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Article

Enhancing the Performance of Landslide Susceptibility Mapping with Frequency Ratio and Gaussian Mixture Model

by
Wenchao Huangfu
1,2,
Haijun Qiu
1,2,3,*,
Weicheng Wu
4,
Yaozu Qin
4,
Xiaoting Zhou
5,
Yang Zhang
6,
Mohib Ullah
1 and
Yanfen He
1
1
College of Urban and Environmental Sciences, Northwest University, Xi’an 710127, China
2
Institute of Earth Surface System and Hazards, Northwest University, Xi’an 710127, China
3
Shaanxi Key Laboratory of Earth Surface System and Environmental Carrying Capacity, Northwest University, Xi’an 710127, China
4
Key Laboratory of Digital Lands and Resources, Faculty of Earth Sciences, East China University of Technology, Nanchang 330013, China
5
School of Architectural Engineering, Jiangxi Science and Technology Normal University, Nanchang 330013, China
6
State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai 200241, China
*
Author to whom correspondence should be addressed.
Land 2024, 13(7), 1039; https://doi.org/10.3390/land13071039
Submission received: 25 May 2024 / Revised: 2 July 2024 / Accepted: 9 July 2024 / Published: 10 July 2024

Abstract

:
A rational landslide susceptibility mapping (LSM) can minimize the losses caused by landslides and enhance the efficiency of disaster prevention and reduction. At present, frequency ratio (FR), information value (IV), and certainty factor (CF) are widely used to quantify the relationships between landslides and their causative factors; however, it remains unclear which method is the most effective. Moreover, existing landslide susceptibility zoning methods lack full automation; thus, the results are full of uncertainties. To address this, the FR, IV, and CF were used to analyze the relationship between landslides and causative factors. Subsequently, three distinct sets of models were developed, namely random forest models (RF_FR, RF_IV, and RF_CF), support vector machine models (SVM_FR, SVM_IV, and SVM_CF), and logistic regression models (LR_FR, LR_IV, and LR_CF) using the analysis results as inputs. A Gaussian mixture model (GMM) was introduced as a new method for landslide susceptibility zoning, classifying the LSM into five distinct levels. An accuracy evaluation of the models and a rationality analysis of the LSM indicated that the FR is superior to the IV and CF in quantifying the relationship between landslides and causative factors. Additionally, the quantile method was employed as a comparative approach to the GMM, further validating the effectiveness of the GMM. This research contributes to more effective and efficient LSM, ultimately enhancing landslide prevention measures.

1. Introduction

Landslides, notable for their sudden occurrence and severe impacts, highlight the critical need for effective landslide susceptibility mapping (LSM). LSM is crucial because it forecasts regions potentially prone to future landslides, therefore playing a significant role in landslide prevention and mitigation [1,2]. With advancements in the Geographic Information System (GIS) and Remote Sensing (RS), various models have been developed to achieve LSM, encompassing both qualitative and quantitative approaches [2,3,4,5]. The heuristic model, a common qualitative approach, often suffers from low accuracy and reduced credibility. This is primarily due to its heavy reliance on expert opinion and researcher knowledge, which are significantly influenced by human factors [6,7,8]. Quantitative models include deterministic and data-driven models [9]. Deterministic models often employ an infinite slope model to simulate shallow landslides triggered by rainfall. However, their applicability is limited to comparatively large areas and depends heavily on detailed local information, such as soil and hydrological parameters [10,11]. Data-driven statistical models in quantitative LSM require environmental factors to conform to a normal distribution. This assumption of linearity poses a significant challenge, as it is relatively difficult to meet in practical scenarios. This highlights the need for the continued development and refinement of LSM techniques to enhance their reliability and applicability in diverse geographical and environmental contexts [12].
To solve this problem, various machine-learning models are used for LSM. Machine-learning models are artificial intelligence technologies that only need to provide enough training data for the algorithm to automatically construct models and adapt to new scenarios without human input [13,14,15,16]. They are nonlinear in nature [17,18,19]. The variables input to a machine-learning model can be of many types, and no particular statistical rules need to be taken into account [20,21,22,23]. The application of machine-learning models in LSM has gradually matured, such as artificial neural networks (ANN) [24,25], decision tree (DT) [26], linear classifier [27], extreme learning machine (ELM) [28], support vector machine (SVM) [29], and ensemble learning [13,17,21,26,30]. Many scholars have compared the performance differences of machine-learning models in LSM, and although there are differences, they all achieve better performance than the traditional methods [3,4,31]. In addition, several hybrid methods are also gradually being applied to LSM, and they can integrate the advantages of various models and achieve excellent results [32,33,34,35]. Examples of these include the self-organizing map network (SOM)-based ELM model (SOM-ELM) [9] and rough set_SVM [36,37].
Quantifying the relationship between landslides and their causative factors is a crucial step in LSM. The analysis results are used as input to construct machine-learning models, which are fundamental in LSM based on machine-learning models [2,14]. The frequency ratio (FR), information value (IV), and certainty factor (CF) have been widely applied by many scholars to quantify the relationship between landslides and their causative factors, and then the obtained FR, IV, and CF values are used as inputs to construct machine-learning models to achieve LSM [15,25]. The three methods are similar in that they all calculate the relationship between the subset of each disaster factor and the landslide distribution, and then they use the corresponding formula to calculate the FR, IV, and CF values, which characterize the relationship between landslides and causative factors [38,39,40,41]. Using them as input data enables machine-learning models to mine the internal correlation between landslides and causative factors. Therefore, the quality of the input data is crucial for constructing a machine-learning model, as it determines the effectiveness of the model and the rationality of the final LSM. However, it remains unknown which method—the FR, IV, or CF—produces the most effective machine-learning models for LSM when their quantified results are used as inputs. Hence, this is explored using commonly used machine-learning models, including random forest (RF), support vector machine (SVM), and logistic regression (LR) models. In addition, landslide susceptibility zoning, i.e., classifying landslide susceptibility prediction results into several susceptibility levels, is crucial for the development of landslide prevention measures [19]. The natural break, quantile, and equal interval methods are frequently used as landslide susceptibility zoning methods [42,43]. However, these traditional methods lack statistical analyses and complete automation, resulting in the LSM results being full of uncertainties [44]. To overcome the existing problems and improve the accuracy of the final LSM, a Gaussian mixture model (GMM) was proposed as a landslide susceptibility zoning method in this study.
The purpose of this study is to improve the accuracy of LSM. We employed three methods—the CF, FR, and IV—to quantify the relationship between landslides and their causative factors. The analysis results were then used as inputs to construct various machine-learning models with the aim of predicting landslide susceptibility. Additionally, a GMM was introduced to classify these landslide susceptibility prediction results into five susceptibility levels, namely very high, high, moderate, low, and very low, therefore producing the final LSM. The differences between various LSM results were analyzed, and the performance of the different models was compared to determine the most effective method for quantifying the relationship between landslides and their causative factors. Moreover, we compared the LSM results obtained from the GMM with those derived from the quantile method to verify the effectiveness of the GMM. Ultimately, this research contributes to improving the efficiency of landslide prevention and reduction efforts.

