## 6 Conclusions  
In this study, considering landslide spatial aggregation, we proposed the DFR method to establish the connection between landslide occurrence and predisposing factors. Furthermore, the DFR method was applied to an LHA study in the section of the KKH between Kashi and Khunjerab, based on the AHP and RF models. Finally, a landslide risk map of the study area was generated with the landslide hazard and vulnerability. The new findings and main conclusions of this study are as follows:  
1. The DFR method can effectively quantify the degree of landslide spatial aggregation and has a good application effect. Based on the ROC curve and distribution patterns of the LHIs, the model evaluation indicates that the DFR method can practically improve the prediction performance of LHA models.
2. Compared with the AHP model, the RF model has higher accuracy in this study. Furthermore, the prediction performance of the DFR-RF model is the best. The landslide hazard map generated by a single type of LHA model often has high uncertainty, and it is better to comprehensively analyze the performance of multiple LHA models to determine the final LHIs.
3. The coverage of zones with high and very high landslide risks is very small, and they are mainly distributed along the roads on the southern side of Aoyitake Town. The zones with medium landslide risks are largely concentrated in the Gaizi River valley between Aoyitake and Bulunkou, and some are also found around Dabudaer and the county town of Taskorgan. Our research provides a reference for local disaster risk prevention and control.  
Conceptualization, X.Y. and Y.S.; methodology, Y.S.; software, X.Y.; validation, Q.M. and H.M.; formal analysis, X.Y.; investigation, Y.S., X.Y., P.S. and I.A.; resources, X.Y.; data curation, Y.S.; writing--original draft preparation, X.Y.; writing--review and editing, Y.S.; project administration, Y.S.; funding acquisition, Y.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Science and Technology Partnership Program of the Shanghai Cooperation Organization and International Science and Technology Cooperation Program, the Xinjing Department of Science and Technology (Grant No. 2023E01005), the Third Xinjiang Scientific Expedition Program (Grant No. 2022 xjdk1305) and the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019 QZKK0904).  
Not applicable.  
The original contributions presented in this study are included in this published article, and further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
AHP Analytic hierarchy process  
AUC Area under the curve  
CI Consistency index  
CR Consistency ratio  
DFR Dual-frequency ratio  
FR Frequency ratio  
GDP Gross domestic product  
KKH Karakoram Highway  
LHA Landslide hazard assessment  
LHI Landslide hazard index  
LRA Landslide risk assessment  
NDVI Normalized difference vegetation index  
PF Predisposing factor  
PGA Peak ground acceleration  
RF Random forest  
RI Random index  
ROC Receiver operating characteristic  
VF Vulnerability factor