Near-surface PM2.5 prediction combining the complex network characterization and graph convolution neural network

Abstract

Massive studies focus on the prediction of main pollutants, to improve air quality by revealing the evolution of pollutants. However, existing prediction methods mostly emphasize the fitting analysis of time series, but ignore the spatial propagation effect among nearby places, resulting in a low prediction accuracy. To address this issue, this paper proposes a novel synthesis prediction method to simultaneously excavate the time series changing law and the spatial propagation effect. This method combines a characterization model named air quality spatial-temporal network (AQSTN) and a neural network model called graph convolution neural network (GCN). Firstly, by calculating three correlation coefficients, the time series of most related meteorological factors and aerosol data are gained for feature construction. The geographic distances between locations are computed to evaluate the spatial propagation cost. After that, AQSTN with locations as nodes and propagation relations as edges is constructed, compositing the temporal and spatial relationships. The network is regarded as graph data and input into GCN in chronological order. Secondly, GCN processing graph-structured data fits the optimal parameters in the training stage, simultaneously analyzes the spatial and temporal dimensions of the target site and its adjacent sites. And, the predicted ${\rm{PM}}_{2.5}$ concentration is gained in the test stage. The near-surface monitoring data of Beijing-Tianjin-Hebei area are adopted for experiment. Compared with the second-best model, the RMSE value of AQSTN-GCN is 6.85% lower, MAE value is 13.79% lower, MSE value is 13.23% lower, and MAPE value is 21.53% lower.

Appendix. The complex network

A complex network [52,53,54] can be regarded as a set of individuals, which have independent characteristics and are interconnected with each other. In this set, each individual can be regarded as a node in the graph, and the interconnection between nodes can be regarded as an edge in the graph. A simple undirected unweighted network can be denoted by G(V, E). Here, $V=\left\{ v_1, v_2, \dots , v_N\right\}$ is the node set, and $E=\left\{ e_1, e_2, \dots , e_M \right\}$ is the edge set. Each edge corresponds to a tuple of nodes, that is $e_x=\left\{ v_i,v_j \right\}$. Normally, any complex system that contains a large number of constituent units (or subsystems) can be studied as a complex network when the constituent units are abstracted into nodes and the interactions between the units are abstracted into edges [55,56,57,58,59,60]. Complex networks generally have the following three characteristics (Fig. 14).

Small world Despite the large scale, most networks can find a fairly short path between any two nodes. Simply speaking, there exits the fact that a single node that have a small number of interrelationships with others can connect the whole world. Supposing that the distance between two nodes $v_i$ and $v_j$, marked as $d_{ij}$, is equal to the number of edges in the shortest path connecting the two nodes, the average distance in graph G(V, E) can be expressed as $\left\langle d \right\rangle =\frac{1}{N(N-1)}\sum _{i\ne j}d_{ij}$ where N is the number of nodes. Then, if the average degree is fixed, the network is considered to have a small-world effect when the average distance increases at or less than the logarithmic rate following the growth of the number of nodes.

Fig. 14

The diagram of communities of the complex network

Scale-free p(k) is defined as the proportion of the number of nodes with the degree of k in the network to the total number of nodes, namely the degree distribution of nodes. The empirical study shows that the degree distribution of complex networks approximately follows the form of power function, i.e., $p(k)\propto k^ {-\gamma }$. Here, $\gamma$ is the power exponent. Since the function has the invariant power exponent, such networks are called scale-free networks. The power function decays slowly, allowing the existence of some high-degree nodes (pivot nodes), which have a critical impact on the overall structure and function of the network.

Community structure Intuitively speaking, community structure means that the network consists of many communities, with close boundaries within communities and few boundaries between communities, as shown in Fig. 12. The most widely used measure of community is called Modularity. Modularity is essentially a description of the extent to which a real network has more internal edges than the corresponding random network, defined as $Q=\frac{1}{2M} \sum _{i\ne j}\left( A_{ij}-\frac{k_ik_j}{2M} \right) \delta ^{ij}$. Here, A is adjacency matrix, M is the total number of edges. If node $v_i$ and node $v_j$ belong to the same community, $\delta ^{ij}=1$, otherwise 0.