A comparative study of composite kernels for landslide susceptibility mapping: A case study in Yongxin County, China

Catena 183 (2019) 104217

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A comparative study of composite kernels for landslide susceptibility mapping: A case study in Yongxin County, China Yi Wanga, Hexiang Duana, Haoyuan Hongb,c,d,

T

⁎

a

Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China, 430074 Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China c School of Geography, Nanjing Normal University, Nanjing, 210023, China d Jiangsu Center for Collaborative Innovation in Geographic Information Resource Development and Application, Nanjing, 210023, China b

ARTICLE INFO

ABSTRACT

Keywords: Landslides susceptibility Support vector machine Composite kernels Gaussian radial basis function Geographic information systems

In this study, an effective kernel-based learning framework for landslide susceptibility mapping (LSM) is presented through an implementation of support vector machines (SVMs) with different composite kernels. Kernelbased classification methods are very popular in statistical classification and regression analysis because they can effectively address intractable issues such as the curse of dimensionality, limited known samples and noise corruption. The most representative of such methods is the SVM technique. Although SVMs have recently been widely used in LSM, they were defined using only the attribute value of each influencing factor and did not consider the high dependency between the adjacent vector-valued grid cells. This caused a labelling uncertainty. To solve this problem, it is necessary to combine both the influencing factor's attribute features and spatial dependency information in the SVM. In this work, we present two forms of composite kernels to combine the two aforementioned types of information: 1) constructed through a single kernel with stacked vectors; 2) built through summation kernels under different restrictions. The main advantages of the proposed framework are twofold. First, the integration of the two types of information can improve the predictive capability of the SVMs by removing the isolated class noise in the LSM results. Second, other useful information can be extracted from the spatial domain, such as the structural features of grid cells within and outside of landslide areas. The SVM comparisons were based on data from Yongxin County, China, containing 364 past landslide occurrences that were separated randomly into a training set (70%) and a validation set (30%). The geo-environmental setting of the study area was analysed and sixteen influencing factors were selected. The validation of these SVMs was performed using the receiver operating characteristic (ROC) and the area under the ROC curve (AUC). Experimental results demonstrate that all the SVM-based landslide susceptibility maps have similar spatial distributions upon visual inspection. Specifically, the mountainous zones in the north and south of the study area are characterized by high and very high susceptibility values, respectively, whereas the central part of the study area is categorized as the least susceptible zone. Meanwhile, the composite kernel-based learning framework can achieve a better prediction accuracy than the original SVM. From quantitative analysis, the four SVMs with a summation kernel obtain the AUC values above 0.8900, which is 0.0117 higher than that of the original SVM. Furthermore, a weighted scheme in the summation kernel can result in AUC values that are at least 0.0014 higher than a directional scheme.

1. Introduction Landslides are natural disasters that can prove destructive to human activities and inevitably cause a large number of casualties and economic losses (Pisano et al., 2017). China is one of the most active landslide areas in the world, and major landslides have occurred almost every year and killed > 100 people over the past decade (Balamurugan et al., 2016; Behnia

⁎

and Blais-Stevens, 2018; Hong et al., 2016). Therefore, it is necessary to study theories and technology for understanding landslide hazards. Furthermore, landslide susceptibility analysis can provide an important foundation and scientific support for local government management and land use authorities to assess landslide hazard risks in a certain region (Hung et al., 2016; Mao et al., 2017). Landslide susceptibility analysis has attracted scientific attention in

Corresponding author at: Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China. E-mail address: [email protected] (H. Hong).

https://doi.org/10.1016/j.catena.2019.104217 Received 10 April 2018; Received in revised form 10 April 2019; Accepted 11 August 2019 0341-8162/ © 2019 Elsevier B.V. All rights reserved.

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landslide investigations. Based on this analysis, two groups of qualitative and quantitative methods have been effectively used for landslide susceptibility mapping (LSM). Qualitative methods mainly depend on known information such as expert experience (Ada and San, 2018; Feizizadeh et al., 2014; Hong et al., 2017b; Pourghasemi et al., 2012). Commonly used qualitative methods include: 1) geomorphological mapping methods that are determined by geological circumstances as defined by researchers (Reichenbach et al., 2005); 2) heuristic or indexbased methods - a set of fuzzy methods are based on researchers' professional assumptions (Ercanoglu and Gokceoglu, 2002; Pourghasemi et al., 2012); 3) analysis of landslide inventories to predict the spatial distributions of future landslides based on those of historical landslides. Therefore, the performance of qualitative methods mainly depends on the quality and integrity of available inventories (Galli et al., 2008). In addition, other popular knowledge-driven methods have been presented for LSM, such as weighted linear combination (Akgun et al., 2008), ordered weighted average (Feizizadeh et al., 2014), and multicriteria evaluation (Pradhan and Kim, 2016). On the other hand, quantitative methods mainly perform mathematical analyses and establish probabilistic statistical models that explore the relationship between landslides and environmental factors. These methods are considered more objective than the qualitative methods (Arnone et al., 2016; Sezer et al., 2017). Conventional quantitative methods such as frequency ratio (FR) (Lee and Pradhan, 2007), logistic regression, naïve Bayes (Pham et al., 2017a) and weight of evidence (Ilia and Tsangaratos, 2016) have demonstrated their effectiveness for LSM. Recently, machine learning methods have been widely employed in LSM, such as neural network models (Aditian et al., 2018; Lian et al., 2015), random forest (Pham et al., 2017a; Pham et al., 2017b) and decision tree (Chen et al., 2018; Hong et al., 2018). These methods still have their own defects, such as poor precision, low efficiency and difficulty of explanation (Ba et al., 2017; Barik et al., 2017; Hong et al., 2017a; Luo and Liu, 2018; Wang et al., 2017; Wang et al., 2019). Specifically, it is difficult to understand the internal mechanisms of the neural network and random forest

