Introduction

Landslides are important natural hazard events that occur frequently in China and around the world. Steep topography, heavy precipitation, weak lithological units, adverse anthropologic treatments to land, and earthquakes are among the factors primarily responsible for landslide occurrence (Althuwaynee et al. 2015; Hong et al. 2017; Ma et al. 2015; Yuan et al. 2013, 2015, 2016). Because the occurrence location, size, and volume of landslides are reasonably predictable parameters, the potential for mitigation of their adverse effects is much greater compared with earthquakes. Specifically, landslide susceptibility maps that show the spatial occurrence probability of such events have been used for regional land use management by decision makers because of their effectiveness and ease of production. In this context, many studies conducted in the last two decades have focused on landslide susceptibility mapping.

Close inspection of published reports of landslide susceptibility studies reveals that several datasets and assessment methodologies have been developed and discussed (Broeckx et al. 2018; Hong et al. 2018; Pham et al. 2018; Pourghasemi and Rahmati 2018; Reichenbach et al. 2018; Shirzadi et al. 2017). Although there is no consensus regarding the optimal dataset and assessment methodology, some datasets (e.g., slope angle, lithology, and land use/cover) have been accepted widely as fundamental in landslide susceptibility mapping (Youssef et al. 2015). Certain assessment methodologies have also been adopted in many landslide susceptibility studies, e.g., the analytical hierarchy process (Kumar and Anbalagan 2016; Pourghasemi and Rossi 2016), frequency ratio (Regmi et al. 2014; Wang et al. 2016), statistical index (SI) (Nasiri Aghdam et al. 2016; Zhang et al. 2016a), evidential belief function (EBF) (Ding et al. 2017; Pourghasemi and Kerle 2016; Zhang et al. 2016b), logistic regression (LR) (Raja et al. 2017; Tsangaratos et al. 2017), and weights of evidence (WoE) (Ding et al. 2017; Wang et al. 2016). Given this variety in datasets and methodologies, it is important to compare the results obtained by different methods and datasets to determine the optimal combination.

In addition to the above statistical methods, more sophisticated machine learning methods, such as artificial neural networks (Chen et al. 2017b; Tien Bui et al. 2016; Yilmaz 2010), kernel logistic regression (KLR) (Tien Bui et al. 2016), support vector machine (Chen et al. 2017c; Pham et al. 2015; Pradhan 2013; Tien Bui et al. 2016), random forests (Chen et al. 2017g; Hong et al. 2016; Pourghasemi and Kerle 2016), decision trees (Althuwaynee et al. 2014; Hong et al. 2015; Pradhan 2013), multivariate adaptive regression splines (Chen et al. 2017d; Pourghasemi and Rossi 2016), and derivative approaches of artificial neural networks (Chen et al. 2017a; Nasiri Aghdam et al. 2016; Pradhan 2013; Tien Bui et al. 2012) have also become popular assessment methodologies through integration with developing GIS technologies.

Two of the major drawbacks of bivariate statistical approaches, such as EBF, SI, and WOE, are that strict assumptions must be defined prior to conducting any study (Benediktsson et al. 1989) and that the relationships between conditioning factors are largely neglected. Conversely, machine learning methods do not require any statistical assumptions and they are capable of handling data with various measurement scales; however, they cannot be used to evaluate the relationships between individual factor classes and landslides.

Given the above, it may be concluded that complex and nonlinear problems could be handled using ensemble methods (Tehrany et al. 2014). In this context, the main aim of this study was to investigate the effectiveness of the ensemble methodologies of KLR with bivariate EBF, SI, and WoE models based on comparison of the results obtained. The second purpose, of course, was to build a landslide susceptibility map for the study area that could be used by local decision makers for effective land use planning purposes. The investigation of the use of the EBF, SI, WoE, and KLR ensembles constitutes the novelty of this study.

Materials and methods

The methodology design comprised five steps: (1) spatial data preparation including landslide inventory and conditioning factors; (2) estimation of the EBF, SI, and WOE methods; (3) selection of conditioning factors; (4) construction of landslide susceptibility maps using three bivariate models and three ensemble models; and (5) assessment and validation of model performance (Fig. 1).

