Typical correlation analysis of test data.

In response to the problem that current multi-city multi-pollutant prediction methods based on one-dimensional undirected graph neural network models cannot accurately reflect the two-dimensional spatial correlations and directedness, this study proposes a four-dimensional directed graph model that can capture the two-dimensional spatial directed information and node correlation information related to multiple factors, as well as extract temporal correlation information at different times. Firstly, A four-dimensional directed GCN model with directed information graph in two-dimensional space was established based on the geographical location of the city. Secondly, Spectral decomposition and tensor operations were then applied to the two-dimensional directed information graph to obtain the graph Fourier coefficients and graph Fourier basis. Thirdly, the graph filter of the four-dimensional directed GCN model was further improved and optimized. Finally, an LSTM network architecture was introduced to construct the four-dimensional directed GCN-LSTM model for synchronous extraction of spatio-temporal information and prediction of atmospheric pollutant concentrations. The study uses the 2020 atmospheric six-parameter data of the Taihu Lake city cluster and applies canonical correlation analysis to confirm the data’s temporal, spatial, and multi-factor correlations. Through experimentation, it is verified that the proposed 4D-DGCN-LSTM model achieves a MAE reduction of 1.12%, 4.91%, 5.62%, and 11.67% compared with the 4D-DGCN, GCN-LSTM, GCN, and LSTM models, respectively, indicating the good performance of the 4D-DGCN-LSTM model in predicting multiple types of atmospheric pollutants in various cities.