An RVM-Based Model for Assessing the Failure Probability of Slopes along the Jinsha River , Close to the Wudongde Dam Site , China

Assessing the failure potential of slopes is of great significance for land use and management. The objective of this paper is to develop a novel model for evaluating the failure probability of slopes based on a relevance vector machine (RVM), with a special attention to the characteristics of failed slopes along the lower reaches of the Jinsha River, close to the Wudongde dam site. Seven parameters that influence the occurrence of landslides were selected as environmental factors; namely lithology, slope angle, slope height, slope aspect, slope structure, distance from faults, and land use. A total of 55 landslides mapped in the study area were used to train and test the RVM model. The results suggest that the accuracy of the model in predicting the failure probability of slopes, using both training and testing data sets, is very high and deemed satisfactory. To validate the model performance, it was applied to 28 landslide cases identified in the upper reaches of the Jinsha River, where environmental and geological conditions are similar to those of the study area. An accuracy of approximately 92.9% was obtained, which demonstrates that the RVM model has a good generalization performance.


Introduction
Landslides are among the most notable geological processes that frequently occur in mountainous regions, resulting in financial losses measured in hundreds of billions of euros annually, injuries, and fatalities [1][2][3].These disasters have caught unprecedented attention in the world; lots of researchers are continuously carrying out relevant research, mainly focusing on the prediction of landslides [4,5].
Various approaches have been developed for landslide hazard assessment, and can be grouped into three broad categories; analytic, statistical, and soft computing methods [6].Analytic approaches consider the failure mechanisms of slopes and can provide an accurate prediction for the instability of slopes.However, when the study area is large, application of these approaches may be difficult.Statistical analyses such as discriminant analysis [4,7], logistic regression [8,9], and Bayes learning [10,11], are deemed to be more suitable for geological hazard assessment in large and complex areas [12,13].With the development of science and technology, soft computing techniques, such as data mining and artificial intelligence, have also been widely used in geological hazard assessment.Examples of these approaches include artificial neural networks [14][15][16][17], genetic algorithms [18,19], decision trees [20,21], and support vector machines [22][23][24][25].However predictions provided by these methods are not probabilistic.
Hybrid methods, which are established by combining statistical approaches and artificial intelligence, have also been adopted for assessing geological hazards; these include artificial neural network (ANN)-Bayes analysis [14], ANN-fuzzy logic [26], and neuro-fuzzy inference systems [27,28].However the ANN-based approaches cannot provide objective and steady assessment results because their outcomes are operator dependent [13,15].
The Bayes learning algorithm is considered to be an effective tool for knowledge representation and reasoning under the influence of uncertainty [10].Based on this algorithm, a recently developed machine learning technique, relevance vector machine (RVM), was originally introduced by Tipping [29].As a Bayesian treatment of the sparse learning problem, the RVM can yield a probabilistic output [30].
In this study, a novel empirical model for slope failure analyses based on RVM is presented.We selected the lower reaches of the Jinsha River close to the Wudongde dam site as the study area; 55 landslides mapped in the region were utilized to train and test the RVM model.To evaluate the validity of the model, it was applied to another landslide site where the environmental conditions are similar to those of the study area.

Study Area
The study area (Figure 1) lies along the lower reaches of the Jinsha River and is the reservoir region of the Wudongde hydropower station, which is located in the mountains separating the Sichuan and Yunnan provinces.The occurrence of landslides not only poses a threat to human lives and properties, but also affects the stability of the Wudongde dam.Thus assessing the failure potential of slopes in this area is of great significance.
Sustainability 2017, 9, 32 2 of 17 Hybrid methods, which are established by combining statistical approaches and artificial intelligence, have also been adopted for assessing geological hazards; these include artificial neural network (ANN)-Bayes analysis [14], ANN-fuzzy logic [26], and neuro-fuzzy inference systems [27,28].However the ANN-based approaches cannot provide objective and steady assessment results because their outcomes are operator dependent [13,15].
The Bayes learning algorithm is considered to be an effective tool for knowledge representation and reasoning under the influence of uncertainty [10].Based on this algorithm, a recently developed machine learning technique, relevance vector machine (RVM), was originally introduced by Tipping [29].As a Bayesian treatment of the sparse learning problem, the RVM can yield a probabilistic output [30].
In this study, a novel empirical model for slope failure analyses based on RVM is presented.We selected the lower reaches of the Jinsha River close to the Wudongde dam site as the study area; 55 landslides mapped in the region were utilized to train and test the RVM model.To evaluate the validity of the model, it was applied to another landslide site where the environmental conditions are similar to those of the study area.