2. Materials

2.1. Study Area

Nankang is in the west of Jiangxi Province, China, and it lies within longitudes of 114°29′09″ E~115°55′24″ E and latitudes of 25°28′00″ N~26°14′24″ N. The study area is 85.45 km long from north to south and 42.6 km wide from east to west, with a total area of 1742.68 km2 (Figure 1). Nankang is in a tropical humid monsoon climate zone, where the climate is mild and humid, with warm temperatures in winter and cool temperatures in summer, as well as sufficient precipitation. The annual average rainfall is 1461.6 mm. The rainfall is concentrated from March to June, accounting for about 46.5% of the annual precipitation. Moreover, the region is characterized by a highly complex lithology; well-developed geological structures, including faults and folds; intense road cutting, excavation, and residential construction; mining; water conservation; and hydropower development. Artificial engineering activities weaken slope stability, especially in geologically fragile areas. The cumulative effect of the aforementioned factors exacerbates the susceptibility to geological disasters, especially landslides, posing significant environmental challenges in the region.

2.2. Data and Sources

A landslide inventory was obtained through a visual image interpretation, field investigations, and government reports, and it included all aspects of the landslides, such as coordinates, type, and shape. These landslides took place in the last ten-year period of 2011–2021. Although landslides have various characteristics, previous studies have proven that it is acceptable to categorize them together into one group for LSM [45,46]. There are 1145 landslide samples in the inventory, with a total area of 2.12 km2, or roughly 0.12% of the whole studied region. The spatial distribution characteristics of the landslides are distinct, mainly concentrated in the south and north of the study area, with relatively few in the central basin. The field surveys indicated that over 80% of the landslides in the study area currently remain in an unstable state. These are primarily classified into soil, debris, and rock landslides, with soil landslides constituting the majority—more than 80% of the total occurrences. Additionally, the volume of these landslides is typically less than 100,000 m3, and their thickness is less than 10 m, classifying them as small, shallow landslides. The landslide inventory was divided into a training set (TS, 70%) and a validation set (VS, 30%). To enhance the modeling process, an equal number of non-landslide samples were selected, as they provide essential information on the unfavorable conditions under which landslides occur. For successive susceptibility modeling and validation, these non-landslide samples were also split into a TS and a VS in the same proportion as the landslides.
To accomplish our research goals, we obtained and prepared topographic data, geological data, meteorological data, hydrological data, human activity data, and the normalized differential vegetation index (NDVI) in accordance with field analyses and the work of other authors [2,13,14,15,47,48,49,50,51]. The corresponding 12 causative factors related to landslide occurrence were obtained through data processing. Geological data, including lithology and faults, were extracted from 1:50,000 geological maps provided by the 264 Geological Team of Jiangxi Nuclear Industry. Topographic data, including elevation, slope, aspect, relief amplitude, and the topographic wetness index (TWI), were extracted from a digital elevation model (DEM), ASTGTM V003, with a 30 m resolution, which was obtained from the National Aeronautics and Space Administration (NASA) (https://earthdata.nasa.gov/) (accessed on 3 July 2023). The meteorological data comprised the monthly precipitation of the period of 2008–2010; they were obtained from ground stations and used to determine the average annual precipitation using the Inverse Distance Weighted (IDW) interpolation method. The hydrological and human activity data, including river and road systems, respectively, were downloaded from the Google Earth platform. Land use in the human activity data was determined using Landsat5 TM images acquired on 15 November 2008 from the Geospatial Data Cloud (https://www.gscloud.cn/) (accessed on 3 July 2023). The NDVI was the multiyear mean data calculated from Landsat5 TM images of the period of 2005–2010. Considering the accuracy and feasibility of the calculation, 12 thematic layers of environmental factors related to landslide occurrence were converted to the raster format with a 30 m spatial resolution for subsequent LSM.