Fig. 1
figure 1

Flowchart of the used methodology

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Study area

The study area (Chongren County), which is located in the region 27°25′N–27°56′N, 115°49′E–116°17′E, covers an area of about 1520 km2 in Jiangxi Province (China) (Fig. 2). Chongren County has a subtropical monsoon climate. The average annual temperature is 17.7 °C (Hong et al. 2017). The high frequency of intense rainfall during April–August accounts for 79.5% of the annual total. The average rainfall in May and June is 265 and 305 mm, respectively.

Fig. 2
figure 2

Location map of the study area

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The rivers in Chongren County belong to the Fu River system. The total flow path is up to 910 km, and the drainage density is 0.6 km−2. The main rivers within the study area are the Chongren and Yihuang rivers. Geologically, the Chongren area is located within the depression belt uplift in central–southern Jiangxi Province, and it is a transition zone between the Yu Mountains and the Gan-Fu Plain. The strata outcropped in the study area are mainly pre-Sinian, Sinian, Cambrian, Carboniferous, Triassic, Jurassic, Cretaceous, and Quaternary. The main lithologies are limestone, shale, sandstone, slate, and igneous rocks (Fig. 3).

Fig. 3
figure 3

Geological map of the study area

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Database

Landslide inventory

The compilation of a landslide inventory is the first step in landslide susceptibility modeling, and various methods for this process have been applied in different studies (Harp et al. 2011; Moosavi et al. 2014). Landslide inventory maps are effective and easily comprehensible products for geomorphologists, decision makers, planners, and civil defense managers (Galli et al. 2008). However, the advantages and limitations of applying new remote sensing data and technologies in the production of landslide inventory maps have been discussed in previous work (Guzzetti et al. 2012). Thus, in light of the above analysis, this study adopted field surveys, historical records, and high-resolution satellite images coupled with Google Earth™ technology to produce the landslide inventory map.

In the current study, 222 landslide events were identified and mapped with projected area in the Chongren area. Through investigation of the landslide inventory map, the largest landslide was found to be 15,000 m2, the smallest landslide was 2.5 m2, and the average was 841.3 m2 (Hong et al. 2017). In the Chongren area, local government reports show only 19.1% of the total number of landslides are large-sized landslides (>800 m2) that affect 1365 people (http://www.jxcr.gov.cn/). Medium-sized (200–800 m2) landslides account for 25.4% of the total, and they affect 1019 people. Small-sized landslides (<200 m2) account for 55.5% of the total, and they affect 875 people.

Conditioning factors

The causes of landslide development and occurrence are complex and diverse, and there is no clear agreement with respect to the precise reasons for their manifestation (Domínguez-Cuesta et al. 2007). The complex nature of the development of landslides (Jiménez Sánchez et al. 1999) has caused many researchers to investigate how landslide occurrence might be affected by various conditioning factors, e.g., the topographical, geological, and environmental conditions (Zêzere et al. 1999). Therefore, the selection of appropriate conditioning factors is a challenging task. Some previous studies have assumed that the use of increased numbers of conditioning factors would enhance the precision of a landslide susceptibility map (van Westen et al. 2003). However, other research has indicated that conditioning factors with reasonable quality are necessary for producing accurate landslide susceptibility maps (Jebur et al. 2014). Thus, according to a literature review (Broeckx et al. 2018; Pourghasemi 2014; Reichenbach et al. 2018) and our actual analysis of the geo-environmental characteristics of the study area and data availability, this study considered 15 landslide conditioning factors that were grouped into three categories: topographical, geological, and environmental.

Topographical factors

Topographical factors, such as slope angle, slope aspect, altitude, plan curvature, profile curvature, stream power index (SPI), sediment transport index (STI), and topographic wetness index (TWI), were derived based on 1:50,000 topographic maps (http://www.jxgtt.gov.cn/). Among them, slope angle was used to classify the degree of steepness of hills and mountains (Iwahashi et al. 2003). The initial slope angle is an important factor that affects the peak strength of the slope material, and it controls the source of material available for landslides (Chen et al. 2016). Therefore, in this study, slope was selected as a conditioning factor.

Slope aspect is defined as the direction in which a slope faces and it relates to the degree of solar exposure. Aspect also influences both the vegetation coverage and the daily ranges of temperature and relative humidity of a slope (Jonathan et al. 2006). Many articles have discussed the relationship between slope aspect and landslides; however, there is a lack of consensus regarding its adoption as a conditioning factor. Because slope aspect has been shown to influence landslides triggered by rainfall (Beullens et al. 2014), slope aspect was selected as a conditioning factor in this study.