Study Area
The study area (Figure 1) lies along the lower reaches of the Jinsha River and is the reservoir region of the Wudongde hydropower station, which is located in the mountains separating the Sichuan and Yunnan provinces.The occurrence of landslides not only poses a threat to human lives and properties, but also affects the stability of the Wudongde dam.Thus assessing the failure potential of slopes in this area is of great significance.The elevation ranges from 740 to 3900 m.This area experiences a low-latitude plateau subtropical monsoon climate characterized by plenty of sun and large evaporation capacity throughout the year [31].The mean annual temperature is 20.9 °C.It receives a mean annual rainfall varying from 600 to 800 mm, while the mean annual evaporation is 698 mm.

Geological and Geomorphological Settings
From the tectonic standpoint, the study area is located in the eastern section of the Tethys-Himalaya tectonic domain, which is one of the tectonic zones of the Himalaya characterized by intense compressing and folding.The predominant regional structures are large-scale faults constituting the famous Chuan-Dian N-S tectonic belt [32].A total of 13 regional faults are situated in this region and dominantly trend approximately N-S (Figure 2).Several strong earthquakes have been triggered by these faults since 1955 [33], such as the Lazha earthquake (magnitude scale 6.7,The elevation ranges from 740 to 3900 m.This area experiences a low-latitude plateau subtropical monsoon climate characterized by plenty of sun and large evaporation capacity throughout the year [31].The mean annual temperature is 20.9 • C. It receives a mean annual rainfall varying from 600 to 800 mm, while the mean annual evaporation is 698 mm.

Geological and Geomorphological Settings
From the tectonic standpoint, the study area is located in the eastern section of the Tethys-Himalaya tectonic domain, which is one of the tectonic zones of the Himalaya characterized by intense compressing and folding.The predominant regional structures are large-scale faults constituting the famous Chuan-Dian N-S tectonic belt [32].A total of 13 regional faults are situated in this region and dominantly trend approximately N-S (Figure 2).Several strong earthquakes have been triggered by these faults since 1955 [33], such as the Lazha earthquake (magnitude scale 6.7, 1955) which was triggered by the Tanglang-Yimeng fault, and the Panzhihua earthquake (magnitude scale 6.1, 2008), triggered by the Mopanshan-Lvzhijiang fault.The geology is comprised of two major components; a pre-Sinian crystalline basement and a Sinian-Cretaceous sedimentary cover.The former is mainly composed of a range of metamorphic rocks (phyllite, slate and schist), which widely outcrop along the Jinsha River.The latter consists of limestone, sandstone, mudstone, and shale formations and is also widespread.
The geomorphological settings reflect the complex interplay between the geological and structural conditions of the area.Steep topographical characteristics predominate this region, with the average slope angle ranging from 30° to 45°.The valleys present a mountain canyon geomorphology.Geomorphic features include cliffs, ridges, gorges, rocky slopes, and Quaternary deposits along the river valleys.The distribution and extension of the river network and ridges is controlled by the structures to some extent.The effect of high relief and structural control is also well reflected by deep gorges and narrow valleys carved by numerous channels.
Phyllite, slate, schist, shale, and mudstone are strongly weathered and fractured and are prone to slope failures.Quaternary deposits composed of alluvial and eluvial deposits often outcrop as a cover layer on the riverbed and gentle slopes and are affected by transitional or rotational landslides triggered by the undercutting of the Jinsha River.

