F observations and residuals (Figure eight) showed a slight underestimation of intense higher values, which was standard for many regression models on account of data measurement errors and modeling uncertainties [98]. The residuals presented typical distribution (Figure 9), and their averages were close to zero, indicating minimal bias inside the independent test. The average SHapley Additive exPlanations (SHAP) [99,100] score of each and every covariate was summarized as a measure of function value (Supplementary Figure S1). Offered that the proposed GGHN was a nonlinear modeling method, Pearson’s linear correlation amongst every covariate plus the target variable (PM2.five or PM10 ) couldn’t quantify such a nonlinear relationship. Compared with Pearson’s correlation, the SHAP worth superior quantified the contribution of every single covariate to the predictions. Compared with other seven standard solutions which includes a full residual deep network, regional graph convolution network, random forest, XGBoost, regression kriging, kriging along with a generalized additive model, the proposed geographic graph hybrid network enhanced test R2 by 57 for PM2.five and 47 for PM10 , and independent test R2 by 87 for PM2.5 and 88 for PM10 ; correspondingly, it decreased test RMSE by 119 for PM2.five and 61 for PM10 , and independent test RMSE by 146 for PM2.five and 158 for PM10 . Specifically, although GGHN had education R2 (0.91 vs. 0.92.94) related to or slightly reduced than that of a full residual deep network and random forest, it had AAPK-25 Cancer significantly far better testing and independent testing R2 (0.82.85 vs. 0.71.81) and RMSE (13.874.51 /m3 vs. 15.517.63 /m3 for PM2.five ; 23.544.34 /m3 vs. 24.980.34 /m3 for PM10 ), which indicated much more improvement in generalization and extrapolation than the two strategies. Compared with generalized additive model (GAM), the proposed geographic graph hybrid network achieved the maximum improvement in testing (R2 by 57 for PM2.five and 87 for PM10 ) and independent testing (R2 by 57 for PM2.five and 78 for PM10 ).Table two. Coaching, testing and BSJ-01-175 Purity & Documentation Site-based independent testing for PM2.5 and PM10 . Strategy Geographic graph hybrid network (GGHN) Complete residual deep network Variety Training Testing Site-based independent testing Instruction Testing Site-based independent testing Education Testing Site-based independent testing Coaching Testing Site-based independent testing Instruction Testing Site-based independent testing Instruction Testing Site-based independent testing Coaching Testing Site-based independent testing Education Testing Site-based independent testing PM2.5 R2 0.91 0.85 0.83 0.92 0.81 0.72 0.67 0.66 0.65 0.94 0.79 0.77 0.68 0.67 0.66 0.70 0.72 0.55 0.55 0.54 0.54 0.53 RMSE ( /m3 ) 9.82 13.87 14.51 9.71 15.51 17.63 20.46 20.72 20.98 9.31 17.34 16.35 20.89 21.56 21.69 19.23 18.76 22.98 22.65 27.41 27.34 26.89 R2 0.91 0.84 0.82 0.92 0.81 0.71 0.68 0.65 0.65 0.94 0.78 0.76 0.65 0.65 0.62 0.71 0.70 0.56 0.55 0.42 0.45 0.46 PM10 RMSE ( /m3 ) 17.02 23.54 24.34 16.23 24.98 30.34 33.38 33.39 33.78 14.95 28.87 28.56 34.78 35.78 35.45 30.41 30.03 37.78 38.45 57.92 59.67 47.Local GNNRandom forestXGBoostRegression krigingKrigingGeneralized additive modelRemote Sens. 2021, 13,14 ofFigure 7. Scatter plots between observed values and predicted values ((a) for PM2.5 ; (b) for PM10 ).Figure eight. Scatter plots amongst observed values and residuals inside the site-based independent testing ((a) for PM2.5; (b) for PM10).Figure 9. Histograms with the residuals inside the site-based independent testing ((a) for PM2.5.