2.3. Landslide Causative Factors

The occurrence of a landslide is the result of many factors, and the mechanics mainly depend on geological conditions, geomorphic factors, rainfall, etc. [52,53,54]. When a structure is constructed in a region, the slope soil will be cut and separated into a discontinuous state by various structural planes. This causes the condition of downward sliding. In particular, when steep inclined structural planes of parallel and vertical slopes and slow inclined structural planes of up and down slopes develop, landslides easily occur [15,16,17,18,19]. The material foundation of a landslide is rock and soil mass, especially loose rock and soil mass, which has a lower clay content and a higher looseness. The cohesion of loose rock and soil mass is low, and the particles inside the rock and soil mass are prone to relative displacement when subjected to external forces, resulting in a reduction in shear strength. When there is a sliding surface on the rock and soil mass, the sliding surface easily erodes under the action of external forces, such as rain, which further reduces the shear strength and increases the possibility of the rock and soil mass sliding along the sliding surface [15]. A slope with a particular inclination is the foundation of a landslide. When the slope increases, the gravitational potential energy of the material on the slope body also increases, the supporting force of the lower part of the slope body decreases, and the gravitational action of the upper part of the slope will lead to the internal stress concentration of the slope body, thus increasing the possibility of slope instability [1,19]. Rainfall results in a large amount of rainwater infiltrating the slope body, and the rock and soil body will gradually change into a water-saturated state, causing an increase in the weight of the rock and soil body and the shear stress on the sliding surface. Rainwater infiltration also has lubrication and softening effects on the rock and soil. Lubrication reduces the friction between the rock and soil particles and the overall stability of rock and soil. The softening effect reduces the cohesive force, matrix suction, and shear strength of the rock and soil mass, thus inducing a landslide [13,14,15]. In addition, the occurrence of a landslide is also related to many inducing factors, for example, the continuous erosion and immersion of surface water, such as rivers at the slope foot, and unreasonable human engineering activities. Through extensive environmental investigations and data processing related to landslides, 12 causative factors were identified. These include topographic, geological, meteorological, hydrological, human activity, and NDVI elements. Based on the GIS and RS platforms, we retrieved the raster layer of each causative factor. Except for land use, aspect, and lithology, which are discrete factors, the rest are continuous factors with uninterrupted values. According to previous research conclusions [2,5,7], this study divided the causative factors into several subsets. The causative factors of landslides are presented as follows:
Topographic data: Elevation is an important factor in LSM (Figure 2a), and a link between elevation and landslides has been found in previous studies [55]. Vegetation type, stratigraphic lithology, human activities, etc., vary at different elevations. Elevation has a certain controlling effect on landslide development. The slope alters the potential energy of the deposits located above the higher regions, further influencing stability. As the slope becomes steeper, the potential energy inevitably increases under the action of gravity, thus reducing the stability of the slope [56] (Figure 2b). Aspect has a great influence on mountain ecology. The physical characteristics of various rocks and soils are affected by different aspects, and the pore pressure of groundwater is also affected, thus changing the original stability of the slope [13,14]. In addition, different aspects also cause different degrees of rainfall and rock weathering (Figure 2c). Relief amplitude is derived from the topographic cutting depth. An increase in relief amplitude provides more gravitational potential energy for the material, as well as increasing the slope, and the stress state of the slope becomes more concentrated, thus enhancing the downward sliding trend of the material [5,7,19] (Figure 2d). The TWI helps to identify rainfall runoff patterns, potential areas of increased soil water content, and areas of stagnant water. A large TWI value indicates that soil moisture is high and that the soil is more likely to slip and lead to a landslide (Figure 2e) [11].
Geological data: Lithology has a great influence on slope stability [15]. Slopes composed of plutonic intrusive rocks, thick layers of hard sedimentary rocks, gneiss, quartzite, and similar materials are generally more stable. However, the presence of extensively developed joints and interspersed weak structural planes can significantly increase the likelihood of forming interbedded or unconformity surfaces, which are conducive to landslide occurrences [13] (Figure 2k). Faults are widely developed in the Earth’s crust and are one of the most important structures. The emergence of fault structures creates many fracture zones, and fracture zones develop on both sides of them; this can create pathways for groundwater flow, which may accelerate the deformation and sliding of slopes. Consequently, fault structures are closely associated with the occurrence of induced landslides [13,14,15]. Given this relationship, proximity to faults was identified as a key causative factor for landslides, as illustrated in Figure 2h.
Meteorological data: Precipitation is the primary trigger for most landslides in southern China. Its impact is primarily evident as rainwater, along with melting snow and irrigation water, infiltrates slope soils. This infiltration increases the weight of the soil and rock, softens the rock, and reduces soil strength, making slopes with suitable terrain prone to landslides [13,14,15]. Consequently, the annual average precipitation was selected as a causative factor for landslides, as depicted in Figure 2l.
Hydrological data: The development of a river system causes the prolonged lateral erosion and downcutting of the river valley bank slope to different degrees, which not only forms a free surface prone to collapse and sliding but also provides a source for the formation of landslides [13,14,15,19]. Thus, the development of river systems is closely linked to the occurrence of induced landslides. Consequently, proximity to rivers was identified as a significant causative factor for landslides (Figure 2g).
Human activity data: Unreasonable excavation at the base of a slope during road construction can compromise the structural integrity of the slope, creating a free surface. This alteration often leads to slope instability and subsequently triggers landslides [13,14,15,57]. According to the field investigation, the landslides are mostly distributed on both sides of the road. Thus, the proximity to roads was selected as a causative factor of landslides (Figure 2f). Land use belongs to human engineering activities that are based on the natural characteristics of the land. Land use indirectly induces landslides by affecting soil and water loss, rainfall infiltration, and surface structure characteristics (Figure 2j) [58,59,60].
The NDVI effectively reflects the status of land vegetation cover. Dense vegetation can act as a barrier against rain, mitigating the impact of precipitation on slopes. Conversely, areas with a lower vegetation density are more prone to weathering, resulting in decreased shear strength and poorer slope stability. Additionally, the growth process of vegetation, particularly root splitting, can compress and damage rock fracture walls, increasing water infiltration and further destabilizing slopes [58,61]. Therefore, the NDVI was selected as a causative factor for landslides (Figure 2i).

3. Methods

This study is mainly divided into five parts: (1) the collection and assignment of landslide and non-landslide samples, with values of “1” for landslides and “0” for non-landslides, along with causative factors; (2) an analysis of the relationship between landslides and causative factors using FR, IV, and CF methods; (3) the construction of machine-learning models, using the analysis results from the previous step as inputs and whether a landslide occurred (“1” and “0”) as output, with multiple models utilized for predicting landslide susceptibility; (4) landslide susceptibility zoning using a GMM; and (5) an exploration of the optimal method among FR, IV, and CF and the verification of GMM’s effectiveness through a performance evaluation of the models and a rationality analysis of LSM. Figure 3 shows the research process.

3.1. Relationship Analysis between Landslides and Causative Factors

3.1.1. FR Method

The FR model has been widely used in LSM [39,62,63]. The FR is a univariate probability analysis method. The principle is to analyze the relationship between the distribution of hazards and the subset of each causative factor and to calculate the probability of hazards occurring in different subsets of each causative factor.
F R = x i / X i y i / Y i
where xi is the landslide area in the subset of causative factors; Xi is the total area of the landslides; yi is the area of the subset of causative factors; and Yi is the total area under study.

3.1.2. IV Method

The IV model is a method proposed by Van Westen that uses the concept of information entropy to analyze landslide susceptibility under the combined effects of various factors [64]. Based on the actual situation of landslides, the measured values of factors affecting the development of landslides are converted into information values affecting landslide susceptibility.
I = i = 1 n l n X i / X Y i / Y
where X is the total area of the landslides; Xi is the landslide area in each subset of causative factors; Y is the total area under study; and Yi is the area of each subset of causative factors.