Landslide Identification
Landslide identification was carried out using SPOT5 remote sensing images and field surveys.The SPOT5 images, which were obtained by the SPOT5 satellite launched in 2002 with a multispectral resolution of 10 m and a panchromatic resolution of 2.5 m, have been largely utilized in geological hazard surveys.A series of field investigations, aimed at the confirmation of the mapped landslides through remote sensing images and the investigation of the link between the occurrence of landslides and environmental factors, were conducted.In general, there are three main types of landslides present in the study area; translational movements (55 locations), rock falls (26 locations), and debris flows (239 locations).Each type of landslide has different mechanism requiring separate study for the spatial prediction of landslides.Therefore, in this study, only the 55 translational landslides (Figure 3) were used for analysis.At the time of fieldwork, 44% of the slope movements were classified as active, while the class of dormant movements corresponds to 33%, and 23% of the slope movements were considered stabilized.The highest frequency of landslide phenomena was recorded in mudstones and metamorphic rock formations (phyllite, slate, and The geology is comprised of two major components; a pre-Sinian crystalline basement and a Sinian-Cretaceous sedimentary cover.The former is mainly composed of a range of metamorphic rocks (phyllite, slate and schist), which widely outcrop along the Jinsha River.The latter consists of limestone, sandstone, mudstone, and shale formations and is also widespread.
The geomorphological settings reflect the complex interplay between the geological and structural conditions of the area.Steep topographical characteristics predominate this region, with the average slope angle ranging from 30 • to 45 • .The valleys present a mountain canyon geomorphology.Geomorphic features include cliffs, ridges, gorges, rocky slopes, and Quaternary deposits along the river valleys.The distribution and extension of the river network and ridges is controlled by the structures to some extent.The effect of high relief and structural control is also well reflected by deep gorges and narrow valleys carved by numerous channels.
Phyllite, slate, schist, shale, and mudstone are strongly weathered and fractured and are prone to slope failures.Quaternary deposits composed of alluvial and eluvial deposits often outcrop as a cover layer on the riverbed and gentle slopes and are affected by transitional or rotational landslides triggered by the undercutting of the Jinsha River.

Landslide Identification
Landslide identification was carried out using SPOT5 remote sensing images and field surveys.The SPOT5 images, which were obtained by the SPOT5 satellite launched in 2002 with a multispectral resolution of 10 m and a panchromatic resolution of 2.5 m, have been largely utilized in geological hazard surveys.A series of field investigations, aimed at the confirmation of the mapped landslides through remote sensing images and the investigation of the link between the occurrence of landslides and environmental factors, were conducted.In general, there are three main types of landslides present in the study area; translational movements (55 locations), rock falls (26 locations), and debris flows (239 locations).Each type of landslide has different mechanism requiring separate study for the spatial prediction of landslides.Therefore, in this study, only the 55 translational landslides (Figure 3) were used for analysis.At the time of fieldwork, 44% of the slope movements were classified as active, while the class of dormant movements corresponds to 33%, and 23% of the slope movements were considered stabilized.The highest frequency of landslide phenomena was recorded in mudstones and metamorphic rock formations (phyllite, slate, and schist).The smallest landslide covered an area of 0.03 km 2 , while the largest one was 4.2 km 2 .Figure 4 gives some examples of the landslides.
Sustainability 2017, 9, 32 4 of 17 schist).The smallest landslide covered an area of 0.03 km 2 , while the largest one was 4.2 km 2 .Figure 4 gives some examples of the landslides.

Influencing Factors
Landslide hazard assessment is often performed based on the assumption that future landslides will occur in the areas where environmental conditions are similar to those of past and present failures [34].Therefore it relies strongly on identifying landslide scars, characterizing the properties of failed sites, and confirming the link between landslide distribution and spatial variation of parameters [35].There is no standard principle for selecting the influencing parameters because they often vary from one area to another.However it is commonly recognized that the parameter selection depends on the environmental conditions of the study area, the mechanisms of failed slopes, and the scale of analyses [17].It should be implemented according to the data availability and the significance of data in relation to the problem at question [23].
Based on the review of previous literature [13,16,17,25] and field surveys, seven factors that were identified as causative and triggering factors for landslide activity in the study area were selected to predict the failure potential of slopes.They are lithology, slope angle, slope aspect, slope height, slope structure, distance from faults, and land use.This research selected a single slope as a schist).The smallest landslide covered an area of 0.03 km 2 , while the largest one was 4.2 km 2 .Figure 4 gives some examples of the landslides.