methods; this difficulty always results in over-fitting and attribute uncertainty (Hong et al., 2016; Lin et al., 2017). Additionally, the decision tree models tend to cause the over-fitting problem as well. In particular, kernel-based learning techniques have been widely used in statistical classification and regression analyses because they can effectively address intractable issues such as the curse of dimensionality, limited labelled samples and noise corruption. Furthermore, the SVMs using a single kernel (e.g., linear, polynomial or Gaussian radial basis function (RBF)) have been widely used for landslide predictions (Kumar et al., 2017; Peng et al., 2014). However, these single-kernel SVMs only take advantage of the influencing factor's attribute features, but do not consider the high dependency between the adjacent vector-valued grid cells, thus causing labelling uncertainty. To solve this problem, we present in this study a series of composite kernels that combine both the influencing factor's attribute and spatial dependency information. The composite kernel is constructed in two ways: first method includes the two types of information in the SVM by combining them into a stacked vector, and second method builds summation kernels under different restrictions. The two main contributions of this work are summarized as follows. The integration of the two types of information is the first contribution that has been seldom employed for LSM and can effectively improve the predictive capability of the SVM technique. Second, other useful information is extracted from the spatial domain, such as the structural features of grid cells and unique spatial information from grid cells both within and outside of landslide areas. To the best of our knowledge, this is the first time the two types of information in the kernel-based methods for LSM have been integrated. To validate the effectiveness of the proposed framework, the developed SVMs with composite kernels were used for LSM in Yongxin County, China, for comprehensive comparison. To objectively assess predictive capability of these SVMs, the receiver operating characteristic (ROC) curve technique and the measure of area under the ROC curve (AUC) was used to evaluate the resultant landslide susceptibility maps.

Fig. 1. The Location of the study area. 2

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2. Study area

constructed with nine groups of eight directions and flat (no aspect). The factor of distance to fault as was extracted from the geological map were from 0 to 10,217.7 m. The study area was classified by the maximum likelihood method for six object classes with an overall accuracy of 92.4%, including water, residential area, forest land, bare land, farm land and grass land; a land use map is shown in Fig. 3(c). A lithology map was resulted from Fig. 2 with seventeen groups and Table 1 lists descriptions for each group in the study area. The NDVI values can be calculated as follows:

2.1. Description Yongxin County is located in the western part of JiangXi Province, China, covering an area of approximately 2187 km2, and the elevation ranges between 41 and 1398 m above sea level (Fig. 1). The study area has a subtropical humid monsoon climate with abundant rainfall and sunshine. Due to the influence of the monsoon season, precipitation and temperature can vary greatly in time and space, which may create the potential for disastrous events such as droughts, floods, excessive heat and freezing. According to the Jiangxi Province Meteorological Bureau,1 the annual average rainfall during 1951–2015 ranged between 1111.2 and 2241.3 mm. The rainy period is from March to August accounting for 79.2% of the annual rainfall. The geological setting in the study area is part of the South China fold system. Its structural changes are highly pronounced, and its folds and faults are well developed. Excepting the Sinian, Silurian and Tertiary periods, the strata are well distributed in the study area from the Cambrian to Quaternary periods with a total thickness of > 20,000 m. Fig. 2 illustrates the lithological map of the study area with over 30 geological units identified. According to lithofacies and geological time, these units are divided into seventeen groups. Conglomerate, dolomite, sandstone and limestone are the main out-cropped lithological formations. In the study area, there are total 364 landslide locations provided by the local government department of Jiangxi Province, consisting rotational slides (70%) and translational slides (30%). The largest and smallest landslides are 750,000 m2 and 32 m2, respectively. The size of these landslides can be divided into three scales, i.e., large-scale (> 1000 m2), medium-scale (400–1000 m2) and small-scale (< 400 m2), which account for 21.6%, 37.8% and 40.6% of the total landslides, respectively. According to the statistical report from the Meteorological Bureau of Jiangxi Province, the frequency and intensity of rainfall are the major landslide-inducing factors in the study area, rather than earthquakes. In this study, a landslide inventory map was prepared by using historical landslide records, interpretations of satellite images and field survey data (Crozier, 2017).

NDVI =

(NIR Red) (NIR + Red)

(1)

where NIR and Red represent the spectral reflectance obtained in the red (visible) and near-infrared portions of the electromagnetic spectrum, respectively. Since the spectral reflectance defines values between 0.0 and 1.0. The NDVI itself thus varies between −1.0 and +1.0, basically representing greens, where negative values are primarily produced from clouds, snow and water, and values close to zero are mainly formed from rocks and bare soil. Very small values (0.1 or less) of the NDVI function correspond to empty areas of rocks, sand or snow. Moderate values (from 0.2 to 0.3) represent shrubs and meadows, while large values (from 0.6 to 0.8) indicate temperate and tropical forests. The NDVI results were from −0.56 to 0.42 for the study area and the NDVI map with five groups is shown in Fig. 3(d). Both factors of plan curvature and profile curvature were divided into convex, flat and concave groupings. Meteorological conditions are very crucial for the development and occurrence of landslides, especially for rainfall. Based on several previous studies (Althuwaynee et al., 2012; Lee and Pradhan, 2007; Ozdemir and Altural, 2013), we used in this work the annual average rainfall of the study area as a landslide influencing factor. The mean annual precipitation 1960–2015 at 20 rainfall gauge stations was used to create the rainfall map in Fig. 3(e). Precipitation values ranged from 0 to 1942.77 mm as determined by the inverse distance weighted method. The distance to river and distance to road maps were from 0 to 1942.77 m and 0 to 8429.73 m, respectively. The slope ranged from 0° to 67.6° and its map is illustrated in Fig. 3(f) with seven groups. The SPI, STI and TWI values in this study were from 0 to 46,659.5, 0 to 1322.77 and 2.38 to 32.77, respectively.

2.2. Data preparation

3. Backgrounds and methods

In this study, sixteen landslide-influencing factors were selected based on the analysis of the landslide inventory map, including altitude, slope, slope aspect, plan curvature, profile curvature, stream power index (SPI), sediment transport index (STI), topographic wetness index (TWI), landuse, normalized difference vegetation index (NDVI), soil, rainfall, distance to fault, distance to river, distance to road and lithology. Some of these factors are plotted in Fig. 3. A digital elevation model (DEM) for the study area was generated from the ASTER GDEM Version 2.2 These data are widely used by researchers for obtaining global topographic information, including for altitude, slope, aspect, plan curvature, profile curvature, SPI, STI and TWI. Landsat 7 ETM+ satellite images of the study area, which were obtained from the Computer Network Information Center of Chinese Academy of Sciences,3 were used to extract the factors of land use and NDVI. The lithology map was obtained from the China Geology Survey.4 Fig. 3(a) shows the reclassification result of the soil map that was produced with five groups, i.e., RGc, ATc, ALh, ACu and Ach; these groups were compiled in 1995 by the Institute of Soil Science, Chinese Academy of Sciences (ISSCAS) from data of the Office for the Second National Soil Survey of China.5 The aspect map in Fig. 3(b) was