Altitude is defined as the elevation above a ground reference point, which is commonly the terrain elevation. Altitude is considered an important landslide conditioning factor because of its gravitational potential energy.

Plan curvature influences the convergence and divergence of flow across a surface. Profile curvature affects the acceleration and deceleration of downslope flows, and it influences the processes of erosion and deposition (Kritikos and Davies 2015). These two factors were also accepted as conditioning factors in this study.

SPI is a term that describes the potential flow erosion of the topographic surface at a given point. STI also characterizes the processes of erosion and deposition. TWI can be used to quantify the effects of hydrological processes in relation to topography. Therefore, these three factors were also accepted as conditioning factors.

Geological factors

The lithological data were collected from the China Geology Survey (http://www.cgs.gov.cn/) (1:200,000 scale). The lithology map was reclassified into ten groups according to their geological ages and lithofacies (Hong et al. 2017). The distance to fault map was constructed by generating buffers along the fault lines using ArcGIS software (ESRI 2014).

Environmental factors

The NDVI was derived from Landsat-8 Operational Land Imagery (Path/Row: 121/41; date: November 01, 2017; Product ID: LC81210412017305LGN00; available at http://www.gscloud.cn). The value of the NDVI was estimated using the formula: NDVI = (NIR − R)/(NIR + R), where NIR and R are the near-infrared band and red band, respectively. The land use map was also obtained from the same Landsat 7/ETM+ satellite images. Land use was classified into six categories: residential, bare, water, forest, farmland, and grass. The distance to rivers and the distance to roads maps were also constructed by buffering 1:50,000-scale topographic maps.

The rainfall data were provided by the Jiangxi Province Meteorological Bureau (http://www.weather.org.cn). The mean annual precipitation data for the period of 1960–2012 at 18 rainfall stations were used to construct the rainfall map by application of the inverse distance weighted method (Hong et al. 2017).

Finally, all landslide conditioning factors were converted into raster format with 25-m spatial resolution for application with the models (Fig. 4a–o). The detailed classification of the landslide conditioning factors is shown in Table 1. The area grid comprised 2286 rows by 1782 columns, which corresponded to 2,427,151 cells, 222 of which included landslide occurrences.

Fig. 4
figure 4figure 4figure 4figure 4

Thematic maps of the study area: (a) Slope angle; (b) Slope aspect; (c) Altitude; (d) Plan curvature; (e) Profile curvature; (f) SPI; (g) STI; (h) TWI; (i) Distance to rivers; (j) Distance to roads; (k) Distance to faults; (l) NDVI; (m) Landuse; (n) Lithology; (o) Rainfall

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Table 1 Classes of landslide conditioning factors
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Methods

Evidential belief function (EBF)

In 1967, Dempster first proposed the basis of the Dempster–Shafer theory of evidence (Dempster 1967), which was developed further by Shafer in 1976 (Shafer 1976). This method incorporates four basic EBFs: degrees of belief (Bel), disbelief (Dis), uncertainty (Unc), and plausibility (Pls), of which Bel = low probability and Pls = upper probability constitute the main elements of the theory (Dempster 1967). Unc represents the ignorance of one’s belief in a proposition based on given evidence and its value is Pls – Bel. Dis is the belief that a proposition is not true based on given evidence, the value of which is equal to 1 – Pls or 1 – Bel – Unc. The EBF method is popular in many fields of study, such as forest fire susceptibility mapping (Pourghasemi 2016), landslide susceptibility mapping (Ding et al. 2017; Pourghasemi and Kerle 2016; Pradhan et al. 2014; Tien Bui et al. 2015), and groundwater potential mapping (Mogaji et al. 2016; Tahmassebipoor et al. 2016). The estimation of EBFs can be calculated as follows:

$$ Bel(Cij)=\frac{W_{C_{ij(landslide)}}}{\sum_{j=1}^n{W}_{C_{ij(landslide)}}}, $$
(1)
$$ {W}_{C_{ij}(landslide)=}\frac{N\left(T\cap {C}_{ij}\right)/N(T)}{\left[N\left({C}_{ij}\right)-N\left(T\cap {C}_{ij}\right)\right]/\left[N(C)-N(T)\right]}. $$
(2)

