Application of a semi-variogram-based KNN algorithm in the spatial prediction of soil heavy metals

Precise mapping of soil heavy metal distribution is essential for environmental risk assessment and pollution remediation. However, the accuracy of traditional prediction methods remains constrained when facing the sparse monitoring samples and high data variability. To improve prediction accuracy with limited samples, this study integrates geostatistical principles to refine the traditional K-nearest neighbors (KNN) algorithm, leveraging a semi-variogram to guide both weight allocation and K-value optimization. The improved method was applied to the spatial interpolation prediction of soil heavy metals in an industrial plot in northern China and was compared with other conventional methods. The results showed that semi-variogram-based KNN(SV-KNN) model outperformed traditional models such as the inverse Distance Weighting method (IDW), Ordinary Kriging (OK), KNN, the Distance-Weighted KNN (DW-KNN) and Random Forest (RF) in terms of accuracy and stability. The SV-KNN model demonstrated a reduction in Root Mean Square Error (RMSE) by an average of 18.33 %, 17.08 % and 4.78 % for Lead (Pb), Cadmium (Cd), and Arsenic (As) respectively. Concurrently, the coefficient of determination (R²) showed an average increase of 103.70 %, 39.06 % and 113.12 % for Pb, Cd and As, respectively. Wilcoxon significance tests further confirmed that SV-KNN exhibited statistically superior performance over methods in most cases. This indicates that SV-KNN is a more robust and accurate predictive tool for soil heavy metals mapping and pollution assessment.