The flowchart of this study is illustrated in Fig. 4. In this work, the proposed framework mainly consists of four steps: (1) a flood inventory map of the study area is collected and related influencing factors are selected; (2) the input data are converted to a composite map with 3-D data structure; (3) LSM is performed on the study area using SVMs with the proposed composite kernels; (4) the results of these SVMs are compared and assessed. In the following subsections, we first describe 3-D data structure of influencing factor maps. Then, the basic principles of SVM is presented. Finally, the proposed composite kernels for LSM are introduced. 3.1. Data structure of influencing factor maps The selection of a terrain mapping unit is vital for LSM, and four terrain mapping units have been used in the literature (Zêzere et al., 2017). Among them, grid cells are the most popular for raster-based GIS users in modelling landslide susceptibility, and grid cell terrain units (GCTUs) partition the study area into square regions for which a value is assigned for each influencing factor. Once the terrain mapping unit is defined, the next step is to resample different influencing factors to have the same grid size. In this work, a composite map that consists of the influencing factors was

1

http://www.weather.org.cn. http://gdem.ersdac.jspacesystems.or.jp. 3 http://www.gscloud.cn. 4 http://www.cgs.gov.cn. 2

5

3

http://www.issas.ac.cn.

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Fig. 2. The geological map of the study area.

result and zl ≡ {(x1, y1), (x2, y2), …, (xl, yl)} ∈ (ℝB × L)l training samples. Since x values are not linearly separable, the GCTUs are mapped to a kernel Hilbert space H by using a mapping function ϕ(x) to construct the hyperplane. The aim of the SVM is to minimize a cost function to ensure margin maximization and error minimization. The error of SVM can be defined as follows (Vapnik, 1998):

considered as multilayer data, which are a series of spatially aligned influencing factor maps that are extracted by various ancillary data. Fig. 5 shows the 3-D data structure of the composite map. In this figure, these data have two spatial dimensions with the same sizes to the resampled thematic maps and one additional dimension perpendicular to the spatial plane that we refer to as “along-layer” for clarification. In this composite map, each grid cell's value is defined by a feature vector that consists of cell's value for each influencing factor. In this work, we consider each grid cell's features as along-layer information.

1 w 2

min

w, i, b

2

+C i

i

s. t .

yi (w

1

i,

i

0, (2)

i = 1, 2, … , l

3.2. SVM method

(x i ) + b )

where w and b are the weight vector and the bias to define the optimal hyperplane, ξi are the slack variables for non-separable data, and C > 0 denotes a regularization parameter that controls the shape of the discriminant function. Since w is a high-dimensional vector, the above optimization can be solved as a Lagrangian dual problem as follows:

As mentioned in Section 1, intensive contributions have been given to landslide prediction methods in recent years. Among them, SVMs have demonstrated a satisfactory prediction accuracy with limited training samples by performing a nonlinear GCTU-wise classification based on the full along-layer information (Kumar et al., 2017). With X ≡ {1, 2, …, N} representing the number of GCTUs in a composite map x ≡ {x1, x2, …, xN} ∈ ℝB×N which contains B influencing factors, L ≡ {−1, +1} binary labels,y ≡ {y1, y2, …, yN} ∈ LN the final prediction

l

max i

4

i i=1

1 2

l i j yi yj K i = 1, j = 1

(x , x i )

(3)

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3. Some related landslide influencing factor maps. (a) Soil, (b) aspect, (c) landuse, (d) NDVI, (e) rainfall and (f) slope. Table 1 Types of lithology of the study area. Group name

Unit name

Lithology

A B C D E F G H I J K L M N O P Q

Lianhe group, Tangbian group, Hekou group Zhangzong group, Zhongpeng group, Yunshan group Changlong group, Oujia chong group, Huamian gong group, Shi kou group Duier shi group, Jueshan gou group Longtang group, Qi baoshan group, Chang xing group Ba cun group, Liu jiaohe group Gu feng group, Qixia group, Xiao Jiangbian group Huang xie group, Hai hui group, Xi hua group Chang lejie group, Gu poshan group, San jiangkou Group Zishan group, Yang jiayuan group, Hu tian group Dui ershi group, Shi kou Group Xia shan group, Yi jiawang group, Qi ziqiao group Fu fang group, Taihe group, Tang hu group Ba cun group, Shui shi group Ba cun group, Gao tang group

Conglomerate, mudstone Shale Limestone and sandy shale Limestone and siliceous slate Slate, black carbonaceous siliceous slate Coal seam, cherty limestone and siliceous rocks Carbonaceous slate Carbonaceous shale; cherty limestone, siliceous rocks Two long granite Granite Dolomite and coal seam Biolimestone Slate; green slate, carbonaceous slate Sandstone, shale, dolomite, Two long granite Slate, sandstone Green sandstone, silty slate

under two following constrains:

0

i

3.3. Composite kernels for LSM (4)

C

The SVM classification algorithm with a composite kernel for LSM consists of four steps: (1) Spatial information modelling that constructs the spatial feature vectors of the input composite map; (2) kernel construction that defines the along-layer and spatial kernel functions that fulfil Mercer's conditions; (3) kernel combination that develops several kernel functions under different restrictions to combine the along-layer and spatial features in the landslide prediction process; and (4) SVM classification that obtains the final landslide susceptibility of the study area. These four steps are briefly introduced in the following subsections.

and l i yi

=0

(5)

i=1

where α = [α1, α2, …, αq] is a set of Lagrange multipliers and K(⋅, ⋅) is a kernel function and should thus satisfy Mercer's condition. Since the mapping function ϕ(x) has the form of inner products, we can define K (⋅, ⋅) as follows:

K (x i , xj ) =

(x i ) (x j )

(6)

3.3.1. Spatial information modelling In the domain of remote sensing, including spatial features in the classification process can be conveniently implemented using kernelbased methods (Camps-Valls et al., 2014; Fauvel et al., 2013). In this subsection, we introduce two commonly used approaches for modelling spatial information via the kernel-based method for landslide

Then, the decision function can be defined as follows: l

f (x ) =

i yi K i=1

(x , x i ) + b

(7) 5

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Fig. 4. Flowchart of this study.

follows:

EMPk = {MP(PC1 ), MP(PC2),…, MP(PCk )}

(8)

where the EMP is a stacked vector with the dimensionality of k(2n + 1) and includes both the spectral and spatial information of the image. In modelling spatial information for LSM, the two previously mentioned spatial information extraction methods can be exploited. Specifically, for a GCTU xi (i = 1, 2, …, N), its along-layer feature vectors are defined as xiALO ∈ ℝNALO, where NALO is equal to N, meaning each GCTU has its individual along-layer information. Additionally, its spatial feature vector has two forms: one is constructed using the mean or standard deviation of the neighbourhood of the GCTUs per the influencing factor map as xiSPA1 ∈ ℝNSPA1; the other is constructed using an EMP of the composite map comprising the influencing factor maps as xiSPA2 ∈ ℝNSPA2, where NSPA1 and NSPA2 are the numbers of the spatial features. 3.3.2. Kernel construction Once the along-layer and spatial feature vectors xiALO and xiSPA are constructed, kernel functions can be defined under Mercer's conditions. The selection of the kernel function is crucial to the classification performance of the SVM model. The Gaussian RBF kernel is the most widely used in measuring the similarity between two GCTUs. For two vectors xiALO and xjALO, the along-layer kernel can be defined as follows:

Fig. 5. The 3-D data structure of the composite map comprising influencing factor maps.

KALO (xiALO , x jALO) = exp(

susceptibility. For the image classification problem, a simple and effective way to model spatial information is to extract spatial features that account for the surrounding area of the pixels, such as the mean or variance per spectral band (Camps-Valls et al., 2006). Another way to model spatial information for remote sensing images is to use the extended morphological profiles (EMP) method (Benediktsson et al., 2005). The main idea of EMP is to reconstruct the spatial information through morphological (opening/closing) operators while preserving the boundaries of the image. To apply this technique to image classification, the widely used principal component analysis (PCA) transformation is exploited for dimension reduction (Fauvel et al., 2013). Using k and n as the total number of the required principal components (PCs) and the morphological operators, respectively, we can build the morphological profile (MP) for each PC and then stack these MPs to produce an EMP as

x iALO

x jALO 2 ).

(9)

where γ controls the spread of the RBF kernel and ‖⋅‖ denotes the L2 norm. Similarly, the spatial kernel can be constructed using the RBF kernel. The two spatial kernel functions are defined as follows:

K SPA1 (x iSPA1 , x jSPA1) = exp(

x iSPA1

x jSPA1 2 ).

(10)

K SPA2 (x iSPA2 , x jSPA2) = exp(

x iSPA2

x jSPA2 2 ).

(11)

3.3.3. Kernel combination The aim of this work is to explore the composite kernel framework for LSM by including both the spatial and along-layer information. In this subsection, we develop several composite kernel approaches with two strategies. The first strategy includes both the spatial and along-layer information in the classifier by combining them into a stacked vector. 6

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With xi denoting a concatenation of two feature vectors as xi ≡ {xiALO, xiSPA}, the two stacked-feature kernel functions can be defined as follows:

K {ALO,SPA1} (x i , xj ) = exp(

xi

x j 2 ).

(12)

K {ALO,SPA2} (x i , xj ) = exp(

xi

x j 2 ).

(13)

Table 2 Relationship between each influencing factor and landslide occurrence by FR.

As stated in Camps-Valls et al. (2006) and Schölkopf and Smola (2002), if k1 and k2 are two kernels, then μ1k1 + μ2k2 is a new kernel with μ1, μ2 ≥ 0. According to this property, the second strategy for combining the spatial and along-layer information can be performed by building summation kernels under different restrictions:

Influencing factor

Class

No. of GCTUs in domain

Percent of domain (%)

No. of landslide

Percent of landslide (%)

FR

Altitude (m)

< 150 150–250 250–400 400–700 700–1000 > 1000 Flat North Northeast East Southeast South Southwest West Northwest 0–2000 2000–4000 4000–6000 6000–8000 > 8000 Water Forest Grass Farmland Bare Residential Group A Group B Group C Group D Group E Group F Group G Group H Group I Group J Group K Group L Group M Group N Group O Group P Group Q < 0.1 0.1–0.2 0.2–0.3 0.3–0.4 > 0.4 < −0.25 −0.75 > 0.5 < −1 (−1)-0.2 > 0.2 < 800 800–900 900–1000 1000–1100 > 1100 < 200 200–500 500–800 > 800 < 300 300–1300 1300–2300 > 2300

876,142 947,989 822,620 663,718 180,954 35,309 26,229 460,854 409,633 472,022 458,681 466,466 381,226 422,817 428,804 1,605,946 1,030,730 626,737 234,027 29,292 42,077 1,231,417 926,977 468,788 150,316 707,157 784,838 429,108 2311 233,843 77,394 6728 189,655 145,633 17,333 5 423,127 9764 234,472 446,643 48,645 4670 472,563 1,821,056 860,462 763,478 81,671 65 1,242,908 1,369,415 914,409 626,562 1,387,942 1,512,228 27,289 309,590 1,015,248 1,057,419 1,117,186 1,198,190 1,321,706 735,755 271,081 737,514 1,736,532 787,621 265,065

24.84 26.88 23.33 18.82 5.13 1.00 0.74 13.07 11.62 13.38 13.01 13.23 10.81 11.99 12.16 45.54 29.23 17.77 6.64 0.83 1.19 34.92 26.28 13.29 4.26 20.05 22.25 12.17 0.07 6.63 2.19 0.19 5.38 4.13 0.49 0.00 12.00 0.28 6.65 12.66 1.38 0.13 13.40 51.64 24.40 21.65 2.32 0.00 35.24 38.83 25.93 17.77 39.35 42.88 0.77 8.78 28.79 29.98 31.68 33.97 37.48 20.86 7.69 20.91 49.24 22.33 7.52

4 55 127 146 30 2 13 16 53 90 113 48 23 8 0 191 110 55 8 0 0 103 213 12 30 6 3 62 0 39 6 0 18 0 0 0 14 0 46 67 36 2 71 60 74 195 35 0 164 98 102 95 91 178 0 8 113 83 160 88 154 94 28 45 213 84 22

1.10 15.11 34.89 40.11 8.24 0.55 3.57 4.40 14.56 24.73 31.04 13.19 6.32 2.20 0.00 52.47 30.22 15.11 2.20 0.00 0.00 28.30 58.52 3.30 8.24 1.65 0.82 17.03 0.00 10.71 1.65 0.00 4.95 0.00 0.00 0.00 3.85 0.00 12.64 18.41 9.89 0.55 19.51 16.48 20.33 53.57 9.62 0.00 45.05 26.92 28.02 26.10 25.00 48.90 0.00 2.20 31.04 22.80 43.96 24.18 42.31 25.82 7.69 12.36 58.52 23.08 6.04