The numerator in Eq. (2) is the proportion of landslide pixels that occur in factor class Cij, and the denominator is the proportion of non-landslide pixels that occur in factor class Cij. \( {W}_{C_{ij(landslide)}} \) is the weight of Cij that supports the belief that landslides are present more than absent.

$$ {W}_{C_{ij}\left( non- landslide\right)=}\frac{\left[N\left({C}_{ij}\right)-N\left(T\cap {C}_{ij}\right)\right]/N(T)}{\left[N(C)-N(T)-N\left({C}_{ij}\right)+N\left(T\cap {C}_{ij}\right)\right]/\left[N(C)-N(T)\right]}. $$
(3)

The numerator in Eq. (3) is the proportion of landslide pixels that do not occur in factor class Cij, and the denominator is the proportion of non-landslide pixels in other attributes outside factor class Cij. \( {W}_{C_{ij}\left( non- landslide\right)} \) is the weight of Cij that supports the belief that landslides are absent more than present. Therefore, we have the following equations:

$$ Dis\left({C}_{ij}\right)=\frac{W_{C_{ij}\left( non- landslide\right)}}{\sum_{j=1}^n{W}_{C_{ij\left( non- landslide\right)}}}, $$
(4)
$$ Un{c}_{Cij}=1- Be{l}_{Cij}- Di{s}_{Cij}, $$
(5)
$$ Pl{s}_{Cij}= Be{l}_{Cij}+ Un{c}_{Cij}. $$
(6)

Statistical index (SI)

The SI was proposed by van Westen (1997). In the SI method, a weight value of a parameter class is characterized by the natural logarithm of the landslide density in the class divided by the landslide density in the entire map. The equation to calculate the weights is as follows (van Westen 1997):

$$ {W}_{SI}=\ln \left(\frac{Densclass}{Densmap}\right)=\ln \left[\raisebox{1ex}{$\frac{N(Si)}{N(Ni)}$}\!\left/ \!\raisebox{-1ex}{$\frac{\sum N(Si)}{\sum N(Ni)}$}\right.\right], $$
(7)

where WSI is the weight for the given parameter class, Densclass is the landslide density within the parameter class, and Densmap is the landslide density within the entire map. N(Si) is the number of landslide pixels in parameter class i, and N(Ni) is the number of pixels in the same parameter class.

Weights of evidence (WoE)

As one of the most popular models, the WOE method adopts the Bayesian theory of conditional probability to quantify spatial associations between evidence layers and known mineral occurrences (Agterberg 1989; Bonham-Carter 1994). In this study, we use the WOE for modeling large-scale landslide susceptibility spatial prediction. Recently, many researchers have applied WoE in various ways, such as mineral prospective mapping (Zeghouane et al. 2016), flood susceptibility (Rahmati et al. 2016), landslide susceptibility mapping (Ding et al. 2017), and groundwater potential (Mogaji et al. 2016; Tahmassebipoor et al. 2016). It is worth noting that conditional independence is the most important issue to be considered in the WOE method (Zhang et al. 2014). Hence, the WOE is determined by the calculation of positive and negative weights W+ and W−, which can be expressed as follows:

$$ {W}^{+}=\ln \frac{p\left\{B|A\right\}}{p\left\{B|\overline{A}\right\}}, $$
(8)
$$ {W}^{-}=\ln \frac{p\left\{\overline{B}|A\right\}}{p\left\{\overline{B}|\overline{A}\right\}}. $$
(9)

In the above two equations, p represents the probability, ln is the natural log, B is the presence of a potential landslide predictive factor, \( \overline{B} \) is the absence of a potential landslide predictive factor, A is the presence of a landslide, and \( \overline{A} \) is the absence of a landslide. Thus, W+ indicates that the predictable variable is present at the landslide locations and W− indicates the absence of the predictable variable. In landslide susceptibility prediction, we use the studentized contrast C/S(C) to measure and reflect the spatial association between the landslide conditioning factors and landslide occurrence, where C is the weight contrast and S(C) is the standard deviation of C. These can be expressed as follows:

$$ C={W}^{+}-{W}^{-}, $$
(10)
$$ S(C)=\sqrt{S^2{W}^{+}+{S}^2{W}^{-}}, $$
(11)

where S2W+ is the variance of the positive weights and S2W− is the variance of the negative weights.

