F observations and residuals (Figure eight) showed a slight underestimation of intense high values, which

F observations and residuals (Figure eight) showed a slight underestimation of intense high values, which was typical for most regression models resulting from data measurement errors and modeling uncertainties [98]. The residuals presented typical distribution (Figure 9), and their averages were close to zero, indicating minimal bias within the PSB-603 Epigenetic Reader Domain independent test. The typical SHapley Additive exPlanations (SHAP) [99,100] score of each and every covariate was summarized as a measure of function significance (Supplementary Figure S1). Given that the proposed GGHN was a nonlinear modeling system, Pearson’s linear correlation involving each covariate and the target variable (PM2.5 or PM10 ) couldn’t quantify such a nonlinear connection. Compared with Pearson’s correlation, the SHAP worth better quantified the contribution of each covariate towards the predictions. Compared with other seven common methods including a complete 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 improved test R2 by 57 for PM2.5 and 47 for PM10 , and independent test R2 by 87 for PM2.five 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 . Specially, while GGHN had instruction R2 (0.91 vs. 0.92.94) Icosabutate Epigenetics equivalent to or slightly decrease than that of a full residual deep network and random forest, it had significantly greater 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 additional improvement in generalization and extrapolation than the two procedures. Compared with generalized additive model (GAM), the proposed geographic graph hybrid network accomplished the maximum improvement in testing (R2 by 57 for PM2.5 and 87 for PM10 ) and independent testing (R2 by 57 for PM2.five and 78 for PM10 ).Table 2. Training, testing and site-based independent testing for PM2.five and PM10 . Strategy Geographic graph hybrid network (GGHN) Full residual deep network Form Instruction Testing Site-based independent testing Education Testing Site-based independent testing Training Testing Site-based independent testing Education Testing Site-based independent testing Education Testing Site-based independent testing Instruction Testing Site-based independent testing Instruction Testing Site-based independent testing Training 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.Neighborhood 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 8. Scatter plots among observed values and residuals inside the site-based independent testing ((a) for PM2.5; (b) for PM10).Figure 9. Histograms of your residuals inside the site-based independent testing ((a) for PM2.five.