# Meta-Extreme Learning Machine for Short-Term Traffic Flow Forecasting
## 1 Introduction  
The study of intelligent traffic management and control systems has become a hot topic in the construction of modern transportation systems. Among them, the key to achieving forward-looking traffic management and control is to achieve higher forecast accuracy for short-term traffic flows [1]. Short-term traffic flow forecasting is particularly important. Due to the time sequence of traffic flow, the practical application value of short-term forecasting is higher than that of long-term forecasting. A proven and effective short-term traffic flow forecasting model can improve traffic quality in several ways, including reducing travel costs [2], reducing carbon emissions due to traffic congestion, and improving the efficiency of traffic operations [3]. Currently, short-term traffic flow forecasting techniques are applied in many domains, including transit routing models [4], rail transit ridership [5], and dockless shared like demand [6]. However, it is challenging to build an accurate and stable short-term traffic flow forecasting model because of the nonlinear and stochastic characteristics of the traffic flow [7]. In addition, other external factors can also interfere with the accuracy of the forecast, such as unanticipated traffic accidents or unplanned traffic controls. During the past decades, researchers have contributed a series of new theories and methods in the field of traffic flow forecasting. Traffic flow forecasting is broadly grouped into three categories, namely, traditional machine learning models, dynamics-based models, and deep learning models. First, traditional machine learning models include \(k\)-nearest neighbor (\(k\)NN) [2], support vector machine (SVR) [8], ensemble learning [9], etc. For example, [PERSON] et al. proposed a two-stage hybrid model to determine the combinationof hyperparameters for the extreme learning machine [10]. [PERSON] et al. proposed a noise-immune extreme learning machine, which takes advantage of the gravitational search algorithm (GSA) to search for an optimal global solution and used the extreme learning machine (ELM) to forecast traffic flow [11]. [PERSON] et al. proposed a hybrid model using the GSA to optimize SVR for short-term traffic flow forecasting in [12]. [PERSON] et al. also proposed using KNN regression models for short-term traffic flow forecasting [2]. Moreover, an ELM model with the particle swarm optimization (PSO) algorithm was proposed by [PERSON] et al. [13]. An extreme gradient boosting-based learning model enhanced by wavelet denoising was proposed by [PERSON] et al. [14], which was easy to implement and effective. An ELM optimized by GSA for short-term traffic flow prediction [15] was proposed by [PERSON] et al. Second, dynamics-based models include auto-regressive integrated moving average (ARIMA) [16; 17; 18], historical average (HA), Kalman filter (KF) models [3; 19; 20], exponential smoothing (ES), seasonal auto-regressive integrated moving average [21; 22], etc. For example, [PERSON] et al. designed a KF for accurate traffic flow forecasting by identifying the noises in the traffic flow data [19]. [PERSON] et al. proposaed a hybrid dual KF for short-term traffic flow forecasting [3]. Furthermore, [PERSON] et al. proposed embedding a fixed-point algorithm to update the posterior estimate of the KF, which is derived from maximum correlation entropy,  
To solve the problem that the KF derived from the maximum correlation entropy criterion is insensitive to non-Gaussian noise [20]. From the 20 th century to the present, artificial intelligence and machine learning have made significant progress. Deep learning models have been applied in the field of complex nonlinear short-term traffic flow forecasting, including deep belief network [23], fuzzy logic system methods [24; 25], deep feature fusion model [26], etc. [PERSON] et al. proposed training stacked autoencoders to improve the accuracy of traffic flow forecasting [27].