# Unequal Interval Dynamic Traffic Flow Prediction with Singular Point Detection
## 2 Related Work  
According to the time interval, traffic flow prediction can be classified into short-term prediction and long-term prediction. [PERSON] et al., pointed out that short-term prediction aims to forecast the traffic trend in the next few seconds to hours based on real-time and historical traffic information [11], while [PERSON] et al., mentioned that long-term prediction forecasts a full day or weeks of traffic in the future [12]. This paper mainly focuses on the short-term prediction of traffic flow. Many researchers designed various prediction models and adjusted parameters to increase performance. [PERSON] et al., proposed a stochastic Lagrangian traffic flow model to capture the transition points in traffic flow [13]. The model used an unscented Kalman filter to update the parameters and real-time information that were probed from the first and last vehicles in the cell. Based on the prediction results, an advanced warning was provided for stop-and-go traffic jams. The model combined traffic prediction and data completion via Graph Laplace to recover missing data and predicted the traffic flow in a large-scale network [14]. [PERSON] et al., used a digital twin-assisted real-time traffic data prediction method to analyze the traffic flow and velocity data to realize a quick response with high accuracy [15]. The duration of real-time data was collected by 5G, and the prediction slot was fixed to 15 min in the experiments. [PERSON] et al., proposed a microscopic model that identifies drivers' response to increase the reaction and sensitivity of traffic flow prediction [16]. Based on the application of machine learning methods, analysis of historical flight tracks, weather forecasts, and airport operational data was used in multilayer clustering to predict the results. [PERSON] et al., focused on the influences of traffic conditions on decision makers and proposed the traffic-condition-aware ensemble approach by stacking multiple predictions [17]. The model collected spatiotemporal patterns embedded in traffic flow by a convolutional neural network, and the extracted high-level features weighted the values of parameters. The improvements of prediction models achieved high accuracy in traffic flow forecasting. However, the complexity is usually quantified by the number of internal parameters [5]. The system needs to spend time on debugging the parameters in the complex road network. Additionally, the parameters should be updated and trained once the scenario changes. Due to the computing time and the scenario limitation, the insights and structure of a traffic flow signal can benefit traffic prediction [5]. Some studies have studied the relative algorithms and methods on time-varying or spatial series to analyze the traffic flow signal. [PERSON] et al., performed time series analysis on traffic flow data and performed smoothing and standardization processing to obtain a stable time series as a model input [18]. The first layer of the model learned the input time series, and the further layers learned and were trained to reduce prediction errors. The evaluation increased by 5 min among simulations to test the prediction accuracy. The singular point is the intrinsic property of the time-varying traffic flow signal. As a nonstationary sequence, the singular point marks that the previous steady state is broken by a traffic jam or accident. The methods are used to detect and predict the agnostic points of the signal. [PERSON] et al., proposed a hybrid model to predict a short-term traffic flow combining an autoregressive integrated moving average model (ARIMA) and wavelet neutral network (WNN), which can improve the accuracy of prediction [19]. Long short-term memory (LSTM) with an attention mechanism was used for traffic flow forecasting [20]. The study of a traffic flow's regular pattern can achieve the robustness of a training dataset. [PERSON] et al., tried to solve the prediction issue via convolutional neural networks (CNN) and LSTM [21].