Influencing Factors
Landslide hazard assessment is often performed based on the assumption that future landslides will occur in the areas where environmental conditions are similar to those of past and present failures [34].Therefore it relies strongly on identifying landslide scars, characterizing the properties of failed sites, and confirming the link between landslide distribution and spatial variation of parameters [35].There is no standard principle for selecting the influencing parameters because they often vary from one area to another.However it is commonly recognized that the parameter selection depends on the environmental conditions of the study area, the mechanisms of failed slopes, and the scale of analyses [17].It should be implemented according to the data availability and the significance of data in relation to the problem at question [23].
Based on the review of previous literature [13,16,17,25] and field surveys, seven factors that were identified as causative and triggering factors for landslide activity in the study area were selected to predict the failure potential of slopes.They are lithology, slope angle, slope aspect, slope height, slope structure, distance from faults, and land use.This research selected a single slope as a

Influencing Factors
Landslide hazard assessment is often performed based on the assumption that future landslides will occur in the areas where environmental conditions are similar to those of past and present failures [34].Therefore it relies strongly on identifying landslide scars, characterizing the properties of failed sites, and confirming the link between landslide distribution and spatial variation of parameters [35].There is no standard principle for selecting the influencing parameters because they often vary from one area to another.However it is commonly recognized that the parameter selection depends on the environmental conditions of the study area, the mechanisms of failed slopes, and the scale of analyses [17].It should be implemented according to the data availability and the significance of data in relation to the problem at question [23].
Based on the review of previous literature [13,16,17,25] and field surveys, seven factors that were identified as causative and triggering factors for landslide activity in the study area were selected to predict the failure potential of slopes.They are lithology, slope angle, slope aspect, slope height, slope structure, distance from faults, and land use.This research selected a single slope as a computing unit [16], and values of the influence factors were derived for each slope in the database.Table 1 presents the factors and their classes used in this study.The frequency distribution of landslide occurrence in each class is shown in Figure 5.
Table 1.Landslide influencing factors and their classifications.

Description
Class ID

Lithology
Lithology has been considered to be one of the main parameters influencing the stability of slopes.Since different lithologic units have different slope stability performances, they are very important for landslide prediction [4].The large surface development of formations, such as schist formations, flysch sediments, and metamorphic rock formations with anisotropic geomechanical behavior, facilitates the manifestation of abundant slope failures.The lithology was derived from a lithologic map at a 1:100,000 scale and was grouped into three categories (Table 1) according to Peng et al. [25] and Fourniadis et al. [36].Figure 5a shows that approximately 87% of the landslides occurred on Quaternary deposits, strongly weathered sandstones, mudstones, and metamorphic rocks (phyllite, slate and schist).

Slope Angle
Slope angle is an essential factor controlling the stability of a slope.The shear stress induced by gravity increases with the increase of the slope angle; therefore landslides tend to occur more frequently on steeper slopes [24].The slope angle was measured from the slope profile that was derived from the digital elevation model (DEM).Note that a slope angle of 10° was taken as the threshold because very few slopes less than that angle have failed [16].The slope angle of the study area was divided into five classes (Table 1): 0°-10°, 10°-20°, 20°-30°, 30°-40°, and >40°.Figure 5b illustrates that the largest numbers of landslides were recorded in the classes of 20°-30° (49.1%) and 10°-20° (32.7%).

Slope Height
Slope height denotes the difference value between the head and tail elevations of a slope.A slope with higher height often indicates a higher probability of experiencing a landslide event [37,38].The slope height was directly derived from the DEM.As listed in Table 1, the slope height was partitioned into four classes according to Zhao et al. [38] and flied surveys.The distribution of landslides in the height classes is show in Figure 5c.

