# Landslide Susceptibility Mapping Combining Information Gain Ratio and Support Vector Machines: A Case Study from Wushan Segment in the Three Gorges Reservoir Area, China

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Study Area

#### 2.2. Methodology

#### 2.2.1. Information Gain Ratio

_{i}(landslide, non-landslide) is a classification set of sample data, and the following formula can obtain the information entropy of the factors:

_{1}, T

_{2}, …, T

_{m}) split from T regarding the causal factor F is estimated as:

#### 2.2.2. Support Vector Machines

_{i}, x

_{j}) = 1, 2…, n, the following function can solve the optimal separating hyperplane:

_{i}is the positive slack variables for the data points that allow for penalized constraint violation, and C is the penalty parameter that controls the trade-off between the complexity of the decision function and the number of training examples misclassified. The function can be converted into an equivalent dual problem based on the Wolf duality theory:

_{i}are Lagrange multipliers and C is the penalty. Then, the decision function, which will be used for the classification of new data, can be written:

**K**(x

_{i}, x

_{j}) is the kernel function. The radial basis kernel was adopted as kernel function for the SVM model in this study.

#### 2.2.3. Artificial Neural Networks

_{min}is the minimum value of the learning rate, η

_{max}is the maximum value of the learning rate, and d is the delay rate. In this study, the initial rate, the maximum and minimum learning rate, and the delay rate are 0.3, 0.1, 0.01, and 30, respectively.

#### 2.2.4. Classification and Regression Tree

**X**

_{m,p}, we sorted all samples by these attributes, and the average value of two adjacent values was taken as the separating points, which was called η

_{s}(s = 1, 2…, m−1). The data set

**X**

_{m,p}was divided into two subsets according to the value taken on attribute F, the subset

**X**

_{1}larger than η

_{s}and the subset

**X**

_{2}smaller than or equal to η

_{s}. The GINI coefficients of this classification method can be expressed as:

**X**

_{1}| is number of samples of subset

**X**

_{1}, |

**X**

_{2}| is number of samples of subset

**X**

_{2}, and

**I**(X) can be calculated using the following formula:

**X**

_{j}| is the number of samples in dataset

**X**

_{j}, and |

**C**

_{j}| is the number of samples belonging to

**C**

_{j}in data set

**X**

_{j}.

**X**

_{m,p}contained m data and p attributes, each attribute corresponded to m-1 partition points, and the GINI coefficient of each partition point was ${\mathit{G}}_{F}^{{\eta}_{\mathrm{s}}}\left(X\right)$, then the point, which had minimum GINI coefficient, was selected to partition the dataset

**X**

_{m,p}.

#### 2.2.5. Logistic Regression

_{i}(i = 1, 2…, n) is the predictor variables, and β

_{i}(i = 1, 2…, n) is the coefficient of the LR model.

#### 2.3. Data Preparation and Analysis

#### 2.3.1. Landslide Inventory Map

^{2}, and the area of single landslide ranged from 1664 m

^{2}to 1.06 km

^{2}. Most of the landslides in this study area occurred on the bank of the Yangtze River and the gully.

#### 2.3.2. Landslide Causal Factors

_{s}is the catchment area of the basin and β is the slope. The SPI can be divided into four categories (Figure 2f): [0,2), [2,4), [4,8), [8, +∞); their information values were 0.262, −0.020, −0.327, and −0.436, respectively (Table 1).

#### 2.4. Landslide Causal Factors Selection

#### 2.4.1. Multicollinearity Analysis

#### 2.4.2. Factor Selection Using Information Gain Ratio

## 3. Results and Accuracy Analysis

#### 3.1. Landslide Susceptibility Modelling

#### 3.2. Accuracy Statistic

#### 3.3. Using ROC Curve

## 4. Discussion

_{2}b

^{3}, T

_{2}b

^{4}) had a positive effect on landslides in this area, and their average merit values were 0.061 and 0.029, respectively (Figure 3). A total of 62% of the landslides were within 300 m from the Yangtze River, and nearly 60% of the landslides were with the stratigraphic lithology of T

_{2}b

^{3}and T

_{2}b

^{4}, which were regarded as the main stratum of landslide in the TGRA [37].

