Performance of logistic regression and support vector machine conjunction with the GIS and RS in the landslide susceptibility assessment: Case study in Nakhon Si Thammarat, southern Thailand

3.1 Landslide inventory map

The landslide inventory map reveals the locations of existing landslides, see Fig. 1. It has been produced by the landslide database in Thailand from 1989 to 2022, interpretation from remote-sensing images, and field investigations. All 365 landslides were identified in this area. They were converted to 8025 landslide pixels of 30 × 30 m each. These landslide pixels were subsequently merged with 2772 pixels of 30 × 30 m each representing areas without landslides, which were chosen randomly from regions unaffected by landslides. The total count of landslide and non-landslide pixels was separated into train and test datasets. After the landslide susceptibility models were created using the training dataset, the testing dataset was utilized to evaluate and validate the models’ effectiveness.

3.2 Landslide influencing factors

Here, the picking of triggering factors is critical for understanding the underlying mechanisms and drivers of landslide occurrence. These triggering factors are chosen based on their known influence on slope stability and their relevance to the specific geological, topographical, and climatic conditions of the study area. Therefore, eleven influencing landslide factors shown in Fig. 3 are chosen according to findings from prior research, such as Phien-Wej et al. (1993), Tanavud et al. (2000), Kanjanakul et al. (2016), and Sujitapan et al. (2023) of the characteristics and mechanism of landslide occurrences in this area. They can be divided to three categories: topographical, environmental, and geological groups (Chen et al., 2018). The topographical factors comprise elevation, slope angle, curvature, aspect, distance to rivers, and distance to roads. Normalized Difference Vegetation Index (NDVI), Normalized Difference Water Index (NDWI), and rainfall are determined as environmental factors, while lithology and distance to faults are geological factors. The details of the eleven factors are explained below and summarized in Table 1.

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Fig. 3

Map of eleven influencing landslide factors: (a) elevation; (b) slope angle; (c) aspect; (d) curvature; (e) distance to rivers; (f) distance to roads; (g) NDVI; (h) NDWI; (i) rainfall intensity; (j) lithology; and (k) distance to faults.

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3.3 Machine learning algorithms for modeling approach

Here, the logistic regression and SVM are used for landslide susceptibility mapping. They offer different approaches to identifying and predicting areas at risk of landslides based on available data and input factors. In this section, we first verify which factor discussed above has a statistical effect on the landslide occurrence by using a hypothesis test on the logistic regression model. The hypothesis test shows the P-values for each considered factor in which we can eliminate the uncorrelated factors. The results show that rainfall intensity, aspect, and NDWI data do not affect the landslide occurrence. We can now consider the 8 remaining factors affecting landslide susceptibility: elevation, slope angle, curvature, distance to rivers, distance to roads, NDVI, lithology, and distance to faults.

4.1 Landslide susceptibility map evaluation

The landslide susceptibility maps with probability value (0–1) are shown in Fig. 4. In the maps, each pixel size 30 × 30 meters is categorized into five classes: very low (0–0.13), low (0.13–0.33), medium (0.33–0.58), high (0.58–0.83), and very high (0.83–1.00) using the natural break method. Fig. 4(a) is the map created by the method of logistic regression. The maps generated by the support vector machine with the linear kernel (LR), the radial basis function (rbf) kernel, and the polynomial kernel are shown in Fig. 4 panels (b), (c), and (d), respectively. These generated landslide susceptibility maps adhere to two spatial effectiveness criteria when utilizing the four models: (1) the high-susceptibility category encompasses only mountainous regions, and (2) the most of landslide pixels are present in this category. Fig. 4 is consistent with the elevation map of this area (Fig. 3a) that regions with high elevation are susceptible to landslides, while low-elevation areas, such as river basins and coastal plains characterized by low elevation and flat terrain, are devoid of landslide occurrences. This pattern of landslide distribution highlights the susceptibility of hilly areas to landslides, as manifested in the susceptibility map.

Furthermore, the proportion of susceptible zones included by all models are also revealed in Fig. 5. The results show that all models cover over 55% of the area with a very low susceptible zone, which constitutes a majority of the entire study area. All SVM models exhibit very high susceptible zones of 17%–20%. In contrast, they categorize the low to high susceptible zones homogeneously with the areas of 5%–10%. The very high susceptible zone of the logistic regression model covers 13% of the total area which is a comparatively smaller portion than the SVM models. However, the rationality of the Landslide Susceptibility Model (LSM) was also assessed by frequency ratio (fr), which is the proportion of the number of landslides within each susceptibility class. All models exhibited a consistent pattern, demonstrating a higher concentration of landslides in the highly susceptible zones and fewer occurrences in low-lying regions (Fig. 4). The highest frequency ratio of landslides relating to the very high susceptible zone is SVM with the rbf kernel model (fr $=$ 4.44) followed by SVM with the polynomial kernel (fr $=$ 4.43), logistic regression (fr $=$ 4.39), and SVM with the linear kernel (fr $=$ 4.30).