Lithology
Lithology has been considered to be one of the main parameters influencing the stability of slopes.Since different lithologic units have different slope stability performances, they are very important for landslide prediction [4].The large surface development of formations, such as schist formations, flysch sediments, and metamorphic rock formations with anisotropic geomechanical behavior, facilitates the manifestation of abundant slope failures.The lithology was derived from a lithologic map at a 1:100,000 scale and was grouped into three categories (Table 1) according to Peng et al. [25] and Fourniadis et al. [36].Figure 5a shows that approximately 87% of the landslides occurred on Quaternary deposits, strongly weathered sandstones, mudstones, and metamorphic rocks (phyllite, slate and schist).

Slope Angle
Slope angle is an essential factor controlling the stability of a slope.The shear stress induced by gravity increases with the increase of the slope angle; therefore landslides tend to occur more frequently on steeper slopes [24].The slope angle was measured from the slope profile that was derived from the digital elevation model (DEM).Note that a slope angle of 10 • was taken as the threshold because very few slopes less than that angle have failed [16].The slope angle of the study area was divided into five classes (Table 1): 0 • -10 • , 10 • -20 • , 20 • -30 • , 30 • -40 • , and >40 • .Figure 5b illustrates that the largest numbers of landslides were recorded in the classes of 20 • -30 • (49.1%) and 10 • -20 • (32.7%).

Slope Height
Slope height denotes the difference value between the head and tail elevations of a slope.A slope with higher height often indicates a higher probability of experiencing a landslide event [37,38].The slope height was directly derived from the DEM.As listed in Table 1, the slope height was partitioned into four classes according to Zhao et al. [38] and flied surveys.The distribution of landslides in the height classes is show in Figure 5c.

Slope Aspect
Aspect controls some microclimatic parameters, such as exposure to sunlight and winds, rainfall intensity, and soil moisture [17].It was obtained from the DEM and was categorized into four classes according to Conforti et al. [17], as shown in Table 1.The relationship between lithology and failed slopes is presented in Figure 5d.

Slope Structure
Slope structure represents the spatial relationship between the rock strata and slope face.Slopes in the study area were measured from field investigations and were classified into four structural categories (Table 1): anti-dip, insequent, transverse, and dip-bedded.Field investigations demonstrate that dip-bedded slopes are prone to failures because of the erosion of slope toes caused by the Jinsha River. Figure 5e indicates that slope failures predominantly occurred on dip-bedded slopes, occupying 70.9% of the landslides in the area.However only 5.5% of the landslides occurred on anti-dip slopes.

Distance from Faults
Field evidence suggests a strong influence of tectonic settings on the occurrence of landslides [39].The distance from faults was obtained from the geological map of the region (1:100,000).Approximately 49.1% (Figure 5f) of slope failures occurred in the sites with a minimum distance of less than 500 m from faults.

Land Use
Land use has been used as a predisposing factor in landslide hazard assessment.It was divided into three classes (Table 1) based on field surveys.Figure 5g shows that barren land and residential land have significant influence on the occurrence of landsides, and both of them occupy 41.8% of slope failures.