## 5. Conclusions

_{2}b

^{3}and T

_{2}b

^{4}); (2) IGR is an effective method for evaluating the importance of landslide indicators, and eliminating the less important factors can effectively improve the prediction accuracy in landslide susceptibility modelling; and (3) the SVM model shows the best performance in this study area, and thus it can be recommended for susceptibility modelling in TGRA and other landslide-prone regions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Yu, M.; Huang, Y.; Zhou, J.; Mao, L. Modeling of landslide topography based on micro-unmanned aerial vehicle photography and structure-from-motion. Environ. Earth Sci.
**2017**, 76, 520. [Google Scholar] [CrossRef] - Avelar, A.S.; Netto, A.L.C.; Lacerda, W.A.; Becker, L.B.; Mendonça, M.B. Mechanisms of the Recent Catastrophic Landslides in the Mountainous Range of Rio de Janeiro, Brazil; Springer: Berlin/Heidelberg, Germany, 2013; pp. 265–270. [Google Scholar]
- Fan, X.; Xu, Q.; Scaringi, G.; Dai, L.; Li, W.; Dong, X.; Zhu, X.; Pei, X.; Dai, K.; Havenith, H.-B. Failure mechanism and kinematics of the deadly June 24th 2017 Xinmo landslide, Maoxian, Sichuan, China. Landslides
**2017**, 14, 2129–2146. [Google Scholar] [CrossRef] - Cui, P.; Zhou, G.G.D.; Zhu, X.H.; Zhang, J.Q. Scale amplification of natural debris flows caused by cascading landslide dam failures. Geomorphology
**2013**, 182, 173–189. [Google Scholar] [CrossRef] - National Geological Disaster Bulletin. Available online: http://www.cigem.cgs.gov.cn/gzdt_4839/dwdt_4861/201904/t20190417_479382.html (accessed on 17 April 2019).
- Wang, F.; Zhang, Y.M.; Huo, Z.T.; Peng, X.M.; Wang, S.M.; Yamasaki, S. Mechanism for the rapid motion of the Qianjiangping landslide during reactivation by the first impoundment of the Three Gorges Dam reservoir, China. Landslides
**2008**, 5, 379–386. [Google Scholar] [CrossRef] - Xu, G.L.; Li, W.N.; Yu, Z.; Ma, X.H.; Yu, Z.Z. The 2 September 2014 Shanshucao landslide, Three Gorges Reservoir, China. Landslides
**2015**, 12, 1169–1178. [Google Scholar] [CrossRef] - Cascini, L. Applicability of landslide susceptibility and hazard zoning at different scales. Eng. Geol.
**2008**, 102, 164–177. [Google Scholar] [CrossRef] - Corominas, J.; van Westen, C.; Frattini, P.; Cascini, L.; Malet, J.P.; Fotopoulou, S.; Catani, F.; Van Den Eeckhaut, M.; Mavrouli, O.; Agliardi, F.; et al. Recommendations for the quantitative analysis of landslide risk. Bull. Eng. Geol. Environ.
**2014**, 73, 209–263. [Google Scholar] [CrossRef] - Bui, D.T.; Tuan, T.A.; Klempe, H.; Pradhan, B.; Revhaug, I. Spatial prediction models for shallow landslide hazards: A comparative assessment of the efficacy of support vector machines, artificial neural networks, kernel logistic regression, and logistic model tree. Landslides
**2016**, 13, 361–378. [Google Scholar] - Yin, K.L.; Yan, T.Z. Statistical prediction models for slope instability of metamorphosed rocks. In Proceedings of the Landslides, Vols 1-3, Rotterdam, The Netherlands, 10–15 July 1988; pp. 1269–1272. [Google Scholar]
- Zhu, C.H.; Wang, X.P.; Soc, I.C. Landslide Susceptibility Mapping: A Comparison of Information and Weights-Of-Evidence Methods in Three Gorges Area; IEEE Computer Society: Los Alamitos, CA, USA, 2009; pp. 342–346. [Google Scholar]
- Ayalew, L.; Yamagishi, H. The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan. Geomorphology