0.04 0.56 1.50 2.13 1.61 0.55 4.80 0.34 1.25 1.85 2.39 1.00 0.58 0.18 0.00 1.15 1.03 0.85 0.33 0.00 0.00 0.81 2.23 0.25 1.93 0.08 0.04 1.40 0.00 1.62 0.75 0.00 0.92 0.00 0.00 0.00 0.32 0.00 1.90 1.45 7.17 4.15 1.46 0.32 0.83 2.47 4.15 0.00 1.28 0.69 1.08 1.47 0.64 1.14 0.00 0.25 1.08 0.76 1.39 0.71 1.13 1.24 1.00 0.59 1.19 1.03 0.80

Slope aspect

(1) If μ1 = μ2 = 1, the two direct summation (DS) kernel functions can be defined as follows: ALO SPA1 KDS (xi , xj ) = KALO (x iALO , x jALO) + K SPA1 (xiSPA1 , x jSPA1).

(14)

ALO SPA2 KDS (xi , xj ) = KALO (x iALO , x jALO) + K SPA2 (xiSPA2 , x jSPA2).

(15)

Distance to fault (m)

(2) If μ1 + μ2 = 1, the two weighted summation (WS) kernel functions can be defined as follows: ALO SPA1 KWS (x i , xj ) = (1

µ) KALO (xiALO , x jALO) + µK SPA1 (xiSPA1 , x jSPA1).

Land use

(16) ALO SPA2 KWS (x i , xj ) = (1

µ) KALO (xiALO , x jALO) + µK SPA2 (xiSPA2 , x jSPA2). (17) Lithology

where μ is a weight to balance the two kernels. 3.3.4. SVM classification From the previous steps, we can next construct a series of SVMs with different composite kernel functions. To ensure the optimal performance of the SVMs, the optimization of the parameters of C and γ is always performed using the randomly selected training set zl. Finally, the final landslide susceptibility map can be obtained by applying the proposed composite kernels into Eq. (7) and thus classify the influencing factor composite image using the optimal C and γ. 4. Results 4.1. Correlation analysis between landslide occurrence and influencing factors

NDVI

To explore the relationship between landslide occurrence and sixteen landslide influencing factors, the classes and the corresponding FR values of each influencing factor are listed in Table 2. In the case of altitude, the highest FR of 2.13 is in the class of 400–700 m, which indicates a high probability of landslide occurrence. For slope, landslides mainly occurred within the class of 10–20° values, which is highly related to landslide occurrence. The relationship between SPI and landslides demonstrates that the highest FR of 6.15 is in the class of 2000–5000, followed by the class of 400–2000 with an FR of 2.13. In the case of STI, the highest and lowest landslide occurrence probabilities can be reached in the classes of 200–300 and > 300, respectively. For land use, the class of grass has a relatively high susceptibility to landslide occurrence. In the case of distance to fault, the FRs become smaller as the distance increases. The conclusions concerning both distance to road and distance to river are very similar. For instance, the FRs of distance to road are slightly above 1 in the classes of 300–1300 m and 1300–2300 m, and the FRs of distance to river are comparable in the classes of 200–500 m, 500–800 m and > 800 m. In the case of NDVI, the two highest FRs of 4.15 and 2.47 are in the classes of 0.2–0.3 and 0.3–0.4, respectively. In the case of lithology, the groups O and P are more prone to high landslide susceptibility. In the case of TWI, the class of > 11 has the highest FR of 2.26. The relationship

Plan curvature Profile curvature Rainfall

Distance to river (m) Distance to road (m)

(continued on next page)

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Table 2 (continued) Influencing factor

Slope (°)

Soil

SPI

STI

TWI

Class

0–10 10–20 20–30 30–40 40–50 50–60 > 60 ATc ACu ALh ACh RGc < 400 400–2000 2000–5000 12,000 > 12,000 < 15 15–100 100–200 200–300 > 300 <5 5–7 7–9 9–11 > 11

No. of GCTUs in domain 1,466,412 1,036,916 620,572 305,484 87,469 9679 200 584,915 346,372 136,843 2,275,477 183,125 3,411,208 99,870 12,610 2675 369 2,701,877 781,291 34,803 6041 2720 1,129,914 1,678,597 546,447 150,377 21,397

Percent of domain (%) 41.58 29.40 17.60 8.66 2.48 0.27 0.01 16.59 9.82 3.88 64.52 5.19 96.72 2.83 0.36 0.08 0.01 76.61 22.15 0.99 0.17 0.08 32.04 47.60 15.49 4.26 0.61

No. of landslide

64 111 95 66 24 4 0 1 77 22 263 1 334 22 8 0 0 198 155 8 3 0 159 141 40 19 5

Percent of landslide (%) 17.58 30.49 26.10 18.13 6.59 1.10 0.00 0.27 21.15 6.04 72.25 0.27 91.76 6.04 2.20 0.00 0.00 54.40 42.58 2.20 0.82 0.00 43.68 38.74 10.99 5.22 1.37

Table 3 The optimal parameters for the SVMs with different kernel functions.

FR

Methods

The optimal parameters C

ALO

SVM ‐ K SVM ‐ KSPA1 SVM ‐ KSPA2 SVM ‐ K{ALO,SPA1} SVM ‐ K{ALO,SPA2} SVM ‐ KDSALO‐SPA1 SVM ‐ KDSALO‐SPA2 SVM ‐ KWSALO‐SPA1 SVM ‐ KWSALO‐SPA2

0.42 1.04 1.48 2.09 2.66 4.00 0.00 0.02 2.15 1.56 1.12 0.05 0.95 2.13 6.15 0.00 0.00 0.71 1.92 2.23 4.81 0.00 1.36 0.81 0.71 1.22 2.26

