# Meta-Extreme Learning Machine for Short-Term Traffic Flow Forecasting
## 3 Experiments
### Performance Evaluation  
We evaluated the performance of our ABC-ELM by comparing the performance of models which are mostly applied to forecasting under the same dataset and reflected by the _RMSE_ and _MAPE_ evaluation criteria, as shown in Tables 3 and 4. Common models applied to linear regression forecasting include:  
* Support Vector Machine (SVM) was proposed by [PERSON] et al. [49]. The setting of SVR can be found at [27]. SVM performs nonlinear classification by a kernel method, which is one of the common kernel learning methods [50]. * Autoregression (AR) is a linear regression model widely cited for forecasting. Especially in the field of applied traffic flow, AR can perform well in the field of traffic flow, which is full of randomness, because it expresses the random variables of the latter through a linear combination of the previous random variables. The parameters of the AR model are the same as those of [27]. * Artificial Neural Network (ANN) is a non-parametric learning model that simulates neuronal activity with a mathematical model and is based on mimicking the structure and function of neural networks in the brain. In this paper, the number of hidden layers of this ANN is one, and the spread of radial basis functions is set as 2000 according to the [51]. * Gray Model (GM) is based on gray system theory and can perform series forecasting, catastrophe forecasting, seasonal catastrophe forecasting, topological forecasting, and integrated system forecasting. We use the most commonly used gray forecasting model GM(1,1) model, which represents a differential equation model of order one and one variable. The GM(1,1) model group, the metabolic model, is the most desirable model. * Kalman filter (KF), as one of the most popular filtering algorithms, is a filtering process based on linear equations to eliminate the effects of noise and other effects in the data, including the system, i.e., the process of making optimal predictions about the system. As suggested in [52], we set the initial state to \([\frac{1}{n},...,\frac{1}{n}]\), where \(N\) is set as eight. * Decision tree (DT) is an intuitive graphical analysis method for classification and regression problem solving, where different states are generated by each decision to form a decision tree, top-down from the root node to the leaf nodes to form different paths i.e., different solutions and to find the desired optimal path. In [53], the authors used the classification and regression tree (CART) to predict the traffic flow, which is robust to missing data. In addition to the above common forecasting models, we also compared the traditional ELM, ELM optimized by Genetic Algorithm (GA), and ELM optimized by Gravitational Search Algorithm (GSA). The data recorded in Tables 3 and 4 are the average value of the data obtained by training 100 times under four datasets, A1, A2, A4, and A8. Tables 3 and 4 show the different two evaluation criteria, MAPE and RMSE scores, for each model with the same dataset, respectively. It can be seen that the ABC-ELM model achieves superior scores compared to the other models on all datasets. In Table 3, ABC-ELM performs well compared to the other models in all four datasets. Compared with the traditional ELM model, the MAPE scores decreased by 4.3%, 3.5%, 6.9%, and 5.4% in the same four datasets A1, A2, A4, and A8, respectively. In Table 4, the RMSEs of the ABC-ELM model are 4.8%, 4.0%, 2.0%, and 5.2% lower than the RMSEs of the traditional ELM model at A1, A2, A4, and A8, respectively. It can be seen that the ABC-ELM model not only has the advantages of fast learning of the traditional ELM model but also has superior performance. In addition, compared with the ANN model, the MAPE scores decreased by 9.6%, 8.6%, 9.8%, and 5.0% in the same four datasets A1, A2, A4, and A8, respectively. In addition, the RMSEs of the ABC-ELM model are also 4.5%, 5.9%, 2.6%, and 1.7% lower than the RMSEs of the ANN model, respectively.