Assessment of Landslide Susceptibility in the Moxi Tableland of China by Using a Combination of Deep-Learning and Factor-Refinement Methods

Abstract

Precisely assessing the vulnerability of landslides is essential for effective risk assessment. The findings from such assessments will undoubtedly be in high demand, providing a solid scientific foundation for a range of critical initiatives aimed at disaster prevention and control. In the research, authors set the ancient core district of Sichuan Moxi Ancient Town as the research object; they conduct and give the final result of the geological survey. Fault influences are commonly utilized as key markers for delineating strata in the field of stratigraphy, and the slope distance, slope angle, slope aspect, elevation, terrain undulation, plane curvature, profile curvature, mean curvature, relative elevation, land use type, surface roughness, water influence, distance of the catchment, cumulative water volume, and the Normalized Vegetation Index (NDVI) are used along roads to calculate annual rainfall. With the purpose of the establishment of the evaluation system, there are 17 factors selected in total. Through the landslide-susceptibility assessment by the coupled models of DNN-I-SVM and DNN-I-LR nine factors had been selected; it was found that the Area Under the Curve (AUC) value of the Receiver Operating Characteristic Curve (ROC) was high, and the accuracy of the model is relatively high. The coupler, DNN-I-LR, gives 0.875 of an evaluation accuracy of AUC, higher than DNN-I-SVM, which yielded 0.860. It is necessary to note that, in this region, compared to the DNN-I-SVM model, the DNN-I-LR coupling model has better fitting and prediction abilities.

1. Introduction

Landslides, recognized as a pervasive geological hazard, are predominantly manifest in mountainous and hilly terrains, exhibiting a high degree of destructiveness [1,2]. They are extensively distributed and occur with greater frequency compared to other geological hazards [3]. The occurrence of major-to-catastrophic landslide events can lead to substantial loss of life and property, and they pose a significant risk to infrastructure projects, thereby indirectly affecting the trajectory of economic growth and the overall security framework [4,5]. The Luding earthquake on 5 September 2022, a magnitude Ms-6.8, inflicted considerable damage upon Moxi Township and the adjacent regions in Luding County, Ganzi Tibetan Autonomous Prefecture, Sichuan Province. Subsequently, on 26 January 2023, a Ms-5.6 earthquake precipitated further devastation, including structural collapses and landslides. The region’s distinctive geological milieu is also prone to frequent minor seismic activities. In light of these conditions, the imperative for implementing landslide susceptibility evaluations within early-warning and risk-mitigation frameworks is heightened, ensuring a more proactive and strategic approach to hazard preparedness.

In the realm of landslide susceptibility evaluation, models are categorized based on the diverse methodologies employed, which theoretically encompass probabilistic, heuristic, deterministic, mathematical-statistical, and machine learning approaches, as informed by landslide inventories [6,7]. Among these, certain models are frequently cited in scholarly research, including Random Forest, Artificial Neural Networks, and Decision Trees. This diversity suggests that the occurrence of landslides is influenced by a multitude of factors, and it is unlikely that all contributing elements are as yet identified. On one hand, the complexity of the interrelations among various factors necessitates the consideration of numerous evaluation criteria to establish a robust susceptibility framework [8,9]. However, certain limitations inherent in machine learning models, as previously noted, may obscure these correlations and fail to yield optimal outcomes [10,11]. This challenges the abstractions derived from earlier machine learning models, prompting a shift towards deep learning algorithms, which are perceived to offer greater accuracy [12]. Among the commonly applied deep learning algorithms are Deep Neural Networks (DNNs), which consist of multiple hidden layers and have been widely recognized for their efficacy across various domains, producing significant results [13]. In the context of susceptibility evaluation, the models that have been employed include the Information (I) model, the Support Vector Machine (SVM) model, and the Logistic Regression (LR) model. These models are often combined to leverage their individual strengths and achieve more precise evaluative outcomes [14,15]. The integration of such models reflects a sophisticated approach to hazard assessment, aiming to distill a comprehensive understanding of the factors that contribute to landslide susceptibility.

