Frequency Ratio–Guided Optimization of Negative Sample Selection and Sample Ratio for Landslide Susceptibility Assessment: A Case Study of the Heishui River Basin, China

In response to the shortage of theoretical support for negative sample selection and the imbalance between positive and negative samples in landslide susceptibility assessment (LSA), this study presents a dual optimization framework of sampling strategy and sample ratio based on the frequency ratio (FR) model and evaluates its performance in the Heishui River Basin using the random forest (RF) model. At the level of negative sample optimization, FR is used to quantify the spatial associations between landslides and environmental factors, delineate non-landslide zones as the source region for negative samples, and systematically compare the performance of five sampling strategies—random, buffer-zone, low-slope, low-density, and FR-optimized sampling. At the level of ratio adjustment, an innovative positive–negative sample ratio model based on the area ratio between susceptible and non-susceptible zones (1:1.3) is proposed, and four additional schemes (1:1, 1:2, 1:2.5, and 1:3) are designed for comparison. The results show that the FR-optimized sampling strategy provides the best discriminative performance, with AUC (area under the curve) = 0.992, Kappa = 0.964, accuracy = 0.982, and F1 score = 0.982, and achieves the highest mean metric value (0.980) and the lowest standard deviation (0.008). The 1:1.3 ratio scheme maintains the highest mean performance (0.982) and the lowest standard deviation (0.007), while yielding the optimal Kappa (0.968) and F1 score (0.982), confirming its advantages in classification balance and model stability. Spatial prediction results indicate that very high and high susceptibility zones are concentrated along both sides of the middle and lower reaches of the Heishui River Basin, occupying only 18.52% of the total area but containing 98.38% of the mapped landslide points, which strongly supports the reliability of the proposed model in identifying landslide risk hotspots. The proposed dual optimization framework not only enhances the robustness of susceptibility mapping but can also be directly applied to risk screening for territorial spatial planning and engineering development in the Heishui River Basin.