A Dual-Space Comprehensive Similarity Framework for Spatial Prediction: Integrating Environmental Feature Similarity and Geographic Proximity

Abstract

Spatial prediction requires determining how sampled observations support estimates at unsampled locations. Existing methods commonly represent these relationships in geographic space, environmental feature space, or through a global statistical relationship between predictors and the target property. We propose a dual-space comprehensive similarity (CS) framework that combines target-oriented environmental similarity (ES) with geographic spatial proximity (SP). ES uses partial least squares screening and principal component transformation, whereas SP derives from scaled geographic distance. Their product gives high influence only to observations supported in both spaces. We embedded CS in individual predictive soil mapping (iPSM), creating iPSM-CS, and evaluated it using 547 soil organic carbon density observations from the Tibetan Plateau. Repeated experiments were conducted using training datasets of 100, 200, and 400 samples, with an independent 27-sample validation set and a 20-sample test set. The 500-sample scenario was evaluated separately using fixed neighbourhood sizes determined before final testing. Across the three repeated sample-size scenarios, iPSM-CS generally produced higher correlation coefficients (r) and lower root mean square error (RMSE) and mean absolute error (MAE) values than iPSM-ES and the benchmark models. In the 500-sample evaluation, iPSM-CS achieved r = 0.79, RMSE = 2.44 kg·m−2, and MAE = 1.93 kg·m−2, compared with r = 0.55, RMSE = 3.34 kg·m−2, and MAE = 2.52 kg·m−2 for iPSM-ES. Top-1 CS and Top-1 ES were significantly negatively associated with relative prediction error in the independent test set, while CS provided a clear stratification of errors across the predefined similarity intervals. The results support the use of dual-space similarity for spatial prediction, although its transferability requires evaluation across additional regions, attributes, and spatial validation designs.