2. Materials and Methods

2.1. Overview of the Research Area

The 9th Seismic Defense Zone of the Moxi tableland is situated within the ancient town’s precincts, occupying a unique position on the Moxi tableland, which is characterized by its Quaternary ice and water deposits. As delineated by the seismic zoning map, this area falls within the 9-degree seismic defense zone. It is strategically positioned adjacent to the Gongga Mountain Scenic Area, with the Hailuogou Glacier Forest Park’s entrance in close proximity [16]. Moxi Town is approximately 304 km from Chengdu, 70 km from Kangding, and 52 km from Luding, serving as a gateway for reception and tourism activities. The transportation infrastructure has been significantly developed, with the main traffic artery now extending to the Moxi–Kangding junction. The historic core of Moxi Ancient Town is nestled on a gently sloping, elevated land platform, surrounded by water, with stone-paved roads being one of its distinctive features. The residential structures are closely aligned on either side of these thoroughfares. The predominant geological strata in this locale consist of former Aurora magmatic rocks (Kangding Complex) and the Quaternary system, which is delineated by a network of fractures. The elevation varies by approximately 300 m, with the topography ranging in elevation from 1668 m to 1370 m. Remote sensing imagery reveals these characteristics, with the study area’s central focus and the northeastern high-elevation regions highlighted in Figure 1, obtained through satellite imagery. Over the recent past, the intensification of anthropogenic activities, coupled with the recurrent natural hazards including earthquakes in the Luding area, has led to the discovery of 19 sites with significant landslide risk potential in the region. The spatial distribution of these landslide-prone areas is illustrated in Figure 2.

2.2. Dataset

The genesis of landslide disasters is influenced by a multitude of factors, encompassing the slope’s terrain and topography, regional geological settings, hydrogeological conditions, climatic environment, and anthropogenic engineering activities, among others. However, the specific contribution of these factors varies with the nature of the landslide event. When examining the causative agents of landslides, it is imperative to tailor the analysis to the contextual particularities of the study area and to judiciously select the most pertinent factors. The judicious choice of landslide-triggering factors is pivotal to the accuracy and reliability of susceptibility assessments [17]. In this study, a comprehensive set of variables was extracted, encompassing geological strata, fault-influence distance, slope gradient, aspect, elevation, terrain ruggedness, planar curvature, profile curvature, mean curvature, relative elevation, surface roughness, land use categorization, impact distance of water systems, cumulative catchment volume, NDVI, and more, in five distinct dimensions: regional geology, terrain and geomorphology, hydrogeology, climate and environment, and human engineering activities, totaling 17 factors, including annual rainfall and the impact distance of roads. The relevant parameters for the aforementioned datasets are detailed in

Table 1. Source of Landslide Impact Factor Data.

Data Class	Hazards	Data Description
Regional geology	Stratigraphic lithology and geological structure	The lithology and geological structure data of the study area are obtained from the 1:200,000 scale geological map of the Yanqiao area compiled and issued by the National (Provincial) Geological Bureau, which is used to extract information such as stratigraphic lithology and geological structure
Topographic features	Slope, elevation, aspect, slope curvature, surface roughness, terrain undulation, relative elevation	Extracting DEM from large-scale DEM data in Luding County, Sichuan Province, with an accuracy of 5 m, is used to obtain terrain and hydrological data such as elevation, slope, aspect, slope curvature, and terrain undulation in the study area
Hydrogeology	The influence of water system on distance, flow direction, and accumulated water concentration
The climate	Rainfall and vegetation index	NDVI data from Luding County, Sichuan Province in 2020, with an accuracy of 30 m
Human engineering activities	Road-impact distance and land use type	Road-impact distance, land use type, China National High-tech Research and Development Program (863 Program) Global Land Cover Remote Sensing Mapping and Key Technology Research Project GlobeLand30 Dataset (30 m resolution), used to obtain land use-type data

.

