Negative sample selection for landslide susceptibility prediction: a hybrid optimization approach using an AHP-KDE multi-ring sampling strategy

• A gradient buffer zone strategy reveals how sample distance affects model performance. • SHAP techniques analyze the spatial heterogeneity of factors in model decisions. • The AHP-KDE multi-ring strategy reduces sample similarity and improves dataset quality. Selecting appropriate negative samples is crucial in landslide susceptibility prediction (LSP), as sampling strategies directly influence model reliability. However, traditional approaches often rely solely on spatial distance, overlooking interval-specific differences and sample representativeness, thereby increasing uncertainty. This study takes Lin’an District, China, as a case, incorporating 12 environmental factors and 163 landslide events. Six sampling intervals were defined at 0.5–1 km, 1–2 km, 2–3 km, 3–4 km, 4–5 km, and 5–6 km around landslide points. Four machine learning models (RF, LR, LightGBM, and MLP) were applied for LSP modeling, and interpretability techniques were used to examine model decision-making under different distance conditions. The analytic hierarchy process (AHP) was employed to evaluate interval significance and guide negative sample allocation, while kernel density estimation (KDE) quantified geographic similarity between positive and negative samples to ensure representative data. Based on these, an AHP–KDE multi-ring sampling framework was established, including interval design, buffer zone weighting, and negative sample selection. Compared with conventional methods, the proposed strategy provides three main advantages: (1) AHP-based buffer zone weighting optimizes sampling and reduces uncertainty; (2) KDE enhances negative sample representativeness and improves dataset quality; and (3) Results demonstrate that the framework effectively overcomes spatial constraints of distance intervals and reduces uncertainty in LSP modeling.