## 3 Problem Statement and Input Data Representation Methods
### Common Forms of Input Representations
#### 3.2.1 Time Series  
The data representation of a time series encompasses the organization and structure of the data points that describe the evolution of a quantity over time. It consists of two fundamental components: the time stamp or index and the corresponding data values. The time stamp indicates when each observation was recorded and can take various formats, such as dates, timestamps, or numerical indices representing time intervals. The data values represent the actual measurements or observations of the quantity of interest at each time stamp. Together, these components form a sequential series of data points that can be analyzed to identify patterns, trends, and relationships over time. Time series, \(\mathbf{s}\in\mathbb{R}^{t}\), can be represented as \(\mathbf{s}=\{s_{1},s_{2},\ldots,s_{t}\}\), where \(s_{t}\) represents the traffic state at time \(t\). Time series \(\mathbf{s}\) is a common way to represent traffic data. It emphasizes the importance of traffic patterns that change over time. For example, [PERSON] et al. [50] provided a comprehensive overview of time series forecasting techniques, including their applications in various fields. Furthermore, in traditional studies, RNNs only utilize the time series of traffic volume as input and do not incorporate any attribute information from the time series data,such as timestamps and days of the week. However, traffic volume varies depending on the time and day of the week. Therefore, in addition to the time series of traffic volume, attribute information can be used as input to enhance the prediction accuracy of RNN methods further. [PERSON] et al. [51] investigated the impact of incorporating attribute information from the time series of traffic volume on prediction accuracy in network traffic prediction. They proposed two RNN methods: the RNN-Volume and Timestamp method (RNN-VT), which uses timestamp information, and the RNN-Volume, Timestamp, Day of the week method (RNN-VTD), which utilizes both timestamp and day of the week information as inputs, in addition to the time series of traffic volume. Some studies have also considered the potential connections between traffic states and their contexts by integrating time series data with contextual factors. For instance, [PERSON] et al. [52] used time series to represent the scenario of short-term traffic speed prediction, where these time series data represent the average speed of all vehicles during specific time intervals, aiming to accurately reflect the movement status of vehicles. They introduce Feature-Injected RNNs (FI-RNNs), a network that combines time series data with contextual factors to uncover the potential relationship between traffic states and their backgrounds. Some studies decompose time series data, such as [PERSON] et al. [53], who used time series to represent traffic flow data in urban road networks. Specifically, the study addresses short-term traffic flow prediction in urban road networks and emphasizes the periodicity and randomness of traffic data. To handle these traffic data, the research is divided into two modules. The first module consists of a set of algorithms to process traffic flow data, providing a complete dataset without outliers through analysis and repair and offering a dataset of the most similar road segment pairs. The second module focuses on multi-time step short-term forecasting. [PERSON] et al. [54] demonstrated that in addition to parameters related to traffic, other features associated with road traffic, such as air and noise pollution, can also be integrated into the input. This study uses time series to represent road traffic data in the city, specifically focusing on the correlation between noise pollution and traffic flow to predict traffic conditions. The noise pollution data provide additional indicators of traffic density and traffic flow. These time series integrate changes in road traffic flow and the associated levels of noise pollution, revealing the interaction between traffic flow and noise pollution.