# Spatial Autocorrelation Incorporated Machine Learning Model for Geotechnical Subsurface Modeling
## 3 Machine Learning Model Prediction Results and Discussion  
### Performance Evaluation of Constructed Machine Learning Models  
Before comparing the model performance, retransformation of the predicted data was performed. The value predicted from machine learning was still in the transformed form, as the result of data transformation explained in Section 2.3.2. Therefore, the predicted value needs to be transformed back into the real form. The formulae to retransform the prediction value are explained in Equations (16) and (17). \[s_{RT}=s_{pred}\times(s_{min}-s_{max})+s_{max}, \tag{16}\]  
\[s_{RT}=10^{s_{pred}}-1, \tag{17}\]  
where \(s_{RT}\) is the retransformed predicted value, \(s_{pred}\) is the direct output prediction value from machine learning, \(s_{min}\) is the minimum value of variable \(v\) and \(s_{max}\) is the maximum value of variable \(v\). Equation (16) is utilized to retransform predicted ground surface elevation, groundwater level, and percent finer than 0.075 mm sieve, while Equation (17) is utilized to retransform the predicted SPT-N value. Next, the performance of machine learning with the EDF and XY coordinate modeling approach is discussed. The performance of the models developed in this study are quantified by RMSE and MAE score. Figure 6 presents the RMSE and MAE score for all constructed regression models, respectively. First, the model performance for ground surface elevation prediction is analyzed. Looking for the lowest RMSE score, the GSE_GPR_EDF_90 (best EDF model) has slightly lower error compared to the GSE_GPR_XY_90 (best XY model) and GSE_GPR_EDFB (EDFB model), with 0.215, 0.221, and 0.289 RMSE score, respectively. Figure 6: _Cont._  
In a similar way, we can identify the best-performing regression models for other targets. The GWL_GPR_EDF_90 and FINER_GPR_EDF_NOPCA show the best EDF model performance for predicting groundwater level and percent finer than 0.075 mm sieve, respectively. There is disagreement for the model with the lowest error for the SPTN prediction, where the SPTN_ANN_EDF_80 model has the lowest RMSE score and SPTN_ANN_EDF_90 has the lowest MAE score. This result indicates that the prediction by SPTN_ANN_EDF_80 model has less large prediction error compared to the error SPTN_ANN_EDF_90 model. This study prefers to tolerate a lower prediction error instead of a lower overall error with several large error values. Therefore, the model with the lower RMSE value is considered to be better. Therefore, the SPTN_ANN_EDF_90 model is considered to be the best-performing model. Overall, the machine learning model with EDF approach shows lower RMSE score by 0.041, 0.046, 1.302, and 1.561 for ground surface elevation, groundwater level, SPT-N value and percent finer than 0.075 mm sieve, respectively, compared to the direct XY coordinate approach. The performance of classification models can be evaluated from the prediction accuracy of the models as presented in Figure 7. The EDF, XY, and EDFB models show high prediction performance identified by the high level of prediction accuracy. All models predict USCS-based soil classification with lowest accuracy level at 96.39% (SC_SVM_EDF_80), which is satisfactory. This result shows that all modeling approaches can be applied interchangeably for USCS-based soil classification in the study area. Detailed look at the performance of each best-performing machine learning model from the EDF, XY, and EDFB approach is achieved by analyzing Figure 8. This figure shows the comparison of predicted values with the observed value from the test data. The GSE_GPR_EDF_90 model for predicting ground surface elevation shows an acceptable prediction with the highest error not exceeding 0.3 m. The highest error noticed from GSE_GPR_XY_NOPCA and GSE_GPR_EDFB model prediction is slightly above 0.4 m and 0.5 m, respectively, which shows a better prediction result using the GSE_GPR_EDF_90 model. The next models to be analyzed are GWL_GPR_EDF_90, GWL_ANN_XY_NOPCA, and GWL_GPR_EDFB, which were constructed to predict the groundwater level.