3.1.3. CF Method

The CF method is a probability model which belongs to bivariate statistical analyses. It was originally proposed by Shortliffe and Buchanan [65], and it was later refined by Heckerman [66]. The fundamental premise of using CF in landslide susceptibility assessments is to extrapolate the unknown from the known. This involves analyzing the pregnant disaster environment where landslides have previously occurred to calculate the relationship between landslides and pregnant disaster environments. These relationship calculations are then extended to the entire area to determine the susceptibility of the whole region [67,68,69,70,71].
C F = P a P s P a ( 1 P s ) ,       P a P s P a P s P s ( 1 P a ) ,       P a < P s
where Pa is the ratio of the landslide area in the subset to the subset area, and Ps is the ratio of the total landslide area to the total study area.

3.2. Machine-Learning Models

RF is a machine-learning model that trains and predicts samples through multiple decision trees [72]. The algorithm disintegrates the same problem into different decision trees and improves the generalization performance of the model through joint learning. An RF model ignores the interaction between factors, and, at the same time, different TSs are constructed via random sampling to generate decision trees, which can reduce the correlation between variables and solve the problem of overfitting. An RF model was constructed using EnMAP-Box 2.1 software mounted on the Interactive Data Language (IDL). Through the iterative calculation of different RF out-of-pocket errors, the smaller the out-of-pocket errors, the higher the prediction accuracy of the corresponding model. Finally, an RF model with a random feature number of 3 and a decision tree of 300 was established for LSM.
SVM is a classifier that excels in mapping low-dimensional, nonlinear data into high-dimensional space, even with limited samples. This capability allows it to identify the optimal hyperplane, enhancing its robustness [29]. An SVM model was constructed using EnMAP-Box 2.1 software mounted on the IDL. The optimal model parameters C0, ε, and γ were 5.0, 0.1, and 0.2, respectively, determined using the cross-validation method.
LR is a nonlinear regression model commonly used in machine learning with binary categorical variables as the dependent variable. It can consider both continuous and discrete variables, and it has been widely used in practice due to its simple mathematical principles and efficient function [2,3,4,14,15]. An LR model was constructed using SPSS model 18.0, and the calculation method is shown in Formulas (4) and (5), where p is the probability of landslide occurrence, with a value range of 0–1; z is the sum of the linear weight values after variable superposition; xm is each environmental factor; and bm and a are the coefficients and constants of the model, respectively.
Z = a + b 1 x 1 + b 2 x 2 + + b m x m
p = 1 / ( 1 + e z )

3.3. Gaussian Mixture Model

The GMM is a machine-learning algorithm for clustering that can classify data into different categories based on probability distributions. When a new data point becomes available, the GMM can determine to which cluster the data point belongs. When some data cannot achieve perfect clustering, they can still produce accurate results because of their robustness to outliers. This makes the GMM a flexible and powerful data clustering tool [73,74]. The GMM is derived from a linear combination of multiple Gaussian distribution functions, and unsupervised classification of the data is performed by calculating the posterior probability of each sample. The data points to be clustered are regarded as distributed sampling points, and the Gaussian distribution parameters are estimated using the Expectation Maximization (EM) algorithm. EM is an algorithm that iterates for maximum likelihood estimation, which can effectively avoid the noise in data and the limitations caused by mixed components. The probability density function of the GMM is:
p M ( x ) = k = 1 K p ( k ) p x k = k = 1 K α k p x μ k , Σ k
where K is the number of Gaussian distributions, i.e., the number of clusters; α k is the probability (prior distribution) of belonging to the Kth Gaussian, whose value is greater than 0; p(x|k) is the probability density of the Kth Gaussian, whose mean vector is μ k ; and Σ k is the covariance matrix. The GMM was constructed in MATLAB2016, and there were five categories of Gaussian clustering; that is, K = 5. Other parameters were estimated using the EM algorithm; the iteration stop threshold of EM was 1 × 10−3, the maximum iteration number was 100, and the initialization time was 1.

3.4. Verification and Reliability Analysis

Overall accuracy (OA), Kappa coefficient (Kappa), precision, recall, F1-score, and mean intersection over union (mIoU) [13,14,15,16,17,61,75,76,77] were selected to assess the accuracy of the machine-learning algorithm, and they are the commonly used evaluation indices in landslide susceptibility prediction [77,78,79]. OA represents the proportion of correctly classified samples among all sample numbers. Kappa is used to verify the consistency of classification results, with a numerical range of 0–1; The closer the value to 1, the closer the predicted results to the truth and the more accurate the classification results. Precision represents the proportion of correctly classified positive samples among all positive samples classified by the classifier. Recall represents the proportion of correctly classified positive samples among all positive samples. F1-score is the weighted harmonic average of precision and recall, avoiding inconsistencies between the two. The mIoU represents the ratio of the intersection and union of two sets of true values and predicted values. These evaluation indices were calculated using a confusion matrix. In addition, the landslide frequency density (FD) was used to verify the rationality of the final LSM, and the FD was calculated according to the ratio of the number of landslides to the corresponding area of the susceptibility level.

3.5. Multicollinearity Diagnosis

The landslide susceptibility prediction indices were optimized by eliminating factors with strong collinearity. Tolerance (TOL) and variance inflation factor (VIF) are generally used as collinearity diagnostic indices [4]. The TOL value is between 0 and 1, and if it is too small (less than 0.1), then collinearity exists between the causative factors. The VIF value represents the strength of collinearity (generally less than 10 as the basis for judgment) [80].

4. Results

4.1. Relationship between Landslides and Causative Factors

Table 1 shows the final classification scheme and the FR, IV, and CF values of each subset of causative factors. The contribution of the causative factors to landslides in different categories can also be seen. For example, landslides mostly occur in low-altitude areas, which is due to frequent human activities in low-altitude areas, and this proves the relationship between landslides and human activities. Slopes ranging from 9° to 18° have a positive impact on landslides. The FR, IV, and CF values also reach the maximum when the average annual precipitation is the highest (1407.2 mm–1439.8 mm), indicating that precipitation has a positive promoting effect on the occurrence of landslides.

