A novel grey prediction model based on tensor higher-order singular value decomposition and its application in short-term traffic flow

Short-term traffic flow prediction is the key to traffic guidance and control and can directly affect the performance of intelligent transportation systems. Traffic flow data has the characteristics of volatility, chaos, and randomness, which affect the accuracy of the prediction model. Based on the multi-dimensional spatio-temporal data characteristics of traffic flow data, this paper combines the tensor higher-order singular value decomposition theory and the modeling mechanism of the classical grey model GM(1,1) model and establishes the grey GM(1,1) model with tensor higher-order singular values. The tensor higher-order singular value decomposition reflects the periodic, multi-modal, and holistic nature of traffic flow data, which can mitigate the volatility and randomness of traffic flow data and improve the accuracy of the model. Then, the new model is applied to highway short-time traffic flow prediction, analyzing the spatio-temporal nature of traffic flow data, giving the detailed steps of model modeling, and analyzing the correlation between the original traffic flow data and tensor approximation data using grey correlation degrees. There are three cases to illustrate the effectiveness of the model. Case 1 shows that the results of MAPE from nine modeling objects are stable at about 5%, which indicates that the new model has some stability; Case 2 shows that the new model is more adaptable to short-time traffic flow prediction based on the results of three different modeling and prediction objects; Case 3 uses the new model to compare it with two traditional grey forecasting models and two optimization models, and the results indicate that the new model has a total MAPE value of 5.172%, which is better than the other four grey forecasting models. Finally, the new model is applied to short-time traffic flow prediction, and its prediction results are consistent with the trend of the original traffic flow data, indicating that it can reveal the real-time characteristics of the traffic system to a certain extent and provide a reliable theoretical basis for traffic planning, control, and optimization.