Kernel logistic regression (KLR)

KLR is one type of logistic regression that applies kernel theory. The main aim of this approach is to classify a large quantity of data in a high-dimensional space because it might be difficult to distinguish in the current dimensional space using a linear logistic regression model (Cawley and Talbot 2005; Tien Bui et al. 2016). We can express the KLR as follows:

$$ \log it\left\{p\right\}=w\cdot \varphi (u)+c, $$
(12)

where w is the vector of the landslide conditioning factors, φ(u) is a nonlinear transformation to each input variable, and c is a bias term. For convenience, φ(u) can be simply calculated, i.e., the cause φ(u)φ'(u) is a certain outcome during the calculation procedure, which evaluates the inner product between the image of input vectors in the feature space:

$$ K\left(u,{u}^{\hbox{'}}\right)=\varphi (u)\cdot {\varphi}^{\hbox{'}}(u). $$
(13)

For a kernel to support the interpretation as an inner product in a fixed feature space, the kernel must obey Mercers’ condition (Mercer 1909). Many kernel functions have been suggested, such as the radial basis function (RBF) and the linear kernel (Lin and Lin 2003). In this study, KLR was used to describe the problem:

$$ K\left(u,{u}^{\hbox{'}}\right)={e}^{\left[\frac{-{\left\Vert u-{u}^{\hbox{'}}\right\Vert}^2}{2{\delta}^2}\right]}, $$
(14)

where δ is a turning parameter that controls the sensitivity of the kernel. According to the represented theorem (Kimeldorf and Wahba 1971; Schölkopf et al. 2001), vector w can be determined by minimizing a cost function, which can be expressed as follows:

$$ w={\sum}_{i-1}^n{\alpha}_i\varphi (u) $$
(15)

where αi,i=(1,2,…,n) is the vector of the landslide conditioning factors. Thus, we obtain the following formula:

$$ \log it\left\{p\right\}={\sum}_{i-1}^n{\alpha}_iK\left(u,{u}^{\hbox{'}}\right)+c. $$
(16)

Construction of training and validation datasets

The values of 15 conditioning factors for the three bivariate models were extracted to the landslide inventory in this study. Landslide locations (grid pixels) were assigned to 1, whereas the same number of non-landslide locations (grid pixels) outside the landslides were assigned to 0. To evaluate the prediction capability of landslide susceptibility models, the landslide inventory and non-landslide dataset should be divided into two subsets, i.e., the training and validation sets (Chung and Fabbri 2003). Therefore, the landslide inventory and non-landslide dataset were split randomly into two parts with a ratio of 70:30 to construct and validate the models, respectively. There were 155 landslide locations and 155 non-landslide locations in the training dataset, while the validation dataset had 67 landslide locations and 67 non-landslide locations.

Correlation analysis of conditioning factors

As the ensemble models are a combination of KLR developed from logistic regression, the assessment of correlation among the landslide conditioning factors is an important issue. There are two parameters for assessing the multicollinearity analysis: tolerance (TOL) and the variance inflation factor (VIF) (Chen et al. 2017f).

$$ TOL=1-{R}^2, $$
(17)
$$ VIF=1/ TOL. $$
(18)

According to the literature, a TOL of less than 0.20 or 0.10 and/or a VIF of more than 5 or 10 implies a multicollinearity problem (O’Brien 2007).

Model performance and validation of landslide susceptibility maps

The performances of three landslide ensemble models were evaluated using the receiver operating characteristic (ROC) curve. The area under the ROC curve (AUC) is a significant measurement for the assessment of the prediction capability of models in landslide modeling (Tien Bui et al. 2016). When the AUC is equal to 1, an ideal model is acquired (Chen et al. 2017e). The AUC can be computed using the following equation:

$$ AUC=\frac{\sum TP+\sum TN}{P+N} $$
(19)

where TP is the number of landslides classified correctly, TN is the number of landslides classified incorrectly, P is the total number of landslides, and N is the total number of non-landslides.

The success rate and prediction rate curves of the landslide susceptibility maps were also used in this study. The curves were obtained by plotting the cumulative percentage of landslide susceptibility maps on the x-axis and the cumulative percentage of landslide pixels on the y-axis. The areas under the curves of the success rate (AUC_T) and the prediction rate (AUC_P) were used to reflect the prediction capability of the landslide susceptibility maps.