γ 2 8 2 4 4 0.5 4 2 0.5

0.0625 4 1 0.03125 0.03125 4 0.03125 8 4

test with perfect discrimination can generate a curve passing through the upper left corner in a ROC plot and the range of the AUC value is between 0.5 and 1, and an AUC value of 1 indicates that the method has superior predictive capability. In the following experiments, the SVM models with different kernel functions were carried out using Matlab 2013b and the LIBSVM software (Chang and Lin, 2011), while ArcGIS 10.2 was used for superimposing the data and obtaining the landslide susceptibility maps. 4.3. Validation and comparison Fig. 6 demonstrates the landslide susceptibility maps of different SVMs by showing the probability of landslide occurrence for each grid. Then, these maps were categorized into five classes of very low, low, moderate, high and very high susceptibility using the natural breaks method. The percentage per class for each landslide susceptibility map is illustrated in Fig. 7. All the susceptibility mapping results have similar spatial distributions for each class, which visually align with the factor maps of altitude, lithology and slope. For instance, the mountainous zones in the north and south of the study area are labelled with high and very high susceptibility values, whereas the central parts of the study area are categorized as low and very low susceptible zones. Furthermore, the very low susceptibility class in all the methods obtained the highest areal percentage at above 32%, followed by the low and moderate susceptibility classes above 18% and 12%, respectively. Finally, SVM ‐ KWSALO‐SPA1 produced the lowest areal percentage of 21.86% in terms of the high and very high susceptibility classes, followed by SVM ‐ KSPA2 with 22.35%. Fig. 8 shows the prediction rate curve of different kernel-based methods, and Table 4 lists the success and prediction rate results of the landslide susceptibility maps in Fig. 6. Several conclusions can be drawn as follows: First, the prediction results achieved by SVMs with a single kernel are comparable, e.g., SVM ‐ K{ALO,SPA1} obtained an AUC value of 0.8808, which is slightly higher than SVM ‐ KALO, whereas the AUC value of 0.8747 by SVM ‐ K{ALO,SPA2} is slightly lower than SVM ‐ KALO because this classifier may suffer from the curse of dimensionality and some spatial features are irrelevant or redundant. Second, for the two DS kernel functions, the AUC value for SVM ‐ KDSALO‐SPA1 is 0.0017 higher than SVM ‐ KDSALO‐SPA2. Nevertheless, the two WS kernel functions are opposite in terms of the two spatial features. For instance, the AUC value by SVM ‐ KWSALO‐SPA2 is 0.0003 better than SVM ‐ KWSALO‐SPA1. Finally, successful predictions by SVMs with a summation kernel occur more often than SVMs with a single kernel. Furthermore, the appropriate settings of the weights for the along-layer and spatial kernels can produce more accurate landslide susceptibility. Specifically, the SVM with DS and WS kernel functions defined in Eqs. (14)–(17) can obtain AUC values above 0.89, which are better than those with KALO, KSPA1, KSPA2, K{ALO,SPA1} or K{ALO,SPA2}. In addition, SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2 are capable of achieving AUC values of 0.8947

between soil type and landslide occurrence indicates that the highest probability of landslide is the class of ACu, followed by the classes of ALh and ACh. The remaining influencing factors of slope aspect, plan curvature, profile curvature and rainfall have a negligible relationship to landslide occurrences. 4.2. Experimental settings For the sake of clarification, we define the acronyms of all the SVMs used in our experiments. Specifically, the SVM classifiers using different kernel functions of KALO, KSPA1, KSPA2, K{ALO,SPA1}, K{ALO,SPA2}, KDSALO‐SPA1, KDSALO‐SPA2, KWSALO‐SPA1 and KWSALO‐SPA2 are named SVM ‐ KALO, SVM − KSPA1, SVM ‐ KSPA2,SVM ‐ K{ALO,SPA1}, SVM ‐ K{ALO,SPA2}, SVM ‐ KDSALO‐SPA1, SVM ‐ KDSALO‐SPA2, SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2, respectively. As defined in Section 3.3.2, the RBF kernel was used by all the SVMs previously mentioned. The optimal values of both the parameters C and γ for the SVMs with different kernel functions were selected by a fivefold cross validation from the range of [2−5, 25], and the values for each method are shown in Table 3. To compute the mean or standard deviation of the neighbourhood of the GCTUs, the window size w in the 3-D composite map was selected for SVM ‐ KSPA1 and SVM ‐ K{ALO,SPA1} as 11 × 11, and for SVM ‐ KDSALO‐SPA1 and SVM ‐ KWSALO‐SPA1 as 5 × 5. The EMP was built based on the first three PCs of the 3-D composite map using a flat disk-shaped structuring element with a radius of 1 with a step of 2. Specifically, the number of openings/ closings n was selected for SVM ‐ KSPA2,SVM ‐ K{ALO,SPA2}, SVM ‐ KDSALO‐SPA2 and SVM ‐ KWSALO‐SPA2 with values of 12, 12, 10 and 8, respectively. To use the weighted summation kernels for LSM, the weight μ was selected as 0.4 and 0.2 for SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2, respectively. To apply these SVMs to the LSM of the study area, 70% of the total of landslide grid cells and an equal number of non-landslide grid cells were randomly selected for training, and the remaining landslide grid cells and an equal number of non-landslide grid cells were used for validation. To assess prediction performance, visual inspection of landslide susceptibility maps, the widely used ROC and AUC are used. The success rate and prediction rate results can be obtained using the training and validation sets, respectively. A 8

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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(i)

(j)

Fig. 6. The landslide susceptibility maps by the SVMs with different kernel functions. (a) SVM ‐ KALO, (b) SVM ‐ KSPA1, (c) SVM ‐ KSPA2 (d) SVM ‐ K{ALO,SPA1}, (e) SVM ‐ K{ALO,SPA2}, (f) SVM ‐ KDSALO‐SPA1, (g) SVM ‐ KDSALO‐SPA2, (h) SVM ‐ KWSALO‐SPA1 and (i) SVM ‐ KWSALO‐SPA2.

and 0.895, which are 0.0014 and 0.0034 higher than SVM ‐ KDSALO‐SPA1 and SVM ‐ KDSALO‐SPA2, respectively. In the last experiments, the statistically significant differences between the SVMs with different kernels were performed. In this work, the Wilcoxon rank sum test was used for comparison. When the p value is < 0.05, the performances of different prediction methods are significant different. Table 5 lists the Wilcoxon rank sum test for the different SVMs previously mentioned. In general, the SVMs with the composite kernels have significant different with those with single

kernels because most of the p values in Table 5 are < 0.05. In particular, the p value of SVM ‐ KALO vs. SVM ‐ K{ALO,SPA2} is 0.339, which demonstrates that the spatial information was used as an aid for the along-layer attributes when using SVM ‐ K{ALO,SPA2}. Therefore, there is a very close correlation between these two methods. Furthermore, the correlation between SVM ‐ KSPA2 and SVM ‐ KWSALO‐SPA2 is very close as well with the highest p value of 0.478. Since the same spatial information is used to construct the two SVMs, they have a very strong correlation. A similar conclusion can be drawn between SVM ‐ KSPA1