Relevance Vector Machine
RVM is based on a Bayesian learning framework and can output the probabilities of class membership.It has the same functional form as the support vector machine (SVM) and shares many of the characteristics of SVM whilst avoiding the SVM's main limitations [40].The structure of the RVM is represented by the sum of product of weights and kernel functions, which is expressed as follows [41]: where w i is the weight and K(x, x i ) is a kernel function.The commonly used kernel is the Gaussian kernel K(x, , where σ is the kernel parameter controlling the sensitivity of the kernel.This function is not sensitive to outliers and can handle the case in which the relationship between class labels and attributes is nonlinear [13]. In this paper, the basic theory of RVM classification is briefly introduced.For further details of RVM, readers can refer to Tipping [29,41] and Bishop [40].For two-class (binary) classification, RVM is used to predict the posterior probability of class membership of one of the classes, given the input x.By applying the logistic sigmoid function σ(y) = 1/(1 + e −y ) to y(x) and adopting the Bernoulli distribution for p(t|w), the likelihood can be written as [40]: where the targets t i ∈ {0, 1}.In this study, 0 and 1 denote the stable and failed cases, respectively.The weights w cannot be analytically obtained and so are denied the closed-form expression for either the weight posterior p(w|t, α) or the marginal likelihood p(t|α), with a hyper-parameter vector α.Therefore, according to Tipping [40], the following approximation procedure proposed by MacKay [42] and based on Laplace's method is utilized: (1) For the current fixed values of α, the most probable weights w MP are found, giving the location of the mode of the posterior distribution.Since p(w|t, α) ∝ p(t|w) p(w|α), this is equivalent to finding the maximum, over w, of log{p(t|w)p(w|α where y i = σ{y(x i ; w)} and A = diag(α 0 , α 1 , α 2 , . . ., α N ) for the current values of α.Since Equation ( 3) is a penalized, logistic, log-likelihood function, iterative maximization is required.The iteratively reweighted least-square algorithm is adopted to find w MP in the following procedure.
(2) Equation ( 3) is differentiated twice to give: where and Φ = [ϕ(x 1 ), ϕ(x 2 ), . . ., ϕ(x N )] T is the N × (N + 1) design matrix with ϕ(x i ) = [1, K(x i , x 1 ), K(x i , x 2 ), . . ., K(x i , x N )] T .This is then negated and inverted to give the covariance ∑ for a Gaussian approximation to the posterior over weights centered at w MP : (3) Using the statistics ∑ and w MP of the Gaussian approximation, MacKay's approach is used to update the hyper-parameter α by where ∑ ii is the ith diagonal element of the covariance ∑, and w MP = ∑Φ T Bt.
During the optimization process, many α i will have large (in principle infinite) values; thus the values of the corresponding weights will tend toward zero.Therefore these weights and the corresponding basis functions are removed from the model and thus play no role in making predictions for new inputs.Those examples remaining with w i = 0 are termed relevance vectors.

Data Processing
RVM models require that each environmental parameter should be represented by a vector of real numbers.In this work, an m-digit number is used to represent an m-category attribute [16].Only one of the digits is one and the others are zero.For example, a four-category attribute (e.g., slope height in Table 1) is represented by (1,0,0,0), (0,1,0,0), (0,0,1,0) or (0,0,0,1).Therefore the seven influencing factors of each slope can be converted into a vector of 27 bites.

Preparation of Training and Testing Data
For a two-class RVM, 'stable' sites are necessary.In this study, 20 'stable' sites were randomly chosen from the non-landslide sites where slope angles are less than 10 • , a value which was taken as the threshold because very few slopes less than that angle have failed.The landslide data and non-landslide data were randomly divided into two groups [16]: (1) group 1, which contained 80% of the landslides (45 cases) and in which the same ratio of the non-landslides (16 cases) formed the training dataset; and (2) group 2, which contained the remaining 20% of the landslides and in which non-landslides was used as testing dataset for verifying the performance of the model.The target values for landslides were given a value of 1, while a 0 value was assigned to those of non-landslides in the training dataset.