2.3. Method Model

DNN is a class of deep learning algorithms inspired by the cognitive processes of the human brain, drawing particularly from the seminal concepts proposed by Hinton and his colleagues [18]. These networks emerge from the multi-layered architecture that emulates the intricate workings of the brain and consist of an input layer, multiple hidden layers, and an output layer. DNN is characterized by its composition of over ten hidden layers and thousands of interconnected network nodes, marking a significant departure from the earlier artificial neural network models [19]. This sophisticated architecture is adept at uncovering the latent structures within data, thereby augmenting the neural network’s proficiency in learning a hierarchy of abstract representations [20]. The inaugural layer of the DNN model is activated when the network receives input data from the problem domain and is tasked with aligning these inputs with the desired objective. It employs a loss function to quantify the discrepancy between the network’s predicted output and the actual target. Subsequently, the network undergoes iterative training through the application of the backpropagation algorithm and an optimization technique, iterating extensively to fine-tune the network weights and thereby minimize the loss function [21].

The approach of informativeness is a traditional statistical methodology utilized in the study of landslide susceptibility, which hinges on the concept of entropy reduction. This method is predicated on the premise that the occurrence of a landslide disaster carries an informational content that can signify the likelihood of its occurrence [22,23]. The informativeness is calculated by assigning unique weights to each landslide-triggering factor, acknowledging that varying weights result in different informational outcomes. The percentage contribution of each factor can be translated into a measure of informativeness. By attributing a weighted value to the informativeness of all contributing factors and aggregating these values, a comprehensive assessment is achieved [24]. Essentially, the greater the informativeness of a particular point, the higher the susceptibility to landslide occurrences [25,26].

The specific information-quantity calculation formula is as follows:

$$I\left(y,x_1{x}_2\cdots x_n\right)={\log }_2\frac{P\left(y|x_1{x}_2\cdots x_n\right)}{P\left(y\right)}$$

(1)

Equation (1) is an attempt to measure the variation in information content for a landslide occurrence (event y) given multiple factors (x_n). This expression does not conform to the standard definition of mutual information. In landslide susceptibility assessment, it signifies how the probability of a landslide is altered when accounting for various contributing factors. Given the complexity of Equation (1) for computational purposes, the equation has been reformulated and simplified as follows:

$$I\left(y,x_1{x}_2\cdots x_n\right)=I\left(y,x_1\right)+I_{X1}\left(y,x_2\right)+\cdots +I_{X1X2\cdots Xn-1}\left(y,x_n\right)$$

(2)

Equation (2) breaks down the overall information content related to landslide occurrence into a sum of individual information contents for each independent factor (x_i). This suggests that the impact of each factor on the likelihood of a landslide is independent and can be calculated in isolation. However, this assumption may not always be valid in practice due to potential interdependencies among different factors. In landslide susceptibility assessment, the area ratio is more favorable for calculation, so the formula is rewritten in the form of area ratio for calculation:

$$I{V}_i=\ln \frac{L_i/L}{A_i/A}$$

(3)

In the context of landslide susceptibility assessment, the utilization of area ratios is often more computationally convenient. Therefore, the formula has been restructured to facilitate calculations using area ratio metrics:

$$IV={\displaystyle \sum _{i=1}^{n}IV=}{\displaystyle \sum _{i=1}^n\ln \frac{L_i/L}{A_i/A}}$$

(4)

where L_i represents probability and A_i represents area. Equation (4) represents the aggregate of all individual factor information quantities (IVi), serving to compute the comprehensive information content for the entire study area’s landslide susceptibility. In the evaluation of landslide susceptibility, this composite information content can be utilized to gauge the overall risk of landslides in the area.

SVM is a sophisticated machine learning technique that is rooted in statistical learning theory [27,28]. In this study, we employ the radial basis function kernel to minimize the induction error, thereby applying it for the evaluation of slope susceptibility [29]. The radial basis function kernel serves as a critical component in the SVM model, enhancing its predictive accuracy:

$${ K(}_{x_i,x_j})=\mathrm{e}\mathrm{x}\mathrm{p}\left\{-\frac{‖x-x_i‖}{2{\sigma }^2}\right\}$$

(5)

where $‖x-x_i‖$ represents the squared Euclidean distance between two eigenvectors. Here, σ denotes an adjustable parameter within the model. The introduction of the SVM approach is a synthesis of previous research insights to form a hybrid model. By integrating DNN, information content (I), and SVM, the hybrid model leverages the strengths of each component: DNN for automatic feature extraction, I for assessing feature significance, and SVM for classification prediction; thus, enhancing the model’s overall hybrid design by merging the capabilities of deep learning, information assessment, and support vector machine classification, offers an efficient, precise, efficacious and dependable approach to assessing landslide susceptibility.

