1. Introduction

2. Study area

Figure 1. Ca Mau research area on the map of Vietnam.

Figure 1. Ca Mau research area on the map of Vietnam.

3. Research Methodology

3.1. AdaBoost

AdaBoost (Adaptive Boosting) is a popular machine learning ensemble technique used for classification and regression tasks and was invented by Freund and Schapire [11]. It aims to improve the performance of weak learners (often referred to as "base classifiers" or "base models") by combining their predictions into a strong overall prediction. The core idea behind AdaBoost is to give more weight to instances that are misclassified by the previous base models, thereby focusing on the difficult cases.

Let's assume a binary classification problem with a target variable consisting of two labels: y ∈ {−1, 1}. Following the boosting method, the predictive function for an input variable xi is denoted as $\widehat{f}(x_i)\text{∈}\{-\mathrm{1,1}\}$ and the target variable y takes one of two values: {−1, 1}. In this case, the training error can be defined as:

$$r=\frac{1}{N}{\sum }_{i=1}^{N}1({\mathrm{y}}_i\ne \widehat{f}(x_i))$$

(1)

Where:

N is the number of training samples.

α_i represents the weight associated with the i-th training samples.

y_i is the actual target value for the i-th samples.

Figure 2. Diagram of the AdaBoosting model. Each individual sub-model is trained on a dataset weighted according to calculations from the pre-model.

Figure 2. Diagram of the AdaBoosting model. Each individual sub-model is trained on a dataset weighted according to calculations from the pre-model.

According to figure 1, the weak models are combined by assigning weights to each based on their performance. Stronger models are given higher weights in making the final predictions $\widehat{f}{(x}_i)$.

$$\widehat{f}(\mathrm{x})=\mathrm{sign}\left[{\sum }_{i=1}^p\mathsf{\alpha }\mathrm{i}{\widehat{f}}^i(\mathrm{x})\right]$$

(2)

In the equation above, the sign(x) function is a function that takes the value 1 if the sign of x is positive and takes the value -1 if otherwise.

3.2. Gradient Boosting

The Gradient Boosting algorithm (GB) was invented and introduced by Jerome H. Friedman in 2001, which involves training weak models sequentially. However, instead of using the model error to weight the training data like ADaboost, residuals are used [12]

Starting from the current model, GB tries to build a decision tree to match the residuals from the previous model. The special feature of this model is that instead of it trying to match the target variable value of y, it will try to match the error value of the previous model. It then adds the training model to the prediction function to gradually update the residuals. Each decision tree in the model chain is very small in size with only a few decision nodes determined by the depth parameter d in the model. The figure below illustrates this process in more detail:

Figure 3. Training method using GB. Decision tree models are arranged in a sequence. Each decision tree is constructed based on the predictions of the preceding decision tree. At each decision tree, the model will attempt to fit the residuals from the previous decision tree.

Figure 3. Training method using GB. Decision tree models are arranged in a sequence. Each decision tree is constructed based on the predictions of the preceding decision tree. At each decision tree, the model will attempt to fit the residuals from the previous decision tree.

4. Data

5. Results and Discussion

5.2. Evaluate model performance

To evaluate model performance we use Receiver Operating Characteristic curve (ROC), Area Under the Curve (AUC), Sensitivity, Specificity and accuracy (Acc).

ROC Curve is a graph that illustrates the relationship between the True Positive Rate (TPR) and False Positive Rate (FPR) of a classification model at different decision thresholds. TPR is the ratio of correctly predicted positive cases (true positives) to the total number of actual positive cases. FPR is the ratio of incorrectly predicted positive cases to the total number of actual negative cases.

AUC is the area under the ROC curve. AUC measures the ability of a classification model to correctly classify positive versus negative instances. AUC typically ranges from 0 to 1, with a higher AUC indicating a better model performance. The relationship between model performance and AUC can be quantified as follows: excellent (0.9-1), very good (0.8-0.9), good (0.7-0.8), fair (0.6-0.7), and poor (0.5-0.6) [21].

The accuracy assessment method using ROC curve and AUC is a valuable tool for validating land subsidence prediction models. The utilization of ROC curve and AUC aids in evaluating result reliability, comparing performance among different models, and identifying the best model for land subsidence prediction purposes.

In evaluating the performance of a predictive model, combining the ROC curve and AUC with other metrics such as accuracy, sensitivity, and specificity will provide a more comprehensive overview of the model's performance [22]. The formula for calculating sensitivity is as follows:

Sensitivity = TP / (TP + FN)

(5)

Where TP (True Positive) is the number of true positive instances correctly identified, and FN (False Negative) is the number of false negative instances incorrectly identified.

The formula for calculating specificity is as follows:

Specificity = TN/ (TN + FP)

(6)

TN (True Negative) is the number of true negative instances correctly identified, and FP (False Positive) is the number of false positive instances incorrectly identified.

Accuracy is calculated according to the formula:

Acc = (TP + TN) / (TP + TN + FN + FP)

(7)

For the Ca Mau research area, with three selected models ADB, GB, XGB, the values are calculated based on the training set in Table 3 and the validating set in Table 4 below, along with the ROC curves on the training and testing datasets.

Figure 7. ROC curves and AUC values of models on training and testing data sets.

Figure 7. ROC curves and AUC values of models on training and testing data sets.

With three predicting models, the accuracy of all three models is very high when the Area Under the Curve (AUC) is greater than 0.8. Among them, XGB achieves the highest accuracy when AUC > 0.9 for both the training and testing datasets. When considering sensitivity which measures the model's ability to accurately identify cases of subsidence within the total number of actual subsidence cases. Therefore, high sensitivity also implies accurately predicting subsidence points distributed in the research area. According to Table 3 and Table 4, sensitivity is greater than 0.8, indicating that accurately predicting subsidence points is very high for the three models.

Regarding specificity, it is a metric that measures the ability of a model to accurately identify non-subsidence cases within the total number of actual non-subsidence cases in the research area. Also, according to Table 3 and Table 4, we can easily observe that on the training set, the accuracy of predicting non-subsidence points is consistently greater than 0.8. However, on the testing set in Table 4, the specificity value of the ADB model is significantly lower, reaching only 0.633. This indicates a considerable number of false predictions of non-subsidence positions. Due to the instability of the ADB model, it is not selected for assessing the land subsidence susceptibility in the Ca Mau peninsular.

Both the GB and XGB models exhibit high overall accuracy (Acc) for both the training and testing datasets, exceeding 0.8, with XGB having slightly higher accuracy. Examining the values under the curve AUC, XGB achieves the highest values for both the training and testing datasets. This may indicate that the performance of the XGB model is superior and could be chosen for creating maps predicting land subsidence susceptibility.

Using the XGB model to create a map predicting the susceptibility to land subsidence, the results were processed using ArcGIS 10.8 software. Employing a classification method to categorize data classes manually in ArcGIS 10.8, the subsidence susceptibility map was divided into five levels such as "Very Low," "Low," "Moderate," "High," and "Very High," corresponding to values "<0.2," "0.2-0.4," "0.4-0.6," "0.6-0.8," and "0.8-1," respectively. The distribution of subsidence susceptibilities from the XGB model is illustrated in Figure 8.

6. Conclusion

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