**2005**, 65, 15–31. [Google Scholar] [CrossRef] - Kawabata, D.; Bandibas, J. Landslide susceptibility mapping using geological data, a DEM from ASTER images and an Artificial Neural Network (ANN). Geomorphology
**2009**, 113, 97–109. [Google Scholar] [CrossRef] - Ermini, L.; Catani, F.; Casagli, N. Artificial Neural Networks applied to landslide susceptibility assessment. Geomorphology
**2005**, 66, 327–343. [Google Scholar] [CrossRef] - Pradhan, B.; Lee, S. Landslide susceptibility assessment and factor effect analysis: Backpropagation artificial neural networks and their comparison with frequency ratio and bivariate logistic regression modelling. Environ. Modell. Softw.
**2010**, 25, 747–759. [Google Scholar] [CrossRef] - Xu, C.; Dai, F.C.; Xu, X.W.; Lee, Y.H. GIS-based support vector machine modeling of earthquake-triggered landslide susceptibility in the Jianjiang River watershed, China. Geomorphology
**2012**, 145, 70–80. [Google Scholar] [CrossRef] - Peng, L.; Niu, R.Q.; Huang, B.; Wu, X.L.; Zhao, Y.N.; Ye, R.Q. Landslide susceptibility mapping based on rough set theory and support vector machines: A case of the Three Gorges area, China. Geomorphology
**2014**, 204, 287–301. [Google Scholar] [CrossRef] - Yao, X.; Tham, L.G.; Dai, F.C. Landslide susceptibility mapping based on Support Vector Machine: A case study on natural slopes of Hong Kong, China. Geomorphology
**2008**, 101, 572–582. [Google Scholar] [CrossRef] - Marjanovic, M.; Kovacevic, M.; Bajat, B.; Vozenilek, V. Landslide susceptibility assessment using SVM machine learning algorithm. Eng. Geol.
**2011**, 123, 225–234. [Google Scholar] [CrossRef] - Everitt, B.S. Classification and Regression Trees. In Encyclopedia of Statistics in Behavioral Science; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2005. [Google Scholar] [CrossRef]
- Pradhan, B.; Lee, S. Regional landslide susceptibility analysis using back-propagation neural network model at Cameron Highland, Malaysia. Landslides
**2010**, 7, 13–30. [Google Scholar] [CrossRef] - Pham, B.T.; Bui, D.T.; Dholakia, M.B.; Prakash, I.; Pham, H.V.; Mehmood, K.; Le, H.Q. A novel ensemble classifier of rotation forest and Naive Bayer for landslide susceptibility assessment at the Luc Yen district, Yen Bai Province (Viet Nam) using GIS. Geomat. Nat. Hazards Risk
**2017**, 8, 649–671. [Google Scholar] [CrossRef] - Shigeo, A. Support Vector Machines for Pattern Classification. In Proceedings of the International Joint Conference on Neural Networks, Washington, DC, USA, 15–19 July 2001; Volume 36, pp. 7535–7543. [Google Scholar]
- Tian, Y.Y.; Xu, C.; Hong, H.Y.; Zhou, Q.; Wang, D. Mapping earthquake-triggered landslide susceptibility by use of artificial neural network (ANN) models: An example of the 2013 Minxian (China) Mw 5.9 event. Geomat. Nat. Hazards Risk
**2019**, 10, 1–25. [Google Scholar] [CrossRef] - Kalantar, B.; Pradhan, B.; Naghibi, S.A.; Motevalli, A.; Mansor, S. Assessment of the effects of training data selection on the landslide susceptibility mapping: A comparison between support vector machine (SVM), logistic regression (LR) and artificial neural networks (ANN). Geomat. Nat. Hazards Risk
**2018**, 9, 49–69. [Google Scholar] [CrossRef] - Budimir, M.E.A.; Atkinson, P.M.; Lewis, H.G. A systematic review of landslide probability mapping using logistic regression. Landslides
**2015**, 12, 419–436. [Google Scholar] [CrossRef][Green Version] - Sestras, P.; Bilasco, S.; Rosca, S.; Nas, S.; Bondrea, M.V.; Galgau, R.; Veres, I.; Salagean, T.; Spalevic, V.; Cimpeanu, S.M. Landslides Susceptibility Assessment Based on GIS Statistical Bivariate Analysis in the Hills Surrounding a Metropolitan Area. Sustainability
**2019**, 11, 23. [Google Scholar] [CrossRef] - Bai, S.B.; Wang, J.; Lu, G.N.; Zhou, P.G.; Hou, S.S.; Xu, S.N. GIS-based logistic regression for landslide susceptibility mapping of the Zhongxian segment in the Three Gorges area, China. Geomorphology
**2010**, 115, 23–31. [Google Scholar] [CrossRef] - Chen, W.T.; Li, X.J.; Wang, Y.X.; Liu, S.W. Landslide susceptibility mapping using LiDAR and DMC data: A case study in the Three Gorges area, China. Environ. Earth Sci.