The LR model represents an advancement in the traditional linear regression framework and is esteemed as a classic multivariate statistical technique [30,31]. This model is extensively applied in the domain of landslide susceptibility assessment, and is renowned for its capacity to discern the binary nature of the dependent variable with a high degree of precision—assigning a value of 1 to instances of landslide occurrence and 0 to instances of non-occurrence. Furthermore, the LR model adeptly elucidates the logistic associations between the set of independent variables (assessment factors). The functional formulation of the LR model is presented as follows:

$$\left\{\begin{array}{c}\ln \frac{p}{1-p}=\alpha +{\beta }_1{x}_1+{\beta }_2{x}_2+\dots +{\beta }_n{x}_n\\ P=\frac{1}{1+e^{-\left(\alpha +{\beta }_1{x}_1+{\beta }_2{x}_2+\dots +{\beta }_n{x}_n\right)}}=\frac{1}{1+e^{-\left(\alpha +{\beta }_x\right)}}\end{array}\right.$$

(6)

2.4. DNN Construction Process

The areas within Moxi Township that had experienced landslides were transformed into grid points. Through a method of trial and error, the optimal training parameters for the neural network model were fine-tuned, and the information for the entire study area was fed into the trained model to generate predictive values. Utilizing a well-trained DNN model, predictions were made across the entire study area, with each grid cell being classified and assigned a susceptibility index, culminating in a total of 822,714 indices. The higher the probability that the model assigns a grid cell to be classified as a “landslide,” the closer the susceptibility index is to 1; conversely, the closer it is to 0. The predictive values for all grid data points (822,714) in the study area were exported and, using ArcGIS software (ArcGIS Pro), linked to the study area’s base map through a data association feature, aligning the predictive values with each grid point in the study area. Thereafter, the “feature to raster” function was employed to vectorize the susceptibility indices of all grid cells, producing a landslide susceptibility assessment map. To enhance visual clarity, the natural breaks method was applied to categorize the indices into five tiers: low, lower-medium, medium, higher-medium, and high, subsequently exporting and visualizing the predictive values. The susceptibility zoning map was then divided into five levels: high susceptibility area, higher-medium susceptibility area, medium susceptibility area, lower-medium susceptibility area, and low susceptibility area. Within the low susceptibility area, a number of grid points equivalent to the landslide geological-disaster grid points (787 points) were randomly selected to serve as non-landslide points.

The rationale behind the construction process was omitted from the article to avoid redundancy. When integrating the factors, they were categorized into five groups, and the number of grids in each group corresponding to different factors, was tallied. Utilizing the information quantity-calculation formula, the information quantity value for each factor was determined. A weighted overlay of all factors yielded the information quantity value for the entire study area. Ultimately, the information quantity values of the nine factors served as input for the SVM model, with the dataset being the one chosen via the DNN method, thus forming the DNN-I-SVM hybrid model, which was then trained. After optimization and parameter selection, the Gaussian Radial Basis Function (RBF) was selected as the kernel function, with the two optimal parameters for the C-SVC type SVM being determined using a five-fold cross-validation approach: the penalty factor C = 10, and the kernel function parameter γ = 0.5. The SVM sample selection mirrored that of the BP neural network, with a total dataset comprising an equal number of positive (landslide points) and negative (non-landslide points) samples, totaling 1574. From this dataset, 70% were randomly chosen for training, and 30% for testing. Upon completion of the training phase, the final DNN-I-SVM model for landslide susceptibility assessment was established, and the results were stratified. To improve visual representation, the natural breaks method was once again used to reclassify the indices into five distinct levels: low, lower-medium, medium, higher-medium, and high.