Fig. 7. Percentage of different susceptibility categories for all landslide susceptibility maps. 9

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and SVM ‐ KDSALO‐SPA1 (or SVM ‐ KWSALO‐SPA1). 5. Discussion To apply the composite kernel framework to LSM, several parameters should be determined for spatial feature extraction. In this section, we use SVMs with composite kernel functions to analyse the impacts of these parameters. Meanwhile, some related issues on the proposed framework are addressed. 5.1. Influence of w In fact, we may obtain different prediction results of the study area using the proposed methods with different values of w and n. To achieve the optimal prediction result, we should select different values of w and n for the two strategies of kernel combination described in Section 3.3.3. Specifically, when using K{ALO,SPA1} or K{ALO,SPA2}, the larger w (n) can provide more spatial information. As a result, more accurate prediction results can be obtained by integrating the spatial and alonglayer information. When using a summation kernel, if w (n) is too large, the difference between the two kernel matrices increases, which reduces classification accuracies; if w (n) is too small, the spatial information is not sufficient to combine with the along-layer information to improve classification accuracies. The influence of w on the prediction results is analysed in this subsection and the influence of n on the prediction results can be referred to Section 5.2. To extract the spatial features using the mean or standard deviation of the neighbourhood of the GCTUs, an optimal window size w in the spatial plane should be defined. To demonstrate the influence of w on the prediction results, the AUC values of SVM ‐ K{ALO,SPA1}, SVM ‐ KDSALO‐SPA1 and SVM ‐ KWSALO‐SPA1 with different w from 3 × 3 to 11 × 11 are listed in Table 6. We observed that the AUC values from SVM ‐ K{ALO,SPA1} are higher when w is increased and the highest AUC value is obtained by this method when w is fixed as 11 × 11. The highest AUC values achieved by SVM ‐ KDSALO‐SPA1 and SVM ‐ KWSALO‐SPA1 can reach 0.8933 and 0.8947, respectively, when w is fixed as 5 × 5, and the AUC values gradually decrease when w is larger than 5 × 5. According to the previous analyses, if there is no prior knowledge, we recommend setting w to 11 × 11 for SVMs with a single kernel and 5 × 5 for SVMs with a composite kernel to ensure satisfactory prediction results.

Fig. 8. The prediction rate curves by the SVMs with different kernel functions. Table 4 Success and prediction rates of the landslide susceptibility maps for the study area. Methods

Accuracy

SVM ‐ KALO SVM ‐ KSPA1 SVM ‐ KSPA2 SVM ‐ K{ALO,SPA1} SVM ‐ K{ALO,SPA2} SVM ‐ KDSALO‐SPA1 SVM ‐ KDSALO‐SPA2 SVM ‐ KWSALO‐SPA1 SVM ‐ KWSALO‐SPA2

Success rate (average)

Prediction rate (average)

0.9784 0.9998 0.8907 0.9489 0.9051 1.0000 0.9051 1 1

0.8783 0.8684 0.8783 0.8808 0.8747 0.8933 0.8916 0.8947 0.8950

Table 5 Pairwise comparison for the different SVMs using the Wilcoxon rank sum test (two-tailed). Pairwise comparison

SVM ‐ KALO

SVM ‐ KSPA1

SVM ‐ KSPA2

5.2. Influence of n

Statistics

vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs. vs.

SVM ‐ K{ALO,SPA1} SVM ‐ K{ALO,SPA2} SVM ‐ KDSALO‐SPA1 SVM ‐ KDSALO‐SPA2 SVM ‐ KWSALO‐SPA1 SVM ‐ KWSALO‐SPA2 SVM ‐ K{ALO,SPA1} SVM ‐ K{ALO,SPA2} SVM ‐ KDSALO‐SPA1 SVM ‐ KDSALO‐SPA2 SVM ‐ KWSALO‐SPA1 SVM ‐ KWSALO‐SPA2 SVM ‐ K{ALO,SPA1} SVM ‐ K{ALO,SPA2} SVM ‐ KDSALO‐SPA1 SVM ‐ KDSALO‐SPA2 SVM ‐ KWSALO‐SPA1 SVM ‐ KWSALO‐SPA2

p value

Significance

0.031 0.399 0.000 0.081 0.000 0.011 0.007 0.000 0.052 0.001 0.076 0.000 0.000 0.003 0.000 0.000 0.000 0.487

Yes No Yes No Yes Yes Yes Yes No Yes No Yes Yes Yes Yes Yes Yes No

To extract the spatial features using the EMP method, the number of openings/closings n should be defined. To demonstrate the influence of n on the prediction results, the AUC values of SVM ‐ K{ALO,SPA2}, SVM ‐ KDSALO‐SPA2 and SVM ‐ KWSALO‐SPA2 with different n values from 2 to 12 with a step size of 2 are listed in Table 7. The highest AUC values were reached for SVM ‐ K{ALO,SPA2}, SVM ‐ KDSALO‐SPA2 and SVM ‐ KWSALO‐SPA2 when n was selected as 12, 10 and 8, respectively. In addition, all the AUC values of SVM ‐ K{ALO,SPA2} with different values of n were lower than those of SVM ‐ KALO, because the SVM with such a kernel may cause information redundancy and create a negative impact Table 6 The AUC values achieved by the three SVMs using different window sizes. The highest AUC values are indicated in bold in each category. w

3×3 5×5 7×7 9×9 11 × 11

10

AUC value SVM ‐ K{ALO,SPA1}

SVM ‐ KDSALO‐SPA1

SVM ‐ KWSALO‐SPA1

0.8766 0.8765 0.8786 0.8795 0.8808

0.8909 0.8933 0.8924 0.8822 0.8778

0.8880 0.8947 0.8924 0.8823 0.8759

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proposed methods. Although we choose these two parameters for comparison according to this strategy, Tables 6–7 show that SVMs with the proposed composite kernels can achieve a better prediction accuracy than that of the original SVM no matter how these two parameters are selected. This means that the proposed SVMs are very robust and reliable, without being sensitive to these parameters. Finally, the given data range for these two parameters in this work can provide researchers with useful information for comparative studies.