4.2. Multicollinearity Analysis of Landslide Causative Factors

Table 2 shows the multicollinearity diagnosis results of the causative factors. It can be seen that the VIF values of all predictive variables are less than 10, and the TOL values are all greater than 0.1, indicating that there is no colinear relationship between the variables. Therefore, the 12 selected causative factors have a positive impact on the occurrence of landslides, and thus, they are all retained for the model construction.

4.3. Landslide Susceptibility Mapping

The FR, IV, and CF values for each subset of landslide causative factors were used as input variables for the machine-learning models. The output variables for these models were designated either “1” for landslides or “0” for non-landslides. To accurately evaluate and compare the effectiveness of FR, IV, and CF and to minimize the chance of random results, nine models were constructed: three RF models (RF_FR, RF_IV, and RF_CF), three SVM models (SVM_FR, SVM_IV, and SVM_CF), and three LR models (LR_FR, LR_IV, and LR_CF). These models were applied across the entire study area to predict landslide susceptibility. The landslide susceptibility prediction results were then classified into five levels using the GMM, namely very high, high, moderate, low, and very low, resulting in the final LSM (Figure 4).
The nine LSMs have similar spatial distribution characteristics in general, in which the high and very high susceptibility levels are mainly concentrated in the south and north of the study area, which is consistent with the distribution characteristics of historical landslides. However, there are differences in the local features of the LSMs, which are due to the various models used to calculate landslide susceptibility. The middle region of the study area is relatively flat and lacks landslide development conditions; the LSM of LR_FR is consistent with the actual ground characteristic, but LR_IV and LR_CF predict more grids of very high susceptibility levels in this region than LR_FR, which is unreasonable. The same prediction results are observed for the LSM of SVM_FR, SVM_IV, and SVM_CF; that is, the LSM of SVM_FR has fewer grids of a very high susceptibility level in the middle flat region, so the LSM of SVM_FR is more reasonable than that of SVM_IV and SVM_CF. The LSMs produced by the RF_FR, RF_IV, and RF_CF models are visually very similar. Notably, the high and very high susceptibility levels are predominantly located in the mountainous regions characterized by low erosional structures and erosional denudation hills. The topographic relief in this area is large, the slope angle is generally 20–40°, the local area can reach 50–60° or more, the vegetation is not developed, and there are good geological disaster development conditions.

4.4. Rationality Analysis of Landslide Susceptibility Mapping

By analyzing the area percentage of each susceptibility level and the percentage of landslide pixels within each susceptibility level, we can compare the rationality of the LSMs obtained from the different models. Generally, an ideal LSM typically exhibits a pattern where the area percentage of each susceptibility level decreases progressively as the susceptibility level increases, while the percentage of landslide pixels within each susceptibility level correspondingly increases [19]. Figure 5a shows the area percentage of the susceptibility level of the LSM based on the different models. It can be seen that the results of the different models follow the same rule; that is, with an increase in the susceptibility level, the area percentage gradually decreases. The area percentages of the high and very high susceptibility levels of LR_FR were 13.12% and 9.15%, which were 1.01% and 4.14% lower than those of LR_CF and 2.10% and 4.21% lower than those of LR_IV, respectively. Similarly, the area percentage of the very high susceptibility level of SVM_FR was 4.09% and 3.27% lower than that of SVM_CF and SVM_IV, respectively, and the area percentage of the high susceptibility level was 1.04% and 0.06% lower than that of SVM_CF and SVM_IV, respectively. The area percentages of the high and very high susceptibility levels of RF_FR were 12.08% and 5.35%, respectively, which were lower than those of RF_CF and RF_IV. Therefore, the area percentages of high and very high susceptibility levels in the LSM obtained using the machine-learning models based on the FR method are more reasonable than those obtained using the machine-learning models based on the IV and CF methods.
Figure 5b shows the pixel percentage of landslides according to the susceptibility level of the LSM based on the different models. It can be seen that, with an increase in the susceptibility level, the pixel percentage of landslides gradually increases. The pixel percentage of landslides of LR_FR in the very high susceptibility level was 74.23%, which was 4.03% and 4.02% higher than that of LR_CF and LR_IV, respectively. The pixel percentage of landslides of SVM_FR in the very high susceptibility level was 76.15%, which was 6.74% and 5.97% higher than that of SVM_CF and SVM_IV, respectively. The pixel percentage of landslides of RF_FR in the very high susceptibility level was 82.17%, which was 6.03% and 6.85% higher than that of RF_CF and RF_IV, respectively. Therefore, the pixel percentage of landslides in the very high susceptibility level of the LSM obtained using the machine-learning models based on the FR method is always higher than that obtained using the machine-learning models based on IV and CF. In summary, the LSM generated by the machine-learning model using the FR method is the most reasonable. It demonstrates the smallest area percentage of the very high susceptibility level yet the largest percentage of landslide pixels within that category. This distribution is advantageous for implementing effective and efficient landslide prevention and reduction strategies.

4.5. Performance Assessment of Models

The performance of the nine models was evaluated using OA, Kappa, precision, recall, F1-score, and mIoU, calculated from a confusion matrix (Figure 6). The OA, Kappa, precision, recall, F1-score, and mIoU of LR_FR were 88.03%, 0.76, 87.28%, 88.61%, 87.94%, and 78.62%, respectively, which were higher than those of LR_CF and LR_IV: they were 1.06%, 0.02, 0.5%, 1.5%, 0.99%, and 1.68% higher than those of LR_CF, and 1.87%, 0.04, 2.24%, 1.62%, 1.94%, and 2.94% higher than those of LR_IV, respectively. The same phenomenon was also observed in SVM_FR, SVM_IV, and SVM_CF; that is, the OA, Kappa, precision, recall, F1-score, and mIoU of SVM_FR were higher than those of SVM_IV and SVM_CF, reaching 90.95%, 0.82, 90.64%, 91.18%, 90.91%, and 83.4%, respectively. RF_FR and RF_CF achieved the same precision (91.23%); however, RF_FR had a higher OA, Kappa, recall, F1-score, and mIoU than RF_CF and RF_IV, reaching 91.24%, 0.83, 91.23%, 91.23%, and 83.89%, respectively. Therefore, machine-learning models based on the FR method achieve higher performance in landslide susceptibility prediction than those based on the CF and IV methods.