Parameter Determination
In an RVM, the controlling parameter (i.e., the kernel parameter σ) needs to be defined.Considering that there is a lack of information in most related papers concerning the determination of the optimal σ for RVM, a procedure of its estimation was conducted, in which several different values of σ were checked to determine which one of them gives better classification capabilities.As landslide hazard assessment is linearly non-separate problem, a cross-validation approach is adopted for the parameter search [13,30].The accuracy is defined as the percentage of correct predictions for slope failure probabilities among all testing slopes [30].In this research, "correct" could be defined as follows: for a failed slope, the model's prediction is considered "correct" if the model's output is greater than 0.5; on the other hand, for a stable slope, it is considered "correct" if the model's output is less than 0.5.In this work, the 4-fold cross-validation technique is used by dividing the training dataset into 4 folds [30]; one fold (25%) is used as the validation set and the combination of the remaining three folds (75%) is used for training.By iterating each fold as the validation set and the aggregation of other folds as the training set, four validation accuracies can be obtained.The average of these accuracies is taken as the cross-validation accuracy (CVA) for a given σ.According to Wang et al. [30], several different values of σ are considered (Table 2).The value which yields the highest CVA is deemed to be the optimal value of σ.As shown in Table 2, the RVM provides the highest CVA value of 98.3% when σ = 4, which is in accordance with the results obtained by Wang et al. [43].Therefore the ideal value of σ is 4.   3 lists the relevance vectors and their corresponding weights.As shown in Table 3, the RVM model employs 27 cases (45%) of the training dataset as relevance vectors, including 17 failed cases and 10 stable cases.It is worth mentioning here that the relevance vectors used in the RVM model represent prototypical examples.These examples exhibit the essential features of the information of the data, and thus are able to transform the input data into the specified targets [44].
The goal of the RVM model is to correctly classify a given slope to the target observation of either failed slope (t = 1) or stable slope (t = 0).For a given slope with particular environmental factors described by a vector x i , its failure probability is represented by p(t = 1|x i ), which is computed by Equation (3).The classification rule of the RVM used in this study is the following: if p(t = 1|x i ) > 0.5, the slope is classified into the occurrence of a landslide; if p(t = 1|x i ) < 0.5, it is divided into the absence of a landslide.The RVM model was applied to predict the failure probabilities of the 60 slopes in the training dataset.The results (Figure 7) show that all the 45 failed slopes have the failure probabilities of more than 0.8, a value which is high enough for the occurrence of a landslide.In addition, the values of failure probability for the 15 stable slopes are all less than 0.25, suggesting that these slopes are impossible for suffering from slope failures.Therefore the prediction accuracy for the 60 slopes reaches 100%.
The goal of the RVM model is to correctly classify a given slope to the target observation of either failed slope (t = 1) or stable slope (t = 0).For a given slope with particular environmental factors described by a vector xi, its failure probability is represented by p(t = 1|xi), which is computed by Equation (3).The classification rule of the RVM used in this study is the following: if p(t = 1|xi) > 0.5, the slope is classified into the occurrence of a landslide; if p(t = 1|xi) < 0.5, it is divided into the absence of a landslide.
The RVM model was applied to predict the failure probabilities of the 60 slopes in the training dataset.The results (Figure 7) show that all the 45 failed slopes have the failure probabilities of more than 0.8, a value which is high enough for the occurrence of a landslide.In addition, the values of failure probability for the 15 stable slopes are all less than 0.25, suggesting that these slopes are impossible for suffering from slope failures.Therefore the prediction accuracy for the 60 slopes reaches 100%.To test the performance of the model, it was then applied to the testing dataset.The failure probability for each slope is listed in Table 4.For the 15 failed slopes, one slope has a probability of approximately 0.83 to fail and the others have failure probabilities of more than 0.95, whivh is very close to 1.All the stable slopes have failure probabilities of less than 0.25.Thus the accuracy of the classification of the slopes in the testing dataset is also 100%.The results demonstrate that the RVM model can provide a stable reliable prediction for landslide hazards in the study area.To test the performance of the model, it was then applied to the testing dataset.The failure probability for each slope is listed in Table 4.For the 15 failed slopes, one slope has a probability of approximately 0.83 to fail and the others have failure probabilities of more than 0.95, whivh is very close to 1.All the stable slopes have failure probabilities of less than 0.25.Thus the accuracy of the classification of the slopes in the testing dataset is also 100%.The results demonstrate that the RVM model can provide a stable reliable prediction for landslide hazards in the study area.

Evaluation of the Model
In this section, 28 landslides mapped in the upper reaches of the Jinsha River, close to the Rimian dam (Figure 1),where environmental conditions are similar to those of the study area [45], were selected as an example to evaluate the performance of the model.The distribution of the landslides is shown in Figure 8. Similar to the study area, this area is also located in the Chuandian N-S tectonic belt, with steep topology controlled by several large-scale faults.The main rock types include limestone, phyllite, schist, and shale.The mean annual precipitation and evaporation range from 350 to 650 mm, and from 750 to 2000 mm, respectively.The annual average temperature varies between 13.8 and 19.2 • C.

