# Landslide Susceptibility Assessment Using the Geographical-Optimal-Similarity Model
## 1 Introduction  
Landslides are among the most common global geohazards, characterised by their concealed nature and devastating power while posing severe threats to lives, property, and urban infrastructure [1]. Landslide susceptibility assessments examine the likelihood, scale, and spatial distribution where landslides occur. Systematic landslide susceptibility assessments optimise resource allocation, mitigate direct landslide losses, and play precautionary and guiding roles in disaster emergency management [2]. Single-method landslide susceptibility assessments primarily include knowledge-driven qualitative and physics- or data-driven quantitative analysis methods [3]. Meanwhile, data-driven assessment methods mainly include mathematical, statistical, and machine learning methods [4]. Landslide susceptibility is investigated using mathematical statistical methods, which establish linear relationships between geographic factors and landslides, such as the Bayesian method [5] and the information value (IV) model [6]. The IV model is frequently used in landslide susceptibility assessments because of its simplicity, low data requirements, and strong utility, especially compared to physically based and machine learning methods [7]. However, the linear assumptions of the IV model prevent it from capturing nonlinear relationships or accounting for spatial correlations between variables, thus overlooking the function of spatial features in landslide susceptibility [8]. Therefore, researchers have integrated the IV model with other approaches to refine assessment accuracy and stability [9; 10; 11; 12], enabling an evaluation incorporating spatial features and nonlinear relationships [3; 13; 14; 15]. In contrast, machine learning methods leverage their strong nonlinear fitting capabilities to automatically identify landslide features and assess susceptibility [16]. Common techniques include random forests (RF), logistic regression (LR), and radial basis function classifiers (RBFC) [17; 18]. Previous studies have compared the performance of LR and RF models in predicting shallow landslide susceptibility in northeast Sicily, highlighting their excellent predictive capabilities [19]. Land use and wildfire were found to be essential factors affecting landslide occurrence. In addition, methods like LR and RBFC have been used for flash flood susceptibility mapping in Nghe An Province, Vietnam [20]. Unlike qualitative methods, data-driven susceptibility assessments offer higher predictive accuracy but demand higher data precision, especially in machine learning methods, which tend to lack interpretability [21]. However, due to restrictions in the accuracy of historical landslide data and the acquisition of standard landslide characteristics, earlier landslide susceptibility assessment methods have inadequately considered the effects of geographical attribute similarity on landslides. Correspondingly, research on the relationship between region-specific landslide geographic-configuration-attributes similarity and susceptibility assessment has also been inadequate [22]. The proposal of geographical similarity theory advances a novel strategy to solve this issue. Geographical similarity suggests that when geographic attributes are similar in separate locations, the geographical structures of those locations are also alike [23]. Because landslides are typically influenced by various environmental factors, a similar geographic environment implies a comparable likelihood of landslide occurrence. Data-driven geographical similarity models can comprehensively account for multiple environmental factors, especially in complicated environments, to infer landslide risk in unknown areas via similar geographical attributes. However, conventional geographical similarity models have limitations in modelling accuracy and speed. To overcome these challenges, researchers have developed a geographical-optimal-similarity (GOS) model based on spatial statistical inference, utilising geographical similarity principles in the inference process.