# An Attention-Based Deep Convolution Network for Mining Airport Delay Propagation Causality
## 2 Problem Formulation
As shown in Figure 2, the delay propagation between airport \(i\) and airport 1 is one-way, between airport \(i\) and airport \(j\) it is two-way, and there is no delay propagation between airport \(1\) and airport \(j\). Figure 1: Airport delay propagation causality. (**a**) No causation; (**b**) Direct causation; (**c**) Indirect causation; (**d**) Both direct and indirect causation. To construct the direct causality network of airport delay propagation as shown in Figure 2, the biggest challenge is how to distinguish direct causality from correlation, indirect causation, and confounding causality:  
1. How to distinguish causality from correlation. The correlation is a mutual relationship between the delays of two airports, which means that the delay of one airport changes and the other airport also changes. It can be a positive correlation or a negative correlation. The \"cause\" airport and the \"effect\" airport in the causal relationship pair of airport delay propagation often show correlation, which can be regarded as a special kind of correlation. Cause and effect are directional, and changes to the cause affect the outcome. Therefore, in order to distinguish the causal relationship from the correlation relationship, it is necessary to observe the delay changes of the \"effect\" airport after a certain period of time by controlling the delay changes of the \"cause\" airport. 2. How to distinguish direct causation from indirect causation. As shown in Figure 2, the delay at the airport will not directly cause the delay at airport 1, but the delay may be propagated to airport 1 through airport \(i\), so there is an indirect causal relationship between airport \(N\) and airport 1. Recently, some researchers used Granger causality [15; 31] and transfer entropy [32] to judge whether there is a causal relationship between airport pairs and build an airport delay causality network according to the causal relationship between airport pairs. Since the airport network is not treated as a whole when judging causality, it is difficult to find indirect causality. Therefore, in order to better distinguish direct and indirect causality, it is necessary to take all airports into consideration when constructing a causal relationship mining model. 3. How to measure the influence degree and propagation delay time of multiple \"cause\" airports on the same \"effect\" airport. Delays at an airport are often the result of the combined action of multiple airports, including delays at the airport itself. Therefore, this causality is also called confounding causation. Figure 3 is a schematic diagram of multiple airports acting on the same airport. If the delays of airport A, airport B, and airport C are propagated to airport Z simultaneously, then airport A, airport B, and airport C are the \"cause\" airports of airport Z. It should be noted that due to the specific differences between the three \"cause\" airports and the \"effect\" airport Z, there will be differences in the delay time of delay propagation. For example, if the distance from airport A to airport Z is farther than the distance from airport B to  
Figure 2: Direct causal network of airport delay propagation. The delay of airport \(v_{i}\) is transmitted unidirectionally to airport \(v_{1}\), while there is a bidirectional delay propagation relationship between \(v_{i}\) and \(v_{j}\). airport Z, then delays from airport A will take longer to propagate to airport Z than delays from airport B will take to propagate to airport Z. In Figure 3, there is a closed loop at airport Z, which means delays in past time periods at airport Z itself affect subsequent time periods.