# Spatial Autocorrelation Incorporated Machine Learning Model for Geotechnical Subsurface Modeling
## 4 Conclusions  
This study discusses the subsurface modeling of geotechnical properties in a study area. Modeling was performed using machine learning methods constructed from popular machine learning algorithms (SVM, GPR, ANN, and kNN). The targets in this study consisted of ground surface elevation, groundwater level, geotechnical properties such as SPT-N value and percentages finer than 0.075 mm sieve, as well as USCS-based soil classification. Subsurface modeling was performed by incorporating spatial autocorrelation into the machine learning model, since closer points tend to have similar properties. This spatial autocorrelation is represented by generating Euclidean distance field (EDF) as the  
Figure 14: Cross-section view along X axis at Y coordinate = 1455 of predicted (**a**) SPT-N value, (**b**) percent finer than 0.075 mm sieve, (**c**) soil classification (X and Y coordinate; 1 unit = 1 m).  
Figure 13: Top view of predicted value: (**a-1-c-1**) ground surface elevation; (**a-2-c-2**) groundwater level; (**a-3-c-3**) SPT-N value at elevation 0 m (**top**) and \(-3\) m (**bottom**); (**a-4-c-4**) percent finer than 0.075 mm sieve at elevation \(-4\) m; and (**a-5-c-5**) soil classification at elevation 0 m, where one unit in X and Y coordinate equal 1 m (1 unit = 1 m).  
new features for machine learning model, replacing the direct XY coordinate as the location information of a query point. The results of the study are summarized as follows:  
* The Euclidean distance field (EDF) can replace raw XY coordinates as spatial input features, as it could represent the existing spatial autocorrelation.
* Applying PCA to the high dimensional EDF features will improve the machine learning model training speed as it reduces the number of features for the learning process, as well as the computational cost.
* Hyperparameter optimization clearly improves the performance by finding the optimum hyperparameters for each algorithm. The optimization of FINER GPR_EDF_NOPCA model shows the improvement in RMSE score from 3.0359 to 2.1242, and from 1.0939 to 0.56282 for MAE score.
* The best-performing machine learning models 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 percentages finer than 0.075 mm sieve, respectively, compared to the direct XY coordinate approach.
* The analysis of MLA based on geotechnical subsurface contours shows that the models with the lowest prediction error on test data do not guarantee that the model is appropriate for the spatial prediction model. The analysis indicates that the ANN model is less appropriate for geotechnical subsurface modeling in this study.
* Machine learning models that could cover wider and deeper subsurface area of prediction for more advanced purposes can be constructed in the future research by conducting a more adequate soil investigation for the machine learning dataset.  
Conceptualization, H.-J.K. and K.B.A.M.; methodology, H.-J.K. and K.B.A.M.; software, K.B.A.M.; validation, H.-J.K. and T.-W.P.; formal analysis, K.B.A.M.; investigation, H.-S.K., [PERSON]-Y.P. and [PERSON]-S.J.; resources, H.-S.K., [PERSON]-Y.P. and [PERSON]-S.J.; data curation, H.-S.K., [PERSON]-Y.P. and [PERSON]-S.J.; writing--original draft preparation, K.B.A.M.; writing--review and editing, H.-J.K. and T.-W.P.; visualization, K.B.A.M.; supervision, H.-J.K.; project administration, H.-S.K.; funding acquisition, H.-J.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1A6A1A0304518511, NRF-2020R11A3A04036506). The APC was also funded by the National Research Foundation of Korea (NRF-2021R1A6A1A0304518511).  
Not applicable.  
Data Availability Statement: Data generated or analyzed during this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.