Table 7 The AUC values achieved by the three SVMs using different numbers of morphological operators. The highest AUC values are indicated in bold in each category. n

2 4 6 8 10 12

AUC value SVM ‐ K{ALO,SPA2}

SVM ‐ KDSALO‐SPA2

SVM ‐ KWSALO‐SPA2

0.8727 0.8735 0.8736 0.8733 0.8738 0.8747

0.8893 0.8889 0.8895 0.8905 0.8916 0.8914

0.8895 0.8929 0.8872 0.8950 0.8940 0.8924

5.5. Influencing factor analysis Precipitation, in particular sudden, intense rain and snow melt, is a key influencing factor which triggers mass movements, increasing the underground hydrostatic level and pour water pressure (Shahabi et al., 2012). The extreme precipitation is a direct reason to landslide occurrences. Guzzetti et al. studied the antecedent rainfall conditions to landslide occurrences and reviewed rainfall thresholds for initiation of landslides worldwide (Guzzetti et al., 2007; Guzzetti et al., 2008). We should comply with the consideration of rainfall intensity and its durations. But in the field of LSM, most researchers directly used the annual precipitation as an influencing factor. For instance, Lee and Pradhan (Lee and Pradhan, 2007) provided the monthly rainfall ranging from 58.6 to 240 mm and used annual data into the frequency ratio and logistic regression methods. Althuwaynee et al. (2012) used historical rainfall data for the past 29 years and statistically distributed the cumulative annual average precipitation. Ozdemir and Altural (2013) prepared an annual rainfall map in the study area with approximately 509–591 mm. Following these pioneering contributions, we introduced the circumstance of rainfall in the study area and used the annual data as an influencing factor for LSM. The four main reasons are described as follows. First, we used annual data as reflection of the climate in the study area. The data demonstrated that the rainy period is from March to August, accounting for 79.2% of the annual rainfall, and it also reflects the local climatic conditions. Second, we admit the uncertainty of rainfall and it is difficult to quantitatively assess its impact. In this work, we focused on landslide spatial prediction. In fact, landslide susceptibility can be considered as the comprehensive assessment of the basic conditions of the disaster and the comprehensive measurement of the existing landslide characteristics, without considering dynamic predisposing factors such as extreme climatic conditions and human engineering activities and involving the problem of when a landslide will occur. Therefore, it is different from timely warning or sequence analyses, without considering the time, frequency and intensity of regional landslides. Third, landslide occurrences consist of many single landslide events. The aim of this work is to find spatial trends in the relationship between LSM and annual rainfall in the study area. However, each landslide event has a different precipitation and duration. Therefore, we cannot take the uniformity of extreme rainfall and its duration as an influencing factor. Finally, we will use extreme rainfall and its duration as a key factor in LSM in future study.

on the prediction results. However, all the AUC values of SVM ‐ KDSALO‐SPA2 and SVM ‐ KWSALO‐SPA2 with different values of n were higher than 0.887. If the spatial kernel in the summation kernel is defined using the EMP method, we can conclude that the SVM with the summation kernel is very reliable for producing accurate landslide susceptibility maps. 5.3. Influence of μ In SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2, the weight μ critically determines the prediction performance by factoring in the contribution of the along-layer and spatial information. Therefore, we performed a 3-D analysis to evaluate the impact of μ on the prediction performance of SVMs with a WS kernel. According to the constraint that the summation of the two weights should be equal to one, we can convert this 3-D analysis to a problem of analysing different μ in terms of AUC. Fig. 9 illustrates the plot of the AUC value with a change of μ from 0 to 1 with a step size of 0.1. In this figure, the appropriate selection of μ can achieve a better AUC value. For instance, the highest AUC values of 0.8947 and 0.895 can be reached for SVM ‐ KWSALO‐SPA1 when μ = 0.4 and SVM ‐ KWSALO‐SPA2 when μ = 0.2, respectively. Furthermore, SVM ‐ KWSALO‐SPA1 is less sensitive to the change of μ than SVM ‐ KWSALO‐SPA2. Specifically, SVM ‐ KWSALO‐SPA1 can obtain an AUC value higher than 0.888 in all cases of different μ, and SVM ‐ KWSALO‐SPA2 can obtain an AUC value above 0.88, except when μ is selected at 0.9 and 1. 5.4. Parameter setting Since the extraction of the local spatial information is required for each grid cell in the proposed framework, the two parameters of w and n should not be too large. Otherwise, they will cause unnecessary complexity in time and space values. Therefore, we define a proper data range for each parameter and choose a certain combination of these two parameters that can produce the optimal prediction results using the

6. Conclusion In this paper, we present a comparative study of composite kernels for LSM by integrating along-layer and spatial information into the landslide prediction process. SVMs with different composite kernels were compared in Yongxin County, China based on an analysis of sixteen influencing factors that were derived from a series of ancillary data. The experimental results confirmed the following conclusions: (1) From a visual inspection, all the prediction maps produced by the SVMs with different kernels have similar spatial distributions of landslide susceptibility, which align with the factor maps for altitude, lithology and slope, e.g., the mountainous zones in the north and south of the study area are characterized by high and very high susceptibility values, whereas the central parts of the study area are

Fig. 9. Impact of μ on the SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2 in terms of the prediction performance. 11

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categorized as the least susceptible zones. (2) In general, using the composite kernel based learning framework, we can achieve higher prediction accuracies than that of the original SVM. For instance, the AUC values obtained by all the SVMs with the compost kernels were 0.0025–0.0167 higher than that of the original SVM (0.8783), except for SVM ‐ K{ALO,SPA2} (0.8747), since this SVM may suffer from the curse of dimensionality and some spatial features are irrelevant or redundant. (3) Among the composite kernel methods, the SVMs with a summation kernel can achieve more accurate prediction accuracies than those of the SVMs with a stacked kernel. Specifically, SVM ‐ KDSALO‐SPA1, SVM ‐ KDSALO‐SPA2, SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2 obtained the AUC values above 0.8900, which were 0.0108–0.0203 higher than those of SVM ‐ K{ALO,SPA1} and SVM ‐ K{ALO,SPA2}. Furthermore, the SVMs with WS kernels are more effective than those with DS kernels. In particular, SVM ‐ KWSALO‐SPA1 and SVM ‐ KWSALO‐SPA2 achieved higher AUC values of 0.0014–0.0034 than those of SVM ‐ KDSALO‐SPA1 and SVM ‐ KDSALO‐SPA2.

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