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Fig. 4

Landslide susceptibility maps generated by each model: (a) logistic regression; (b) SVM with the linear kernel; (c) SVM with the rbf kernel; and (d) SVM with the polynomial kernel.

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Fig. 5

Percentages of each landslide susceptibility level in all models.

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4.2 Accuracy of the maps and model comparison

To compare the accuracy of each model, the training dataset and the testing dataset used in each model need to be the same. In the computation process, we divided the whole dataset into 70% training and 30% testing. We then use the same division to analyze the performance of each model. The performance analysis of the models is present in Table 2. As presented in the support vector machine section, to solve the optimization problem (10) we need to specify the kernel $K(x_i,x_j)$ and the fixed value of the tuning parameter $C$ . The values of $\gamma$ and the tuning parameter $C$ shown in Table 2 have been collected as the best-fitted parameters for each model in the sense that those values produce the highest accuracy on the 70% training dataset. We note here that the process of choosing the best parameters is time-consuming. In the process, we choose $C\in \{1,5,10,15,20,30,35,40,45,50\}$ and $\gamma \in \{0.5,1,1.5,2\}$ that produce the highest accuracy. For larger datasets, the data reduction method can reduce the computer running time. The basic idea of this method is to use a sufficient amount of data for training instead of using all training data to construct the hyperplane. For the SVM with linear kernel, $K(x_i,x_j)=\langle x_i,x_j\rangle$ , the best value of $C$ is $C=1$ . In the SVM with the radial basis function kernel, $K(x_i,x_j)=e^{\gamma {\Vert x_i-x_j\Vert }^2}$ , the best-fitted values of $C$ and $\gamma$ for the training dataset are 30 and 1 respectively, listed in Table 2. The SVM with the polynomial kernel, $K(x_i,x_j)={(\gamma \langle x_i,x_j\rangle +1)}^d$ , degrees $d=2$ , $d=3$ , and $d=4$ have the best-fitted parameters $C=40$ and $\gamma =1$ , $C=20$ and $\gamma =1$ , and $C=20$ and $\gamma =1$ , respectively, shown in Table 2.

In terms of the accuracy prediction on the training dataset, the SVM with the polynomial kernel deg 4 performs the best accuracy of 97.03%, followed by the SVM with polynomial deg 3 (96.53%), the SVM with polynomial deg 2 (96.14%), the SVM with the rbf kernel (96.01%), the SVM with the linear kernel (95.09%), and the lowest accuracy prediction is the logistic regression model (93.83%), see Table 2. Note that the higher accuracy of models on the training data does not imply the high performance of the model because overfitting may occur.

For the testing dataset, the accuracy predictions of the SVM with the polynomial kernel deg 2 and the SVM with the rbf kernel outperform the others with 95.09% and 95.06% accuracies, respectively. They are followed by the SVM with polynomial deg 3 (94.78%), the SVM with polynomial deg 4 (94.63%), the SVM with linear kernel (94.35%), and the logistic regression model (92.95%), see Table 2. This result can be a reason to conclude that the SVM with the polynomial kernel deg 2 and the SVM with the rbf kernel are the outperforming models.

The 10-fold cross-validation tests show that the SVM the polynomial kernel deg 3 produces the highest accuracy at 95.72% followed by the SVM with the polynomial kernel deg 4 (95.67%), the SVM with the rbf kernel (95.46%), the SVM with the polynomial kernel deg 2 (95.45%), the SVM(linear) (94.68%), and the logistic regression model (93.35%), see Table 3. The conducted cross-validation shows that the model performances slightly change when we randomly split the whole dataset into another 70% training and 30% testing.