Evaluation of the Model
In this section, 28 landslides mapped in the upper reaches of the Jinsha River, close to the Rimian dam (Figure 1),where environmental conditions are similar to those of the study area [45], were selected as an example to evaluate the performance of the model.The distribution of the landslides is shown in Figure 8. Similar to the study area, this area is also located in the Chuandian N-S tectonic belt, with steep topology controlled by several large-scale faults.The main rock types include limestone, phyllite, schist, and shale.The mean annual precipitation and evaporation range from 350 to 650 mm, and from 750 to 2000 mm, respectively.The annual average temperature varies between 13.8 and 19.2 °C.Table 5 lists the parameters of these slopes.The failure probabilities of these slopes were predicted using the RVM model, and the results are shown in Table 5.Among the 28 failed slopes, there are only two slopes that were wrongly partitioned into the group of stable ones, whose failure probabilities as calculated by the RVM model are less than 0.5.The prediction accuracy among the 28 slopes is approximately 92.9%, which is deemed satisfactory.Therefore the RVM model with seven triggering factors has a good prediction performance and could be extended to other sites where environmental conditions are similar to those of the study area.Table 5 lists the parameters of these slopes.The failure probabilities of these slopes were predicted using the RVM model, and the results are shown in Table 5.Among the 28 failed slopes, there are only two slopes that were wrongly partitioned into the group of stable ones, whose failure probabilities as calculated by the RVM model are less than 0.5.The prediction accuracy among the 28 slopes is approximately 92.9%, which is deemed satisfactory.Therefore the RVM model with seven triggering factors has a good prediction performance and could be extended to other sites where environmental conditions are similar to those of the study area.

Figure 1 .
Figure 1.Location map of the study area.

Figure 1 .
Figure 1.Location map of the study area.

Figure 3 .Figure 4 .
Figure 3. Landslide map of the study area.

Figure 3 .
Figure 3. Landslide map of the study area.

Figure 3 .Figure 4 .
Figure 3. Landslide map of the study area.

Figure 6
Figure 6 presents a flow chart for the training and testing process.The training dataset was used to train and develop the RVM model.During the training process, many weights will have values very close to zero, and their corresponding basis functions are removed from the model.The examples remaining with w i = 0 are termed relevance vectors and are used for slope failure prediction.Table3lists the relevance vectors and their corresponding weights.As shown in Table3, the RVM model employs 27 cases (45%) of the training dataset as relevance vectors, including 17 failed cases and 10 stable cases.It is worth mentioning here that the relevance vectors used in the RVM model represent prototypical examples.These examples exhibit the essential features of the information of the data, and thus are able to transform the input data into the specified targets[44].The goal of the RVM model is to correctly classify a given slope to the target observation of either failed slope (t = 1) or stable slope (t = 0).For a given slope with particular environmental factors described by a vector x i , its failure probability is represented by p(t = 1|x i ), which is computed by Equation (3).The classification rule of the RVM used in this study is the following: if p(t = 1|x i ) > 0.5, the slope is classified into the occurrence of a landslide; if p(t = 1|x i ) < 0.5, it is divided into the absence of a landslide.
the RVM model employs 27 cases (45%) of the training dataset as relevance vectors, including 17 failed cases and 10 stable cases.It is worth mentioning here that the relevance vectors used in the RVM model represent prototypical examples.These examples exhibit the essential features of the information of the data, and thus are able to transform the input data into the specified targets[44].

Figure 6 .
Figure 6.Flow chart of the training and testing process.

Figure 6 .
Figure 6.Flow chart of the training and testing process.

Figure 7 .
Figure 7. Failure probabilities for slopes in the training dataset.

Figure 7 .
Figure 7. Failure probabilities for slopes in the training dataset.

Figure 8 .
Figure 8. Distribution of landslides close to the Rimian dam site.

Figure 8 .
Figure 8. Distribution of landslides close to the Rimian dam site.

Table 2 .
Validation results obtained by the 4-fold cross-validation approach.

Table 3 .
Relevance vectors and their weights.

Table 4 .
Failure probabilities for slopes in the testing dataset.