Results

Analyses of landslide conditioning factors

Multicollinearity analysis was calculated with the training dataset using IBM SPSS Statistics software. The results, shown in Tables 2 and 3, indicate that there were no multicollinearities among the 15 landslide conditioning factors.

Table 2 Spatial relationship between each landslide conditioning factor and landslide by EBF, SI, and WoE models
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Table 3 Multicollinearity analysis
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In addition to the multicollinearity analysis, the predictive capabilities of the landslide conditioning factors were assessed by applying the KLR model with the RBF kernel function. The results of the most effective conditioning factors of the different ensemble models are shown in Table 4. The results indicate that all factors contributed to the models. Altitude, with the highest average merit (AM) in three ensemble models, was found to be the most important factor, followed in descending order by distance to rivers, distance to roads, STI, TWI, lithology, NDVI, distance to faults, SPI, slope angle, rainfall, aspect, land use, and plan and profile curvatures, respectively. Some factors including rainfall, aspect, land use, and plan and profile curvatures made only small contributions to the landslide modeling. However, as all the AMs had positive values, all 15 conditioning factors were considered in constructing the landslide susceptibility maps.

Table 4 Predictive capabilities of conditioning factors using KLR model
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Ensemble of EBF and KLR models

In this study, the parameters of the EBF method (i.e., Bel, Dis, Unc, and Pls) were obtained using the equations introduced earlier (section “Evidential belief function (EBF)”) for each class of conditioning factors. These parameters were computed based on the ratio between the number of landslides per class and the area of each class. The results of the EBF method can be seen in Table 2.

All Pls weights of the conditioning factors were used as input datasets for the EBF and EBF-KLR methods. For each pixel of the study area, the probability of landslide occurrence (PLO) using a linear logistic regression function (Eq. 12) was computed. The PLOs were reclassified based on the area percentage method to construct the landslide susceptibility map. The landslide susceptibility maps based on the EBF and the ensemble of EBF and KLR are shown in Fig. 5a and b, respectively.

Fig. 5
figure 5figure 5

Landslide susceptibility maps by (a) EBF, (b) EBF-KLR, (c) SI, (d) SI-KLR, (e) WoE, (f) WoE-KLR models

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Ensemble of SI and KLR models

Similar to the process of combination of the EBF and KLR methods, the SI was computed for each class of conditioning factors. Then, the SIs were assigned as weights to each class. Eventually, each conditioning factor was reclassified based on its SI and was determined as an input for overlaying with the landslides to extract the dataset for the KLR algorithm. The results of the SI are displayed in Table 2.

All conditioning factors were reclassified based on their SI and then applied as input datasets for the SI and SI-KLR methods. The PLOs were also reclassified based on the area percentage method to construct the landslide susceptibility map. The landslide susceptibility maps based on the SI and SI-KLR models are shown in Fig. 5c and d, respectively.

Ensemble of WoE and KLR models

In the WoE-KLR ensemble model, the parameters C, S (C), and C/S (C) were calculated first based on their function, as described in section “Weights of evidence (WoE)”. The C/S (C) weights were transferred to each class of conditioning factors. Then, each factor was reclassified and overlaid with the landslide locations to construct a database for computing the PLOs using the KLR algorithm.

Similar to the EBF and SI models, the WoE model was used to establish the spatial relationship between each conditioning factor and the landslide locations. The results of SI are presented in Table 2. Based on the C/S(C) of the WoE model, all conditioning factors were reclassified and applied as input datasets for the WoE and WoE-KLR methods. The PLOs were also reclassified according to the area percentage method to construct the landslide susceptibility map. The landslide susceptibility maps based on the WoE and WoE-KLR models are shown in Fig. 5e and f, respectively.

In order to present a better comparison of landslide susceptibility maps, the five landslide susceptibility classes were determined as very high (5%), high (10%), moderate (15%), low (20%), and very low (50%) for the six landslide susceptibility maps.