4.6. The Contribution of Causative Factors from Different Models

Figure 7 shows the contribution rate of the landslide causative factors obtained using the different models; the contribution rate represents the relative importance of causative factors in landslide events. In LR_FR, LR_IV, and LR_CF, elevation, the TWI, and lithology contributed more to landslides than the other causative factors, with contribution rates of 24.01%, 19.86%, and 8.05% in LR_FR; 21.99%, 13.61%, and 11.86% in LR_IV; and 19.88%, 16.47%, and 11.93% in LR_CF, respectively. In SVM_FR, SVM_IV, and SVM_CF, elevation, lithology, and the average annual precipitation contributed more to landslides than the other causative factors, with contribution rates of 15.29%, 14.21%, and 12.15% in SVM_FR; 13.44%, 12.80%, and 11.44% in SVM_IV; and 15.05%, 15.05%, and 11.75% in SVM_CF, respectively. In RF_FR, RF_IV, and RF_CF, slope, the average annual precipitation, and lithology contributed the most to landslide occurrence, with contribution rates of 23.45%, 14.09%, and 13.08% in RF_FR; 22.92%, 14.45%, and 13.21% in RF_IV; and 22.70%, 14.42%, and 12.31% in RF_CF, respectively.
The field investigation revealed that landslides were mainly concentrated in the southern and northern areas, with fewer landslides in the central flat area. This is because the southern and northern areas are mountainous, with higher elevations, steep terrains, and large slope inclinations, creating conditions for the rock and soil bodies on the slope to slide down. Although elevation has a certain control effect on the development of landslides, a slope with a particular inclination is an essential condition. The study area not only has abundant precipitation but also frequent long-term and high-intensity precipitation, mainly concentrated in March to July, especially June to July, and this coincides with the occurrence time of more than 50% of the landslides. In addition, landslide materials comprise rock and soil mass with a soft structure, a low shear strength, and weathering resistance. Rainwater penetrates the slope, softens the soil and its weak surface, and reduces the strength of the slope, thus inducing a landslide. There are also many human engineering activities, such as road construction in the study area, and excavating the foot of a slope reduces the support of the lower part of the slope, resulting in landslides on both sides of the road. In summary, RF models (RF_FR, RF_IV, and RF_CF) reasonably reveal the main causative factors of landslides in the study area; that is, slope, the average annual precipitation, lithology, and proximity to roads contribute the most to landslides in the study area.

4.7. Comparison of Landslide Susceptibility Zoning Methods

Accurate landslide susceptibility zoning is crucial. To address the shortcomings of existing methods, this study introduced the GMM for landslide susceptibility zoning. To validate the GMM’s effectiveness, its results were compared with those of the quantile method. Figure 8 shows the landslide susceptibility zoning results obtained using the quantile method. The high and very high levels of landslide susceptibility zoning obtained using the two methods show similar spatial distribution characteristics overall, but the areas of moderate, high, and very high levels of the quantile method are significantly larger than those of the GMM. Further observation revealed that the central region of the study area is flat and lacks the necessary landslide pregnancy conditions; however, the quantile method classifies many parts of this region as having a moderate susceptibility level, while the GMM classifies them as having low and very low levels. Therefore, the qualitative analysis results revealed that the landslide susceptibility zoning obtained using the quantile method is less reasonable than that obtained using the GMM.
To quantitatively compare the different landslide susceptibility zoning methods, the frequency density (FD) was calculated according to the ratio of the number of landslides in each susceptibility level and the corresponding area of susceptibility levels. Generally, reasonable landslide susceptibility zoning shows regularity: with an increase in the susceptibility level, the number of landslides in the corresponding unit area also gradually increases; that is, the FD gradually increases [43,81]. The results of the quantile method and the GMM are consistent with this regularity (Figure 9). The FDs of the GMM and quantile methods in the high and very high susceptibility levels were significantly higher than those in the very low, low, and moderate susceptibility levels, and the FD of the very high susceptibility level was the largest, greater than 0.7. Moreover, the FDs in the very high susceptibility level obtained using the GMM and the quantile method reached the maximum in the RF_FR model at 0.92 and 0.86, respectively. Further comparison showed that the FDs in the very high susceptibility level obtained using the GMM were always higher than those obtained using the quantile method in the same model; for example, in LR_CF, LR_IV, LR_FR, SVM_CF, SVM_IV, SVM_FR, RF_CF, RF_IV, and RF_FR, they increased by 0.15, 0.1, 0.05, 0.05, 0.02, 0.06, 0.13, 0.05, and 0.06, respectively. The quantitative analysis results show that the landslide susceptibility zoning obtained using the GMM is more reasonable. Therefore, the GMM is superior to the quantile method in landslide susceptibility zoning.

5. Discussion

Accurate LSM is very important for the development of landslide prevention strategies. In this study, the FR, IV, and CF methods were used to quantify the relationship between landslides and causative factors, and then nine landslide susceptibility prediction models were constructed using the analysis results as input to the machine-learning models. The GMM was introduced as a landslide susceptibility zoning method to obtain the final LSM. The FR, IV, and CF methods were compared using a qualitative analysis and a quantitative evaluation, and the landslide susceptibility zoning results obtained using the quantile method and the GMM were also compared.

5.1. Understanding the Effectiveness of LSM

When relevant authorities develop landslide prevention and reduction strategies, it is crucial that areas with a very high susceptibility level are not only accurately identified but also predictive of more landslide occurrences. This precision can conserve human and material resources and significantly reduce time costs [82]. Compared with machine-learning models based on IV and CF, the LSM derived from models using the FR method not only covered a smaller area of a very high susceptibility level but also included a greater number of historical landslides within this level (Figure 5). In contrast, the very low and low susceptibility levels were not only larger in area but also had a smaller historical landslide percentage, which is a reasonable manifestation of LSM [19,43,81]. In addition, the machine-learning models based on FR for landslide susceptibility prediction always showed better performance than those based on IV and CF (Figure 6). Therefore, the analysis results of the relationship between landslides and causative factors calculated using the FR method were used as the model input; thus, not only could a high-performance landslide susceptibility prediction model be constructed, but also a more reasonable LSM could be obtained. In terms of landslide susceptibility prediction using machine-learning models, the analytical results obtained by quantifying the relationship between landslides and causative factors using the FR method can more comprehensively characterize the internal relationship between the two, so a balance between the accuracy of landslide susceptibility prediction and the efficiency of landslide prevention and reduction can be achieved.