3. Experiments and Results

3.1. Extraction of Landslide Disaster-Causing Factors

The genesis of slope disasters is influenced by a complex array of factors, including topography and geomorphology, regional geological conditions, geological composition, hydrogeological regimes, climatic conditions, and anthropogenic engineering activities. However, it is important to recognize that the impact of these factors varies among different types of landslides. When selecting the factors that contribute to landslides, it is crucial to consider the specific context of the study area, conduct a focused analysis, and identify the most influential factors. The choice of these causative factors is critical, as it significantly impacts the outcomes of the susceptibility assessment. In this study, we have extracted a comprehensive set of factors, including stratigraphy, fault-influence distance, surface slope, slope aspect, elevation, terrain undulation, direction of terrain undulation, planar curvature, profile curvature, mean curvature, relative elevation, surface roughness, land use types, water system-influence distance, catchment accumulation, and the NDVI. These seventeen factors have been carefully considered as part of the analysis. For instance, we have taken into account the volume, NDVI values, annual rainfall per square meter, and the influence of roads, among other indicators, for evaluation. By employing the DNN-I-SVM and DNN-I-LR coupled models, we have assessed the vulnerability of the study area. The evaluation results will be instrumental in informing subsequent disaster prevention strategies and measures.

Moxi Town is nestled within the confines of Kangding County, and the study area is situated within a relatively constrained geographical zone. The region features a singular stratigraphic outcrop, which is exclusively attributed to the Quaternary period. Consequently, the stratigraphic layering cannot be considered as a contributing factor in the analysis of landslide geohazards for this area. To create the geological formation-distance factor map, we utilized the fault buffer feature in the advanced ArcGIS software mapping tools, resulting in a detailed representation, as depicted in Figure 3a.

The factor maps for slope gradient (b), elevation (c), slope aspect (d), and surface roughness (e) were systematically extracted and integrated with a suite of additional maps to provide a comprehensive analysis. These include maps of topographic relief (f), relative elevation (g), slope curvature (h), (i) and (j), influence distance of water systems (k), flow direction (l), catchment accumulation (m), rainfall (n), vegetation cover (o), influence distance of roads (p), and land use types (q). These layers were combined within the ArcGIS environment to delineate potential landslide sites, as illustrated in the subsequent figures.

3.2. Selection of Disaster-Causing Factors

This study meticulously examined 17 landslide-contributing factors across five key perspectives: regional geology, topography and geomorphology, hydrogeology, climatic environment, and human-induced activities. However, the inclusion of a multitude of causative factors can lead to data redundancy, which in turn diminishes the efficiency of model training and fitting. In some instances, this overabundance may even compromise the model’s predictive capability. When numerous factors are considered, there is a tendency for highly correlated variables to be repeatedly selected, which can skew the susceptibility outcomes. Moreover, the selection of causative factors is often based on the empirical knowledge accumulated from past studies, which may not always be applicable to the unique geological and environmental conditions of Moxi Town. To enhance the reliability of the susceptibility analysis, it is crucial to identify and mitigate the impact of high correlation values among the selected factors. To this end, an analysis was conducted to determine the intercorrelations among the 17 causative factors using Spearman’s rank correlation method.

Following the criteria established by Yu Jianying et al., a correlation is considered significant if the absolute value of the correlation coefficient exceeds 0.8. After pinpointing the variables with correlation coefficients exceeding an absolute value threshold of 0.8, and taking into account the intrinsic importance of these factors, eight elements—flow, annual rainfall, land use category, NDVI, flow direction, relative elevation, surface roughness, and mean curvature—were eliminated from consideration. Nine influential factors were consequently preserved. The correlation coefficients for these factors are presented in

Table 2. Factor information scale.