Ensemble models’ performance and comparison

The AUC curve with the training dataset was used to assess the performances of the three ensemble models, as shown in Table 5 and Fig. 6a. The results indicate that all ensemble models have high prediction accuracy according to the AUC values. Additionally, the EBF-KLR ensemble model has the highest AUC value (AUC = 0.814) followed by the SI-KLR ensemble model (AUC = 0.811) and the WoE-KLR ensemble model (AUC = 0.806). The performances of the three ensemble models based on the AUROC with the validation dataset are shown in Table 6 and Fig. 6b. The results indicate the EBF-KLR ensemble model (AUC = 0.753) outperformed the SI-KLR ensemble model (AUC = 0.752) and the WoE-KLR ensemble model (AUC = 0.744). These findings suggest that although all landslide susceptibility ensemble models showed high prediction accuracy, the EBF-KLR ensemble model had the highest prediction capability for landslide susceptibility mapping in the study area.

Table 5 Ensemble models’ performance using training dataset
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Fig. 6
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Comparison of the three ensemble landslide models using the AUROC curve with a the training dataset and b the validation dataset

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Table 6 Ensemble models’ performance using validating dataset
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Validation of landslide susceptibility maps

The validation of the six landslide susceptibility maps produced by the three bivariate models and the three ensemble models were assessed based on the spatial cross-validation procedure mentioned in section “Model performance and validation of landslide susceptibility maps”. The corresponding AUC_T and AUC_P curves are shown in Figs. 7 and 8 and validation of the landslide susceptibility maps is presented in Table 7. For the training dataset, the EBF-KLR model had the highest prediction capability (0.8511), followed in descending order by the SI-KLR model (0.8505), WoE-KLR model (0.8397), EBF model (0.7978), SI model (0.7951), and WoE model (0.7825). For the validation dataset, the EBF-KLR model had the highest prediction capability (0.7615), followed in descending order by the SI-KLR model (0.7595), SI model (0.7503), EBF model (0.7437), WoE-KLR model (0.7286), and WoE model (0.7198). Thus, the results show the ensemble EBF-KLR was the most capable of mapping landslide susceptibility within the study area.

Fig. 7
figure 7

Model validation with the success rate (AUC_T) curve for the six landslide susceptibility maps

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Fig. 8
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Model validation with the prediction rate (AUC_P) curve for the six landslide susceptibility maps

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Table 7 Validation of landslide susceptibility maps
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Landslide density (LD) was also calculated to validate the landslide susceptibility maps. The LD is defined as the ratio between the percentages of landslides and the percentages of each susceptible class (Pham et al. 2016); higher susceptible classes should have higher LDs for reliable landslide susceptibility maps. As mentioned above, the area percentages of each susceptible class were defined as very high (5%), high (10%), moderate (15%), low (20%), and very low (50%). Therefore, it is only necessary to calculate the percentages of landslide locations for each class. The results of the LD analysis are shown in Table 8. It can be observed that the very high class has the highest LD values, followed in descending order by the high, moderate, low, and very low classes. The results also show that the ensemble models yielded better performance than the individual bivariate models, and that the EBF-KLR model improved the performance of the bivariate EBF model more significantly than the other two ensemble models.

Table 8 Landslide density analysis on landslide susceptibility maps
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Discussion

Landslide susceptibility describes the probability of landslide occurrence within a particular area, and the correlation between previous landslide locations and possible conditioning factors (Romer and Ferentinou 2016). In previous decades, many methods including traditional statistical models (Ding et al. 2017; Zhang et al. 2016a) and sophisticated machine learning models (Chen et al. 2017g; Pourghasemi and Kerle 2016; Youssef et al. 2016) have been used in conjunction with the development of GIS technology to predict the spatial distributions of landslides. However, both bivariate and machine learning approaches have their limitations, which could potentially be eliminated by the use of ensemble models. Therefore, it is necessary to explore and to compare new ensemble methods and techniques in application to landslide modeling. Recently, some ensemble machine learning methods have been applied in landslide susceptibility, for example, Shirzadi et al. (2017) used a Naive Bayes trees (NBT) and random subspace (RS) ensemble method for landslide susceptibility mapping at the Bijar region, Kurdistan province (Iran), and their result showed that NBT-RS significantly improved the performance of the NBT base classifier. Hong et al. (2018) found that J48 Decision Tree with the Rotation Forest model presents the highest prediction capability (AUC =0.855); it improved the performance of the J48 Decision Tree base classifier significantly. Pham et al. (2018) integrated the MultiBoost (MB) ensemble and support vector machine (SVM) for modeling of susceptibility of landslides in the Uttarakhand State, Northern India, and their result showed that the MBSVM outperforms the LR and single SVM models. Though many ensemble methods have been applied in landslide susceptibility, until now, there is still no agreement on which is the best ensemble method in landslide susceptibility mapping. In addition, more experiments are needed to compare different areas to find the difference among each method.

