## 5 Discussion  
To analyze the disaster factors of the Lishanyuan landslide and determine the precursors of high-speed deformation of the landslide, we used a combination of PSO-optimized k-means clustering algorithm and the Apriori algorithm to mine the association rules of the monitoring data. The analysis results of the mined strong association rules show that the high-speed deformation process of the Lishanyuan landslide is mainly affected by the combination of short-term rainfall of about 1 day, and long-term heavy rainfall of about 3-7 days. A rainfall within 24 h and a heavy rainfall with a cumulative rainfall greater than 130.60 mm within 7 days can be used as a precursor to identify the high-speed deformation of the landslide. Such a precursor can improve the ability of warning.  
The association rule mining algorithm used in this study has the following main advantage. First, we used the sliding window method to extract features in the feature engineering part. This method improves the data utilization by considering continuous data over a period of time comprehensively, compared to considering only the features at the current moment, thus improving the reliability and representativeness of the obtained features. Second, the original k-means clustering algorithm is optimized by using the PSO algorithm, which effectively prevents the clustering results from falling into a local optimal. Third, the k-means algorithm is simple to implement and only requires a given number of clusters, which is easy to quantify. Other clustering methods that do not require specifying the number of clusters often require specifying other hyperparameters that are difficult to quantify. It is more convenient to directly specify the number of clusters for the control of clustering results. Finally, this study is based on real-time monitoring data, whose sampling intervals are hourly or even on the minute scale. Compared with ultra-long-term monitoring data at the monthly scale, it is richer and pays more attention to short-term deformation patterns of landslides, which is of great significance for early warning.  
Additionally, it should be noted that our improvement of the association rule mining method results in an increase in algorithm complexity. On the one hand, we use the PSO algorithm to optimize the k-means clustering process, which is an evolutionary algorithm that requires uninterrupted iterative computation of many potential solutions, which is very complex and time-consuming. On the other hand, the Apriori algorithm for mining association rules needs to scan the entire transaction database when processing frequent candidate sets, which has high algorithm complexity, a huge amount of calculation, and is very time-consuming. With the improvement of technology and the passage of monitoring time, the number of monitored landslides and the volume of data will also increase sharply in the future. It is an inevitable trend to explore simple and fast data mining algorithms.  
In this study, the Apriori algorithm was used to mine association rules. Therefore, the numerical dataset was converted into a category-type transaction database. This method cannot further quantify association rules and is easily affected by clustering results. Meanwhile, the Apriori algorithm does not consider the time series characteristics of item sets in the mining process of association rules, which results in ignoring the influence of sequence pattern in the mining process. Future research needs to explore a data mining method that uses numerical datasets and considers sequential patterns in order to mine more valuable information.