# An Attention-Based Deep Convolution Network for Mining Airport Delay Propagation Causality
## 3 Methodology
### Causality Verification
#### 3.3.3 Direct Causality Verification Based on Propagation Delay Analysis  
In order to construct a delayed propagation direct causality network, it is necessary to further distinguish direct causality and indirect causality. As shown in Figure 1d, there are two causal paths, \(\mathrm{A}\to\mathrm{B}\) and \(\mathrm{A}\to\mathrm{C}\to\mathrm{B}\), from the \"cause\" airport A to the \"effect\" airport B. The next question is how to judge that the path \(\mathrm{A}\to\mathrm{B}\) is a direct causal path. Obviously, if the propagation delays of paths \(\mathrm{A}\to\mathrm{C}\) and \(\mathrm{C}\to\mathrm{B}\) are smaller than the propagation delays of \(\mathrm{A}\to\mathrm{B}\), then the causal path \(\mathrm{A}\to\mathrm{B}\) can be ruled out as a direct causal relationship. This is because, if there is a direct causal relationship, then the delay time of airport A's delay propagating to airport B must be less than the delay time of airport A's delay propagating to B after the third airport C. For example, the delay propagation from airport A to airport C is 90 min, and the delay propagation from airport C to airport B is 100 min. While the propagation delay from airport A to B is 200 min, it is certain that \(\mathrm{A}\to\mathrm{B}\) is not a direct causal relationship. Furthermore, the delay time for delay propagation is proportional to the flight time. If the delay propagation delay time between two airports is too long, then it can be concluded that the airport causality pair is not direct causality. For example, if the flight time from airport A to airport B is 70 min, and the average airport delay time is 30 min, then the delay propagation delay time cannot exceed 100 min. Based on the above ideas, the following judgments are made on the direct causality and the indirect causality based on the propagation delay. Figure 9 is a flow diagram of direct causality verification based on propagation delay analysis. Figure 8: One-tailed \(t\)-distribution. Let P be the set of airport delay propagation causal relationship pairs. First, delete causal relationship pairs whose delayed propagation delay time is greater than a given threshold, and obtain a set of candidate direct causal relationship pairs \(\overline{\text{P}}\). The specific judgment basis is: for any causal relationship pair \(v_{i}\to v_{j}\) in P, compare the delayed propagation delay time \(d(v_{i}\to v_{j})\) with the given threshold \(d_{0}(v_{i}\to v_{j})\). * If \(d(v_{i}\to v_{j})\geq d_{0}(v_{i}\to v_{j})\), then \(v_{i}\to v_{j}\) is not a direct causal path and should be removed from P;
* if \(d(v_{i}\to v_{j})<d_{0}(v_{i}\to v_{j})\), then \(v_{i}\to v_{j}\) is a candidate direct causality path, which needs to be further verified. The setting of the delay time threshold \(d_{0}\) depends on the \"cause\" airport delay and the flight time between airports. Further, the causal relationship pairs in the set \(\overline{\text{P}}\) need to be verified, that is, a direct causal relationship network of candidate delay propagation is constructed based on the set \(\overline{\text{P}}\). The edges in the network are further removed according to the delay time, and the final delay propagation direct causality network is obtained. The basic idea of deleting edges according to the delay time is: for any edge \(v_{i}\to v_{j}\) in the network, search all paths with \(v_{i}\) as the starting point and \(v_{j}\) as the ending point. If the delay time of \(v_{i}\to v_{j}\) is the smallest, then \(v_{i}\to v_{j}\) is a direct causal relationship; otherwise, it is not a direct causal relationship. The verification according to this idea belongs to a kind of exhaustive method, and the calculation efficiency is relatively low. In fact, as long as the path with the minimum delay time is found, if this path is the edge itself that needs to be verified, a judgment can be made.