**2013**, 70, 673–685. [Google Scholar] [CrossRef] - Wu, X.L.; Niu, R.Q.; Ren, F.; Peng, L. Landslide susceptibility mapping using rough sets and back-propagation neural networks in the Three Gorges, China. Environ. Earth Sci.
**2013**, 70, 1307–1318. [Google Scholar] [CrossRef] - Zhou, C.; Yin, K.L.; Cao, Y.; Ahmed, B.; Li, Y.Y.; Catani, F.; Pourghasemi, H.R. Landslide susceptibility modeling applying machine learning methods: A case study from Longju in the Three Gorges Reservoir area, China. Comput. Geosci.
**2018**, 112, 23–37. [Google Scholar] [CrossRef][Green Version] - Moore, I.D.; Grayson, R.B.; Ladson, A.R. Digital terrain modelling: A review of hydrological, geomorphological, and biological applications. Hydrol. Process.
**1991**, 5, 3–30. [Google Scholar] [CrossRef] - Technical Requirements for Investigation and Evaluation of Collapse, Landslide, Debris Flow. Available online: http://www.mnr.gov.cn/gk/bzgf/201004/t20100406_1971713.html (accessed on 6 April 2010).
- Bui, D.T.; Lofman, O.; Revhaug, I.; Dick, O. Landslide susceptibility analysis in the Hoa Binh province of Vietnam using statistical index and logistic regression. Natural Hazards
**2011**, 59, 1413–1444. [Google Scholar] [CrossRef] - Hanley, J.A.; McNeil, B.J. A method of comparing the areas under receiver operating characteristic curves derived from the same cases. Radiology
**1983**, 148, 839–843. [Google Scholar] [CrossRef] - Miao, H.; Wang, G.; Yin, K.; Kamai, T.; Li, Y. Mechanism of the slow-moving landslides in Jurassic red-strata in the Three Gorges Reservoir, China. Eng. Geol.
**2014**, 171, 59–69. [Google Scholar] [CrossRef][Green Version] - An, K.; Niu, R. Landslide Susceptibility Assessment Using Support Vector Machine Based on Weighted-information Model. J. Yangtze River Sci. Res. Inst.
**2016**, 33, 47–51. [Google Scholar] - Marjanovic, M.; Bajat, B.; Kovacevic, M. Landslide Susceptibility Assessment with Machine Learning Algorithms; IEEE: New York, NY, USA, 2009; pp. 273–278. [Google Scholar]
- Chen, W.; Pourghasemi, H.R.; Panahi, M.; Kornejady, A.; Wang, J.L.; Xie, X.S.; Cao, S.B. Spatial prediction of landslide susceptibility using an adaptive neuro-fuzzy inference system combined with frequency ratio, generalized additive model, and support vector machine techniques. Geomorphology
**2017**, 297, 69–85. [Google Scholar] [CrossRef] - Bilasco, S.; Horvath, C.; Cocean, P.; Sorocovschi, V.; Oncu, M. Implementation of the usle model using gis techniques. case study the somesean plateau. Carpath. J. Earth Environ. Sci.
**2009**, 4, 123–132. [Google Scholar] - Zhou, C.; Yin, K.; Cao, Y.; Ahmed, B. Application of time series analysis and PSO–SVM model in predicting the Bazimen landslide in the Three Gorges Reservoir, China. Eng. Geol.
**2016**, 204, 108–120. [Google Scholar] [CrossRef] - Zhou, C.; Yin, K.; Cao, Y.; Intrieri, E.; Ahmed, B.; Catani, F. Displacement prediction of step-like landslide by applying a novel kernel extreme learning machine method. Landslides
**2018**, 15, 2211–2225. [Google Scholar] [CrossRef][Green Version] - Tang, H.; Wasowski, J.; Juang, C.H. Geohazards in the three Gorges Reservoir Area, China–Lessons learned from decades of research. Eng. Geol.
**2019**, 261, 105267. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) The location of Three Gorges Reservoir area (TGRA) in China. (

