## 3 Experiments
### Experiment Settings  
Detailed descriptions of the architecture and parameter configuration of our STCN are shown in Table 1. It was implemented based on an open-source deep learning framework--Keras [55]. Experiments were run on a workstation with Ubuntu 18.04 installed. This experimental device had only one Nvidia GeForce RTX 2080 Ti graphics card which had 11,019 megabytes of GPU memory. The model was trained based on the optimizer RMSprop [56]. The learning rate was set to 0.001 and the decay parameter was set to 0.9. The batch size was dynamic because this model was trained and tested by day using back-testing, and thus missing data introduce different numbers of samples each day. The loss function was a customized weighted mean squared error (wMSE) defined in Equation (5), where \(w^{t}_{ij}\) stands for the penalty weight applied to different congestion levels because different congestion levels have different priorities. In addition, early stopping was used to prevent overfitting. \[wMSE=\frac{1}{R\times C}\sum_{i=1}^{R}\sum_{j=1}^{C}w^{t}_{ij}\times\left(c^{t} _{ij}-\widehat{c^{t}_{ij}}\right)^{2} \tag{5}\]  
STCN discussed in Section 2.3 was used to compare the accuracy of our proposed pooling method and the other three described above, which are essential to our proposed framework for the representation of road network traffic congestion data in a down-sampled and compressed way to predict traffic congestion. Previous work determined an optimized time lag of 120 min for traffic prediction [57]. Therefore, for all pooling operations, 12 compressed traffic congestion matrices with an interval of 10 min during the past \(12\times 10=120\) min arranged in chronological order were used as input to the STCN model. These input matrices were obtained after grid-based partition of the original traffic congestion matrices using a grid size of \(2\times 2\) and the separate application of each of these four pooling operations. The reason for using a grid size of \(2\times 2\) in our work is twofold. Firstly, it is inspired by its popular utilization in convolutional neural networks [25; 58; 59; 60; 61; 62] and as a default pool size of pooling layers in deep learning \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Layer** & **Name** & **Channels** & **Size** \\ \hline
1 & Inputs & \(1\) & (128, 128) \\ \hline
2 & Convolution & 64 & (3, 3) \\  & Max-Pooling & 64 & (2, 2) \\  & Activation (Relu) & - & - \\  & Batch-Normalization & - & - \\ \hline
3 & Convolution & 32 & (3, 3) \\  & Max-Pooling & 32 & (2, 2) \\  & Activation (Relu) & - & - \\  & Batch-Normalization & - & - \\ \hline
4 & Convolution & 16 & (3, 3) \\  & Max-Pooling & 16 & (2, 2) \\  & Activation (Relu) & - & - \\  & Batch-Normalization & - & - \\ \hline
5 & Convolution & 8 & (3, 3) \\  & Max-Pooling & 8 & (2, 2) \\  & Activation (Relu) & - & - \\  & Batch-Normalization & - & - \\ \hline
6 & Flatten & - & - \\ \hline
7 & LSTM1 & - & (12, 800) \\  & Activation (tanh) & - & - \\ \hline
8 & LSTM2 & - & 800 \\  & Activation (tanh) & - & - \\ \hline
9 & Dropout(0.1) & - & - \\ \hline
10 & Fully Connected & - & 16,384 \\ \hline
11 & Output & 1 & (128, 128) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Architecture and parameter settings of CNN-LSTM. frameworks such as Keras [55] and TensorFlow [63]. Secondly and more importantly, it can strike a balance between demand of computational resources and loss of traffic congestion information due to down-sampling [64; 65]. The output of this model is a compressed congestion matrix at one of six short terms including typical prediction horizons of 10, 30, and 60 min as used in [5; 30], and also 20, 40, and 50 min used in this paper. For all four pooling operations, the ground-truth matrices for the predicted output matrices were obtained after grid-based partition of corresponding original traffic congestion matrices using a grid size of \(2\times 2\) and application of the NNV operation defined by Equation (2).