attention Block  
**MST3D [7]**: this model is architecturally similar to ST-ResNet. The three time dependencies and the external factors are independently modeled and dynamically merged by assigning different weights to different branches to obtain the new forecast. Differently from ST-ResNet, MST3D learns to identify space-time correlations using 3D convolutions. **ST-3 DNet [24]**: the network uses two distinct branches to model the temporal components of _closeness_ and _trend_, while the daily period is left out. Both branches start with a series of 3D convolutional layers used to capture the spatio-temporal dependencies among the input frames. In the _closeness_ branch, the output of the last convolutional layer is linked to a sequence of residual units to further investigate the spatial dependencies between the frames of the _closeness_ period. The most innovative architectural element is the _Recalibration Block_. It is a block inserted at the end of each of the two main branches to explicitly model the contribution that each region makes to the prediction. **3D-CLoST [8]**: the model uses sequential 3D convolutions to capture spatio-temporal dependencies. Afterwards, a fully-connected layer encloses the information learned in a one-dimensional vector that is finally passed to an LSTM block. LSTM layers in sequence allow the model to dwell on the temporal dependencies of the input. The output of the LSTM section is added to the output produced by the network for external features. The output is multiplied by a _mask_, which allows the user to introduce domain knowledge: the mask is a matrix with null values in correspondence with the regions of the city that never have Inflow or Outflow values greater than zero (such areas can exist or not depending on the conformation of the city) while it contains 1 in all other locations. **STAR [6]**: this approach aims to model temporal dependencies by extracting representative frames of _proximity_, _period_ and _trend_. However, unlike other solutions, the structure of the model consists of a single branch: the frames selected for the prediction are concatenated along the axis of the channels to form the main input to the network. In STAR as well, there is a sub-network dedicated to external factors and the output it generates is immediately added to the main network input. Residual learning is used to train the deep network to derive the detailed outcome for the expected scenarios throughout the city. **PredCNN [11]**: this network builds on the core idea of recurring models, where previous states in the network have more transition operations than future states. PredCNN employs an autoencoder with CMU, which proved to be a valid alternative to RNN. Unlike the models discussed above, this approach considers only the temporal component of _closeness_ but has a relatively complex architecture. The key idea of PredCNN is to sequentially capture spatial and temporal dependencies using CMU blocks. **ACFM [25]**: this module is composed of two progressive Convolutional Long Short-Term Memory (ConvLSTM [52]) units connected via a convolutional layer. Specifically, the first ConvLSTM unit takes the sequential flow features as input and generates a hidden state at each time-step, which is further fed into the connected convolutional layer for spatial attention map inference. The second ConvLSTM unit aims at learning the dynamic spatial-temporal representations from the attentionally weighted traffic flow features.