5.2. General Description of Landslide Susceptibility Zoning Methods

Landslide susceptibility zoning is a crucial component of LSM and plays a vital role in guiding final landslide management decisions [83]. In this study, the GMM was employed as the method of landslide susceptibility zoning, categorizing results into five susceptibility levels: very low, low, moderate, high, and very high. The GMM, a clustering algorithm, leverages the EM algorithm for iterative computations. It is adept at handling complex, nonlinear data distributions and fitting multi-modal distributions. Additionally, the GMM allows for the integration of prior information or expert knowledge into the clustering process by adjusting the weights of different Gaussian distributions [73,74]. The quantile method does not require complex calculation or statistical methods, and it can evenly divide data into several zones according to the distribution characteristics of the data so that the numbers of data in each zone are roughly equal. However, the number of zones needs to be set in advance, and the quantile method can only ensure that the amount of data in each zone is roughly equal and cannot guarantee a significant difference in landslide susceptibility in each zone [19]. The FD statistical analysis showed that the GMM had more historical landslides per unit area in the very high susceptibility level than the quantile method, and the nine models were consistent with this rule (Figure 9). The statistical results indicate that the GMM achieves a more reasonable LSM than the quantile method.
The natural break method is often used for landslide susceptibility zoning [5,13,20], but it is effective only when there is a large jump in the dataset and it is not fully automated [44,84]. The K-means algorithm has been used for landslide susceptibility zoning and has been shown to be superior to the natural break and equal interval methods [19]. However, compared with the GMM, K-means cannot deal with more complex distributed data or provide the probability that each data point belongs to a certain cluster, resulting in a lack of interpretability. Therefore, the GMM, as a landslide susceptibility zoning method, is more effective than the existing methods and is conducive to formulating landslide prevention and reduction strategies.

5.3. Rationality Analysis of Grid Resolution

Selecting an appropriate grid resolution is critical for effective LSM. While a low resolution can significantly compromise LSM accuracy, a high resolution increases the complexity of the modeling process [85]. Research indicates that a 30-m grid resolution often yields the most satisfactory LSM outcomes [86,87,88,89]. Consequently, after conducting field investigations and collecting landslide data, a 30-m grid resolution was chosen for this study. This resolution not only accurately represents terrain features but also avoids the complications of excessive computational demands associated with higher resolutions.

6. Conclusions

To assess the effectiveness of FR, IV, and CF in quantifying the relationship between landslides and their causative factors for landslide susceptibility prediction and to reduce the uncertainties associated with LSM, this research employed the analysis results from these methods as inputs to construct three sets of models: RF (RF_FR, RF_IV, and RF_CF), SVM (SVM_FR, SVM_IV, and SVM_CF), and LR (LR_FR, LR_IV, and LR_CF). The GMM was then used to classify the results of these models to produce the final LSM. An evaluation of model performance and a rational analysis of the LSM indicated that the machine-learning models based on the FR method were superior in predicting landslide susceptibility and achieving a more reasonable LSM. Moreover, the RF models reveal that slope, average annual precipitation, lithology, and proximity to roads contribute the most to landslides. A comparative analysis of the LSM results of the quantile method and the GMM confirmed the effectiveness of the GMM as a zoning method, demonstrating its ability to generate more accurate susceptibility zones. This research supports the development of more effective landslide prevention strategies.

Author Contributions

Conceptualization, H.Q. and W.W.; methodology, W.H.; software, W.W.; validation, Y.Q., X.Z., W.H. and Y.Z.; writing—original draft preparation, W.H.; writing—review and editing, H.Q., M.U. and Y.H. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the Key Research and Development Program of Shaanxi (Grant No. 2024SF-YBXM-669), the National Natural Science Foundation of China (Grant No. 42271078), and the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019QZKK0902).

Data Availability Statement

The data presented in this study are available upon request from the corresponding author.

Acknowledgments

We are grateful for landslide data and the Geological Map of Nankang provided by the 264 Geological Team of Jiangxi Nuclear Industry. We thank Weicheng Wu for his help in software support and data processing. We also thank Penghui Ou for his help in field investigation and verification.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

AcronymsComplete names
LSMlandslide susceptibility mapping
FRfrequency ratio
IVinformation value
CFcertainty factor
RFrandom forest
SVMsupport vector machine
LRlogistic regression
GMMGaussian mixture model
TStraining set
VSvalidation set
NDVInormalized differential vegetation index
TWItopographic wetness index
IDLinteractive data language
EMexpectation maximization
OAoverall accuracy
mIoUmean intersection over union
FDfrequency density
TOLtolerance
VIFvariance inflation factor