Correlation Coefficient	Elevation	Slope Orientation	Slope	Fault-Influence Distance	Relief Amplitude	Plan Curvature	Profile Curvature	Distance Affected by Water System	Road-Impact Distance
Elevation	1	0.961	0.325	0.371	0.165	0.534	0.529	−0.47	0.306
Slope Orientation	0.961	1	0.138	−0.475	−0.011	0.703	0.703	0.594	−0.449
Slope	0.325	0.138	1	−0.656	0.704	0.386	−0.48	0.252	0.269
Fault-Influence Distance	0.371	0.475	0.656	1	−0.768	0.671	0.857	−0.192	−0.254
Relief Amplitude	0.165	0.011	0.704	−0.768	1	0.515	0.678	−0.247	0.205
Plan Curvature	0.534	0.739	0.386	0.671	−0.515	1	0.952	−0.54	0.546
Profile Curvature	0.529	0.703	−0.48	0.857	−0.678	0.952	1	−0.385	0.276
Distance Affected By Water System	−0.47	0.594	0.252	−0.192	−0.247	−0.54	0.385	1	−0.477
Road-Impact Distance	0.306	0.449	0.269	−0.254	0.205	0.546	0.276	−0.477	1

By synthesizing findings from prior studies and considering the geological context of the research area, this study has chosen nine evaluative parameters to input into the coupled model. These parameters are as follows: slope direction, slope gradient, proximity to road influences, distance to fault influences, water system-impact distance, planar curvature, profile curvature, elevation, and degree of terrain undulation.

3.3. Coupling Modeling

Following the algorithmic screening based on correlation analysis, a dataset was crafted utilizing nine selected factors. The DNN neural network model was then applied to generate the landslide susceptibility zoning map for Moxi Town, as illustrated in Figure 4a. This map was stratified into five susceptibility levels. The identified causative factors were subsequently reorganized into five distinct groups, drawing upon the collective wisdom from prior susceptibility assessments. A tally of the raster counts for each factor group was conducted, and the information content for each group was calculated using the specified formula, with the outcomes presented in

Table 3. Spearman correlation coefficient matrix of disaster-causing factors.

Factor	Grading Indicators	Landslide Classification Grid Points	Zone Grid Points	Information Value
Elevation	<1400	243	3130	1.58
	1400~1480	242	9405	0.47
	1480~1560	331	14,210	0.37
	1560~1640	52	12,249	−1.33
	>1640	1	15,262	−5.50
Slope Orientation	north	0	1234	0.49
	northeast	0	9433	1.21
	east	0	10,796	0.90
	southeast	158	8828	0.11
	south	166	8357	0.21
	southwest	542	11,499	1.08
	west	3	3268	−2.86
	northwest	0	611	−2.13
Plan Curvature	<6	611	3,878,069	−0.06
	6~12	524	3,078,508	0.01
	12~19	176	1,119,539	−0.07
	19~23	88	431,454	0.19
	>23	127	574,302	0.27
Slope	0–4°	33	28,020	−2.61
	4–7°	233	9811	0.39
	7–10°	285	10,249	0.55
	10–13°	241	5418	1.02
	>13°	77	758	1.84
Road-Impact Distance	<100 m	366	16,654	0.32
	100 m–200 m	274	7212	0.87
	200 m–300 m	205	9788	0.27
	300 m–400 m	187	15,352	−0.27
	>400 m	144	24,846	−1.01
Fault-Influence Distance	<100	954	38,016	0.46
	100–200	15	15,084	−2.77
	200–300	161	11,561	−0.13
	300–400	7	7370	−2.82
	>400	39	1963	0.22
Relief Amplitude	<6	37	28,987	−2.53
	6~10	211	8921	0.39
	10~15	277	9711	0.58
	15~23	143	4371	0.71
	>23	201	2266	1.71
Distance Affected By Water System	<100	46	3862	−0.29
	100–200	0	4444	1.39
	200–300	0	9737	0.41
	300–400	357	19,359	0.15
	>400	773	36,526	0.29

.

The information content values of these nine factors were subsequently input into the SVM model, with the dataset curated by the DNN method forming the basis of the DNN-I-SVM coupled model. After training, this model produced the landslide-susceptibility zoning map depicted in Figure 4b. Similarly, the information content values of the nine factors served as inputs for the LR model, with the dataset selected through the DNN approach constituting the DNN-I-LR coupled model. Once trained, this model yielded the susceptibility zoning map for the DNN-I-LR coupled model, as shown in Figure 4c. The areas of the susceptibility zones determined by the three models were then compared, with the results presented in

Table 4. Comparative analysis table for susceptibility zones across models.

