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<p>Predicting continuous environmental variables from sparse spatial observations remains challenging because global machine learning models can capture nonlinear relationships but often have limited ability to adapt to local spatial heterogeneity, whereas existing similarity-based methods still rely mainly on weighted-average prediction. This study proposes Pattern Similarity Learning (PSL), which uses pattern similarity as a spatially adaptive indicator to guide local nonlinear prediction. PSL first augments the original environmental covariates with three pattern-derived indicators: geocomplexity, positive outlier strength, and negative outlier strength. These indicators describe local heterogeneity and local anomalousness, allowing each covariate to carry both its original value and its local spatial context. For each target location, PSL then measures covariate-space similarity to identify relevant training samples and fits a similarity-weighted local Random Forest using the pattern-enhanced features. In a soil organic carbon prediction case across the conterminous United States (CONUS), five-fold spatial cross-validation shows that PSL achieved the best overall pooled performance among the six models. Compared with Random Forest, PSL increased R² by 0.017 (7.11%), reduced RMSE by 0.017 (1.14%), and reduced MAE by 0.012 (1.69%). These results suggest that using pattern similarity to link local spatial context, sample relevance, and nonlinear learning can improve the spatial adaptability of continuous environmental prediction.</p>

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Pattern Similarity Learning for Spatially Adaptive Soil Organic Carbon Mapping

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月18日

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  • Haiyang Liu,
  • Yongze Song,
  • Pengcheng Zhang,
  • Ning Yang

摘要

Predicting continuous environmental variables from sparse spatial observations remains challenging because global machine learning models can capture nonlinear relationships but often have limited ability to adapt to local spatial heterogeneity, whereas existing similarity-based methods still rely mainly on weighted-average prediction. This study proposes Pattern Similarity Learning (PSL), which uses pattern similarity as a spatially adaptive indicator to guide local nonlinear prediction. PSL first augments the original environmental covariates with three pattern-derived indicators: geocomplexity, positive outlier strength, and negative outlier strength. These indicators describe local heterogeneity and local anomalousness, allowing each covariate to carry both its original value and its local spatial context. For each target location, PSL then measures covariate-space similarity to identify relevant training samples and fits a similarity-weighted local Random Forest using the pattern-enhanced features. In a soil organic carbon prediction case across the conterminous United States (CONUS), five-fold spatial cross-validation shows that PSL achieved the best overall pooled performance among the six models. Compared with Random Forest, PSL increased R² by 0.017 (7.11%), reduced RMSE by 0.017 (1.14%), and reduced MAE by 0.012 (1.69%). These results suggest that using pattern similarity to link local spatial context, sample relevance, and nonlinear learning can improve the spatial adaptability of continuous environmental prediction.