A Statistical-Physical Prior-Guided Framework for Multi-Class Landslide Susceptibility Mapping

Abstract. Regional landslide susceptibility mapping generally treats landslide/non-landslide discrimination as a binary learning task and subsequently divides predicted probabilities into several qualitative classes. This two-stage strategy does not directly represent the susceptibility gradient and may therefore reduce the spatial concentration of historical landslides within the very high susceptibility zone. This study proposes a statistical-physical prior-guided framework for direct five-class landslide susceptibility mapping along the Ancient Qin-Shu Roads in the Qinling-Daba Mountains. A landslide inventory containing 1,407 records and 14 conditioning factors was compiled. First, certainty factor (CF) analysis was used to generate a initial susceptibility map. The Shallow Landsliding Stability model (SHALSTAB) was then introduced to provide a physically meaningful stability mask with which the zonation was corrected and samples of very high, high, moderate, low, and very low susceptibility were constructed. Logistic regression (LR), support vector machine (SVM), extreme gradient boosting (XGBoost), random forest (RF), Feature Tokenizer Transformer (FT-Transformer), and Tabular Prior-Data Fitted Network (TabPFN) were compared under binary and multi-class settings. The results show that RF performed well in both tasks, attaining an area under the receiver operating characteristic curve (AUC) of 91.08 % for binary classification and 92.53 % for multi-class classification. In the binary result, the landslide-prone zone occupied 19.3 % of the study area and contained 87.3 % of the historical landslides, yielding a Hit Optimization Index (HOI) of 1.68. In the corresponding multi-class result, the very high susceptibility zone occupied only 13.5 % of the study area while containing 91.8 % of the historical landslides, with an HOI of 1.78. These findings indicate that multi-class learning provides greater historical-landslide coverage and spatial concentration. Compared with labels derived from CF alone, the SHALSTAB-constrained scheme increased accuracy from 65.05 % to 68.60 %, AUC from 91.30 % to 92.53 %, and HOI from 1.72 to 1.78, demonstrating that physical constraints can improve susceptibility zonation. Shapley additive explanations (SHAP) showed that elevation, land use and land cover (LULC), and distance to roads were the three principal controls on identification of very high susceptibility zones.