Landslide-Susceptibility Zoning	Low-Risk Areas	Lower-Risk Areas	Moderately Prone Areas	Higher-Risk Areas	High-Risk Areas
LR/km2	10.0953	4.0275	2.9808	1.8306	1.2456
SVM/km2	10.467	5.8239	1.9755	2.25	1.6155
percentage-LR	50.03%	19.96%	14.77%	9.07%	6.17%
percentage-SVM	47.29%	26.31%	8.93%	10.17%	7.30%

.

Table 4 is crafted to assess the comparative accuracy between individual models and the ensemble of coupled models. We regard each model as an independent “observer”, allowing us to evaluate the uniformity of their land-zoning classifications. By aligning these findings with practical considerations, we can ascertain the soundness of the landslide-susceptibility zoning.

4. Discussion and Analysis

Utilizing the methodologies described, the landslide-susceptibility distribution map for the research area was generated. A comparative verification of the study’s outcomes was undertaken to ascertain the two coupled models that best fit the characteristics of the study area. This paper predominantly adopts a statistical approach, featuring an analysis with the ROC curve. The comparative outcomes are detailed below:

The ROC curve is a pivotal tool in statistical classification analyses, particularly for datasets of substantial size. It graphically represents the model’s performance by plotting sensitivity against specificity. A ROC curve that extends towards the upper-left corner of the graph signifies a model with superior predictive accuracy, suggesting a near-perfect predictive capability.

Furthermore, the efficacy of the landslide-susceptibility models is assessed through a quantitative measure known as the Area Under the ROC Curve (AUC). A higher AUC value, nearing the threshold of 1, indicates a higher degree of precision in the model’s predictive performance.

A ROC analysis was conducted on the predictions from the two coupled models, with both yielding ROC curves that nearly hugged the upper left corner, indicative of high predictive accuracy, and AUC values surpassing 0.86. Collectively, the ROC validation curves for these models were robust, with AUC values above 0.860 (refer to Figure 5), confirming that both the DNN-I-SVM coupled model (AUC of 0.860) and the DNN-I-LR coupled model (AUC of 0.875) are apt for the landslide-susceptibility assessment within the research area.

Given that in the article a comparison of the zoning capabilities among various models is already present, with an assessment against actual conditions, it is redundant to further illustrate the ROC curves for the standalone models. The objective of crafting a coupled model is to increase the precision of individual models. Furthermore, drawing from an abundance of literature both domestically and internationally, it is observed that the aggregate precision of individual models typically does not surpass that of the coupled models, provided that there is a foundation of rationality.

5. Conclusions

This paper carefully curated nine critical factors from a comprehensive list that encompasses geological strata, distance to faults, slope steepness, slope direction, elevation, terrain ruggedness, planar curvature, profile curvature, average curvature, relative height, surface roughness, land utilization, proximity to water systems, catchment volume, NDVI, annual precipitation, and road-impact distance, to establish an evaluative framework. Utilizing the DNN-I-SVM and DNN-I-LR coupled models for the assessment of landslide susceptibility, the study has arrived at the following key findings:

1. The DNN-I-SVM coupled model delineated the study area into zones of varying landslide susceptibility: low (47.29%), lower (26.31%), moderate (8.93%), higher (10.17%), and high (7.30%). Similarly, the DNN-I-LR coupled model classified the susceptibility into low (50.03%), lower (19.96%), moderate (14.77%), higher (9.07%), and high (6.17%). The high-susceptibility regions are fairly evenly distributed, mainly concentrated in the steep slopes of the southwest and southeast parts of the study area. The eastern and northern expanses of the study area show a lower propensity for landslides, suggesting a more secure status. In contrast, the southwest and southeast parts, especially where slopes are more pronounced, exhibit heightened risk and warrant prioritized protective interventions.

2. Utilizing the accuracy assessment provided by the ROC curve analysis, the DNN-I-LR model was found to be more appropriate for the study area in question than the DNN-I-SVM coupled model. Moreover, the DNN-I-LR model demonstrated enhanced fitting and predictive performance in this particular region.