## 1 Introduction  
A landslide is a common type of geological disaster in mountainous areas worldwide, often causing massive casualties and economic losses [1, 2, 3]. As human activities intensify and extreme climate events occur more frequently, landslides pose increasingly serious hazards [4, 5, 6, 7]. Landslides have a wide distribution range and are highly sudden, posing serious challenges to disaster prevention and control [8, 9, 10]. Landslide risk assessment (LRA) is an important prerequisite for land use planning and actions of disaster risk reduction [11]. In recent years, it has also increasingly attracted the attention of researchers and government departments.  
The landslide risk is commonly defined as the expected value of the losses caused by landslides to people's lives, property, and economic activities in a specific area and during a specific period [12]. It possesses both disaster and social attributes, typically quantified as the product of landslide hazard and vulnerability [6]. Landslide hazard assessment (LHA) is the core procedure of LRA studies [13]. In existing studies, the landslide hazard usually represents the probability of a landslide event occurring in a certain area within a certain period of time [14]. At present, the most commonly used regional LHA models include heuristic models (such as the analytic hierarchy process (AHP)) [15; 16; 17], statistical models (such as the frequency ratio (FR) and statistical index (SI)) [18; 19; 20], and machine learning models (such as random forest (RF) and support vector machine (SVM)) [21; 22; 23; 24]. These models can analyze the relationships between the landslide occurrence and predisposing factors involving geomorphology, geology, hydrology, and land cover [11].  
Among these models, the FR method is computationally simple and can clearly reflect the correlations between predisposing factors and landslide occurrence [22]. Therefore, it is widely applied in LHA studies. Moreover, in combination with other models, it is often used as the input variable when calculating the landslide hazard index (LHI) [19; 20]. However, the FR method does not take into account the phenomenon of landslide spatial aggregation, resulting in high uncertainty in its analysis results. In nature, the internal and external dynamic factors affecting the spatial distribution of landslides are anisotropic [25; 26]. This leads to the existence of various degrees of landslide spatial aggregation in different regions. As a result, it is unreasonable to directly apply the FR method in the establishment of an LHR model without considering the spatial aggregation of landslides. This problem is very common in studies using the FR method. Additionally, some researchers have proposed quantitative indicators such as the CLAI to improve the FR method by quantitatively analyzing landslide spatial aggregation [19; 20; 21; 22]. However, these indicators often ignore the differences in the coverage of predisposing factor classes, resulting in the uncertainty of the LHR model. In view of this situation, we propose the dual-frequency ratio (DFR) method, considering the spatial aggregation of landslides. It has shown excellent application effects in the LHR study of the northwestern region of China [20].  
In this study, we applied the proposed DFR method to an LRA study in the section of the Karakoram Highway (KKH) between Kashi and Khunjerab. By combining the selected 10 predisposing factors and 356 landslide points, we used the original FR method and the DFR method to create spatial datasets for the LHA model. On this basis, we adopted the AHP model and RF model to generate landslide hazard maps. Based on the receiver operating characteristic (ROC) curve and the distribution characteristics of the LHIs, we evaluated the LHA model adopted in this study. Finally, the results of the LHA model with the best prediction performance were used to calculate the landslide risk in the study area.