An InSAR Time-Series Constrained PU-Learning Framework for Landslide Susceptibility Mapping in Karst Regions: Negative-Sample Optimization and Enhanced Spatial Consistency

Landslides are among the most destructive geological hazards in mountainous regions, and are particularly clustered and persistently active in karst areas due to intense karstification, highly dissected topography, and weak slope materials. In existing landslide susceptibility assessments, negative samples are commonly selected using random or empirical strategies, which can mislabel potentially unstable slopes as stable terrain, introduce label noise, and ultimately degrade both model accuracy and physical consistency. To address this issue, we propose a landslide susceptibility assessment framework for karst regions (InSAR–PU) that tightly integrates deformation constraints from interferometric synthetic aperture radar (InSAR) time series with a Positive–Unlabeled (PU) learning–based negative-sample optimization strategy, and explicitly identifies and constrains label uncertainty in negative samples during sample construction to improve the quality of the negative-sample set and the reliability of susceptibility estimates. A typical karst landscape in Longsheng Various Nationalities Autonomous County, Guilin, Guangxi, China, is selected as the study area. In this area, surface deformation rates from 2019 to 2023 are derived using SBAS-InSAR; low-deformation domains are treated as unlabeled samples, and a Bagging-PU scheme is employed to obtain a high-confidence negative-sample set. Six machine-learning models are used to conduct comparative experiments under three negative-sample strategies: random sampling, buffer-based sampling, and the proposed InSAR–PU approach. The InSAR–PU strategy significantly improves classification performance and stability, with all area under the ROC curve (AUC) values exceeding 0.80; the InSAR–PU-RF model achieves an AUC of 0.867 and an overall accuracy (OA) of 86.7%, representing improvements of 4.5% and 2.2% over random and buffer-based sampling, respectively. Shapley Additive Explanations (SHAP) analysis shows that higher-quality negative samples lead to more stable model responses and clearer contributions of key controlling factors such as rainfall, slope, curvature, and distance to roads. A deformation–susceptibility contingency matrix further indicates higher spatial consistency between InSAR–PU predictions and InSAR-derived deformation patterns, while field investigations confirm that time-series deformation signals in typical areas agree with in situ observations. In summary, InSAR–PU provides a transferable negative-sample optimization strategy for landslide susceptibility mapping in complex karst regions, improving predictive accuracy and enhancing the spatial consistency and physical credibility of the results.