The most important step was to select the landslide conditioning factors because they affect the quality of landslide susceptibility analysis (Irigaray et al. 2007; Romer and Ferentinou 2016). However, there are no standard guidelines regarding the selection of landslide conditioning factors (Tien Bui et al. 2016). This study built a landslide susceptibility model using 15 landslide conditioning factors that included topographical, geological, and environmental factors. Then, TOL and VIF were used to establish the absence of multicollinearity among the 15 landslide conditioning factors (Table 3). Subsequently, the classifier attribute evaluation method (Witten et al. 2011) using the KLR model with the RBF kernel function was used to assess the importance of the variables. The results showed that all 15 conditioning factors had positive predictive capability in the model (Table 4); therefore, they were all used to build landslide susceptibility models.

The goodness-of-fits of three ensemble models were evaluated using ROC and AUC values. The results indicated that all ensemble models had high prediction accuracy based on the AUC values. The EBF-KLR ensemble model had the highest AUC values for both the training (AUC = 0.814) and the validation (AUC = 0.753) datasets, followed in descending order by the SI-KLR ensemble model and the WoE-KLR ensemble model (Tables 5 and 6). However, the results also showed that different conditioning factors had different contributions to the models (Table 4). In general, altitude, distance to rivers, and distance to roads were found to be the most important factors for the three ensemble models. Conversely, the factors of land use, profile curvature, and plan curvature yielded the lowest predictive capabilities for the three ensemble models. The normalized predictive capabilities of the conditioning factors for the three ensemble models were used to visualize the relative importance of the 15 conditioning factors (Fig. 9). It was observed that altitude contributed the highest percentages of 10.573, 10.397, and 11.111% for the EBF-KLR, SI-KLR, and WoE-KLR models, respectively; distance to rivers yielded the second highest contributions of 9.688, 9.713, and 9.677%, respectively, and distance to roads yielded the third highest contributions of 9.209, 9.234, and 9.319%, respectively. In contrast, profile curvature yielded the lowest contributions of 1.569, 1.710, and 1.362%, respectively. Therefore, because of the types of input variables and the models used, it was concluded that landslide conditioning factors tend to have different contributions (Tien Bui et al. 2016). Further studies should be undertaken to explore the optimum method for selecting the optimal factors for both this and similar study areas.

Fig. 9
figure 9

Relative importance of conditioning factors for different ensemble models

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To evaluate and compare the three ensemble models with the three individual bivariate models, this study adopted the methods of the AUC_T and AUC_P curves, and LD analysis. The results suggested the three ensemble models showed higher prediction capabilities for both the training and the validation datasets than each of the three individual bivariate models. The EBF-KLR ensemble exhibited the optimal performance, which could improve the performance of the EBF model significantly. However, it should be noted that the other two ensembles also yielded reasonable performance.

Conclusions

This study evaluated landslide susceptibility in Chongren County (China) using novel ensembles of bivariate statistical-methods-based (EBF, SI, and WoE) kernel logistic regression machine learning classifiers. A series of conditioning factors (slope angle, slope aspect, altitude, plan curvature, profile curvature, SPI, STI, TWI, distance to rivers, distance to roads, distance to faults, NDVI, land use, lithology, and rainfall) were used as the inputs to the three hybrid models. A landslide inventory comprising 222 landslides was divided randomly into a training set (70%) for evaluation of the landslide susceptibility models and a validation set (30%) for validation of the model procedure.

The results showed that the three hybrid models were successful at identifying landslide-prone areas. The results also showed that the hybrid models could improve the predictive capability of the bivariate models, and that the EBF-KLR hybrid model yielded the highest predictive capability in landslide susceptibility assessment.

In conclusion, the landslide susceptibility maps produced in the present study may be useful for land use planning and decision making in areas prone to landslides. Moreover, this study also demonstrated the superiority of hybrid models in landslide susceptibility modeling.