The ROC curve and the AUC value of each model shown in Fig. 6 confirm that the SVM with the rbf kernel outperforms the others for both training and testing datasets. For the training dataset, it reaches 0.97734 of AUC followed by the SVM with the polynomial degree 2 (AUC $=$ 0.97499), the SVM with the linear kernel (AUC $=$ 0.95754), and the logistic regression model (AUC $=$ 0.96683). For the testing dataset, the SVM with the rbf kernel shows 0.97313 of AUC followed by the SVM with the polynomial degree 2 (AUC $=$ 0.96904), the SVM with the linear kernel (AUC $=$ 0.95628), and the logistic regression model (AUC $=$ 0.96403). As a point on the ROC curve is the ordered pair of true positive rate and false positive rate values for a given cut point (decision value in the SVM case or probability value in the logistic regression case), a model with the AUC closer to 1 is a better model in general since it implies that there is a cut point which gives the highest value of the true positive rate and the lowest value of the false positive rate. This reason leads us to conclude that the SVM with the rbf kernel is the best method in general for generating a landslide susceptibility map.

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Fig. 6

ROC curves for Test and Train data. The SVM with polynomial kernel deg 2 produces the highest AUC compared to other polynomial degrees.

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4.3 Identification of landslide-prone regions in the study area

According to all landslide susceptibility maps, elevation and slope are the most contributing factors of landslides in this province. Both factors highlight that more than 60% of landslide events had occurred in Khao Luang mountain and low hills in the middle of this province (elevation more than 300 m) with relatively high slope angle (more than 30 degrees). Consequently, these regions are highly susceptible to landslides, corresponded to field observations. Moreover, the lithological factor is also important in triggering landslides. Most of the landslides (more than 70%) were present in the granitic rock of Triassic to Cretaceous age (light pink area in Fig. 1) due to high weathering and erosion in this type of rock. Although the river basin areas in the east part of this province are susceptible to erosion because of their low elevation and destructive forces, they do not qualify as landslide-prone areas.

However, the rise in landslide occurrences in mountainous regions can be linked to a blend of environmental and anthropogenic factors. The heavy rainfall, particularly during the monsoon season can saturate the soil and increase slope instability, leading to landslides. The mountainous terrain is inherently prone to landslides due to steep slopes, fragile geological formations, and tectonic activities. Deforestation and Land Use Changes, such as deforestation, urbanization, and infrastructure development can disturb the natural balance of ecosystems and increase landslide risk. Deforestation, in particular, reduces vegetation cover, which plays a crucial role in stabilizing slopes and preventing soil erosion. Rapid urbanization and unregulated land development practices in Nakhon Si Thammarat may exacerbate landslide hazards by altering drainage patterns, destabilizing slopes, and increasing surface runoff. Improper land use planning and construction on vulnerable slopes can escalate landslide risks. The construction of roads, highways, and other infrastructure projects in mountainous areas can disrupt natural slopes, leading to slope failures and landslides. Poorly designed or maintained infrastructure may exacerbate landslide incidents in Nakhon Si Thammarat. Population growth in mountainous regions of Nakhon Si Thammarat increases human exposure to landslide hazards. Settlements located in landslide-prone areas are particularly vulnerable, especially if adequate disaster preparedness measures are lacking.

Over time, the evolution of these factors, coupled with changing environmental conditions and human activities, has contributed to the escalating trend of landslide incidents in Nakhon Si Thammarat. Understanding these dynamics is crucial for implementing effective risk reduction strategies, land use planning policies, and sustainable development practices to reduce the effect of landslides on communities and the environment.

4.4 Integrating landslide susceptibility models to existing risk management

The landslide susceptibility models (LSMs) generated for Nakhon Si Thammarat can be integrated into existing risk management frameworks or utilized by various stakeholders, such as government agencies or local communities. Government agencies can use the LSMs to point out highly susceptible areas prone to landslides and integrating this data into land use planning processes. Zoning regulations and development restrictions can be implemented to avoid construction in landslide-prone zones. LSMs can also inform decisions regarding the planning, building, and upkeep of infrastructure projects like roads, bridges, and buildings. Government agencies can prioritize investments in landslide mitigation measures for critical infrastructure assets located in high-risk areas.

Furthermore, LSMs can raise awareness among local communities about landslide hazards and the factors contributing to susceptibility. Educational programs and community workshops can empower residents to adopt proactive measures to mitigate risks, such as slope stabilization techniques and evacuation plans. Local communities can collaborate with government agencies and NGOs to implement community-based adaptation measures based on LSM findings. This may include reforestation efforts, watershed management initiatives, and the establishment of early warning systems at the grassroots level. By integrating LSMs into existing risk management frameworks and engaging relevant stakeholders, Nakhon Si Thammarat can enhance its resilience to landslide hazards and mitigate the socio-economic impacts of landslide events effectively.