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Figure 1. (a) Location of Nankang, Jiangxi, China. (bh) Field investigation of landslides.
Figure 1. (a) Location of Nankang, Jiangxi, China. (bh) Field investigation of landslides.
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Figure 2. The landslide causative factors: (a) elevation, (b) slope, (c) aspect, (d) relief amplitude, (e) TWI, (f) proximity to roads, (g) proximity to rivers, (h) proximity to faults, (i) NDVI, (j) land use, (k) lithology, (l) average annual precipitation.
Figure 2. The landslide causative factors: (a) elevation, (b) slope, (c) aspect, (d) relief amplitude, (e) TWI, (f) proximity to roads, (g) proximity to rivers, (h) proximity to faults, (i) NDVI, (j) land use, (k) lithology, (l) average annual precipitation.
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Figure 3. Flowchart of LSM.
Figure 3. Flowchart of LSM.
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Figure 4. The LSMs using different models and the GMM classification method. (a) LR_FR, (b) LR_IV, (c) LR_CF, (d) SVM_FR, (e) SVM_IV, (f) SVM_CF, (g) RF_FR, (h) RF_IV, and (i) RF_CF.
Figure 4. The LSMs using different models and the GMM classification method. (a) LR_FR, (b) LR_IV, (c) LR_CF, (d) SVM_FR, (e) SVM_IV, (f) SVM_CF, (g) RF_FR, (h) RF_IV, and (i) RF_CF.
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Figure 5. Rationality analysis of the LSMs obtained from the different models. (a) Percentage of susceptibility levels, (b) percentage of landslides.
Figure 5. Rationality analysis of the LSMs obtained from the different models. (a) Percentage of susceptibility levels, (b) percentage of landslides.
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Figure 6. Performance assessment of different models.
Figure 6. Performance assessment of different models.
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Figure 7. The contribution of causative factors according to different models.
Figure 7. The contribution of causative factors according to different models.
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Figure 8. The LSMs using different models and the quantile classification method. (a) LR_FR, (b) LR_IV, (c) LR_CF, (d) SVM_FR, (e) SVM_IV, (f) SVM_CF, (g) RF_FR, (h) RF_IV, and (i) RF_CF.
Figure 8. The LSMs using different models and the quantile classification method. (a) LR_FR, (b) LR_IV, (c) LR_CF, (d) SVM_FR, (e) SVM_IV, (f) SVM_CF, (g) RF_FR, (h) RF_IV, and (i) RF_CF.
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Figure 9. Rationality analysis of the LSMs obtained from GMM and quantile classification methods.
Figure 9. Rationality analysis of the LSMs obtained from GMM and quantile classification methods.
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Table 1. The FR, IV, and CF of each subset of causative factors.
Table 1. The FR, IV, and CF of each subset of causative factors.
FactorSubsetFRIVCF
Elevation (m)81–2371.1230.1160.109
237–3940.852−0.161−0.148
394–5500.723−0.324−0.279
550–7060.628−0.466−0.373
706–8630.224−1.498−0.778
863–101900−1
Slope (°)0–90.865−0.145−0.136
9–181.4720.3860.320
18–270.740−0.301−0.261
27–360.337−1.087−0.662
36–460.276−1.289−0.724
46–54.600−1
Aspect (°)−10.613−0.489−0.386
0–22.5; 337.5–3600.852−0.070−0.148
22.5–67.50.781−0.248−0.220
67.5–112.50.700−0.356−0.299
112.5–157.50.887−0.120−0.115
157.5–202.51.1770.1630.150
202.5–247.51.3140.2730.238
247.5–292.51.3070.2680.235
292.5–337.51.0420.0410.039
Relief amplitude (°)0–201.0910.0870.082
20–400.846−0.167−0.156
40–600.409−0.895−0.591
60–8000−1
80–10000−1
100–11300−1
TWI2.8–7.21.1270.1190.111
7.2–11.60.751−0.287−0.251
11.6–16.00.773−0.257−0.228
16.0–20.40.150−1.896−0.847
20.4–24.80.299−1.206−0.701
24.8–29.200−1
Proximity to roads (m)0–300.323−1.1320.790
30–601.6960.5280.708
60–902.3010.8330.559
90–1204.9561.6010.446
>1206.3661.851−0.414
Proximity to rives (m)0–301.3890.3290.280
30–601.6380.4930.389
60–901.8230.6010.451
90–1201.5560.4420.357
>1200.965−0.035−0.036
Proximity to faults (m)0–301.0310.0300.030
30–601.3120.2720.238
60–901.6610.5080.398
90–1201.1890.1730.159
>1200.960−0.041−0.041
NDVI−0.376–−0.17600−1
−0.176–0.02400−1
0.024–0.2230.341−1.075−0.660
0.223–0.4231.1840.1690.154
0.423–0.6231.2780.2450.217
0.623–0.8230.371−0.993−0.629
Land useWater0.612−0.492−0.389
Artificial area0.248−1.393−0.752
Forest land0.439−0.822−0.560
Shrub1.9690.6770.492
Farm land1.0180.0180.018
Bare land0.5210.5210.406
LithologyGranite1.3550.3040.261
Other magmatic rock0.934−0.068−0.067
Metamorphic rock1.0510.0500.049
Sedimentary rock0.951−0.050−0.049
Carbonate rock00−1
Mudstone and shale0.821−0.197−0.179
Average annual precipitation (mm)1244.2–1276.81.1460.1360.125
1276.8–1309.40.793−0.232−0.207
1309.4–1342.01.1310.1230.115
1342.0–1374.60.563−0.575−0.437
1374.6–1407.20.495−0.702−0.506
1407.2–1439.81.4360.3620.303
Table 2. Collinearity of the causative factors.
Table 2. Collinearity of the causative factors.
VariableTOLVIF
Elevation0.6601.516
Slope0.6931.443
Aspect0.9771.024
Relief amplitude0.5591.788
TWI0.8761.142
Proximity to roads0.7741.292
Proximity to rives0.9861.014
Proximity to faults0.9781.022
NDVI0.5951.681
Land use0.7371.356
Lithology0.7761.288
Average annual precipitation0.9541.048
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Huangfu, W.; Qiu, H.; Wu, W.; Qin, Y.; Zhou, X.; Zhang, Y.; Ullah, M.; He, Y. Enhancing the Performance of Landslide Susceptibility Mapping with Frequency Ratio and Gaussian Mixture Model. Land 2024, 13, 1039. https://doi.org/10.3390/land13071039

AMA Style

Huangfu W, Qiu H, Wu W, Qin Y, Zhou X, Zhang Y, Ullah M, He Y. Enhancing the Performance of Landslide Susceptibility Mapping with Frequency Ratio and Gaussian Mixture Model. Land. 2024; 13(7):1039. https://doi.org/10.3390/land13071039

Chicago/Turabian Style

Huangfu, Wenchao, Haijun Qiu, Weicheng Wu, Yaozu Qin, Xiaoting Zhou, Yang Zhang, Mohib Ullah, and Yanfen He. 2024. "Enhancing the Performance of Landslide Susceptibility Mapping with Frequency Ratio and Gaussian Mixture Model" Land 13, no. 7: 1039. https://doi.org/10.3390/land13071039

APA Style

Huangfu, W., Qiu, H., Wu, W., Qin, Y., Zhou, X., Zhang, Y., Ullah, M., & He, Y. (2024). Enhancing the Performance of Landslide Susceptibility Mapping with Frequency Ratio and Gaussian Mixture Model. Land, 13(7), 1039. https://doi.org/10.3390/land13071039

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