**b**) The location of the study area. (

**c**) Elevation map of the study area with landslide distribution (the landslides polygons were obtained from historical landslide data, field investigation, and high-resolution remote sensing image data).

**Figure 2.**Landslide causal factors of the study area: (

**a**) slope, (

**b**) aspect, (

**c**) curvature, (

**d**) plan curvature, (

**e**) profile curvature, (

**f**) SPI, (

**g**) TWI, (

**h**) TRI, (

**i**) lithology, (

**j**) bedding structure, (

**k**) distance to faults, (

**l**) distance to rivers, (

**m**) distance to gully.

**Figure 4.**Landslide susceptibility maps obtained from (

**a**) ANN model, (

**b**) logistic regression (LR) model, (

**c**) SVM model, and (

**d**) classification and regression tree (CART) model.

**Figure 5.**The receiver operating characteristic (ROC) curves of the SVM, ANN, LR, and CART models in landslide susceptibility assessment: (

**a**) training and (

**b**) verifying.

Causal Factor | Category | Pixels in Landslide | Pixels in TD | Proportion of LTL | Proportion of DTD | IV | NC |
---|---|---|---|---|---|---|---|

Altitude (m) | <300 | 17,324 | 81,071 | 68.71 | 20.41 | 1.752 | 0.990 |

300–450 | 6049 | 86,452 | 23.99 | 21.76 | 0.141 | 0.663 | |

450–750 | 1839 | 113,518 | 7.29 | 28.57 | −1.970 | 0.337 | |

>750 | 0 | 116,248 | 0 | 29.26 | −∞ | 0.01 | |

Slope (°) | <6 | 538 | 8342 | 2.13 | 2.10 | 0.023 | 0.598 |

6–15 | 4196 | 30,806 | 16.64 | 7.75 | 1.102 | 0.99 | |

15–24 | 9711 | 102,948 | 38.52 | 25.91 | 0.572 | 0.794 | |

24–33 | 7608 | 129,123 | 30.18 | 32.50 | −0.107 | 0.402 | |

33–51 | 3153 | 118,589 | 12.51 | 29.85 | −1.255 | 0.206 | |

51–75 | 6 | 7481 | 0.02 | 1.88 | −6.306 | 0.01 | |

Aspect (°) | 0–45 | 3427 | 45,388 | 13.59 | 11.42 | 0.251 | 0.849 |

45–90 | 2363 | 39,597 | 9.37 | 9.97 | −0.089 | 0.283 | |

90–135 | 3380 | 43,368 | 13.41 | 10.92 | 0.296 | 0.99 | |

135–180 | 4067 | 60,128 | 16.13 | 15.13 | 0.092 | 0.707 | |

180–225 | 2058 | 44,740 | 8.16 | 11.26 | −0.464 | 0.01 | |

225–270 | 1750 | 33,824 | 6.94 | 8.51 | −0.295 | 0.141 | |

270–315 | 3180 | 50,727 | 12.61 | 12.77 | −0.018 | 0.424 | |

315–360 | 4987 | 79,517 | 19.78 | 20.01 | −0.017 | 0.566 | |

Curvature | −24 to −1 | 3254 | 369,402 | 12.91 | 92.98 | −2.849 | 0.01 |

−1 to 3 | 21,577 | 26,749 | 85.58 | 6.73 | 3.668 | 0.99 | |

3–7 | 372 | 993 | 1.48 | 0.25 | 2.562 | 0.663 | |

7–27 | 9 | 145 | 0.04 | 0.04 | −0.032 | 0.337 | |

Plan curvature | −13 to −1.5 | 562 | 13,106 | 2.23 | 3.30 | −0.566 | 0.5 |

−1.5 to 1.5 | 24,231 | 372,725 | 96.11 | 93.82 | 0.035 | 0.99 | |

1.5–10.5 | 419 | 11,458 | 1.66 | 2.88 | −0.795 | 0.01 | |

Profile curvature | −18 to −2 | 397 | 11,732 | 1.57 | 2.95 | −0.907 | 0.01 |

−2 to 2 | 24,319 | 372,535 | 96.46 | 93.77 | 0.041 | 0.99 | |

2–18 | 496 | 13,022 | 1.97 | 3.28 | −0.736 | 0.5 | |

Stream power index (SPI) | 0–2 | 13,724 | 180,391 | 54.43 | 45.41 | 0.262 | 0.99 |

2–4 | 4304 | 68,746 | 17.07 | 17.30 | −0.020 | 0.663 | |

4–8 | 3196 | 63,159 | 12.68 | 15.90 | −0.327 | 0.337 | |

>8 | 3988 | 84,993 | 15.82 | 21.39 | −0.436 | 0.01 | |

Topographic wetness index (TWI) | 0–4.5 | 18,990 | 289,614 | 75.32 | 72.90 | 0.047 | 0.663 |

4.5–6.5 | 4856 | 85,391 | 19.26 | 21.49 | −0.158 | 0.337 | |

6.5–8.5 | 954 | 14,335 | 3.78 | 3.61 | 0.069 | 0.99 | |

>8.5 | 412 | 7949 | 1.63 | 2.00 | −0.292 | 0.01 | |

Terrain roughness index (TRI) | 1–1.2 | 22,324 | 278,274 | 88.55 | 70.04 | 0.338 | 0.99 |

1.2–1.4 | 2645 | 93,562 | 10.49 | 23.55 | −1.167 | 0.663 | |

1.4–1.6 | 239 | 18,431 | 0.95 | 4.64 | −2.291 | 0.337 | |

Distance to rivers (m) | >1.6 | 4 | 7022 | 0.02 | 1.77 | −6.800 | 0.01 |

0–150 | 9958 | 41,767 | 39.50 | 10.51 | 1.910 | 0.99 | |

150–300 | 5659 | 35,396 | 22.45 | 8.91 | 1.333 | 0.794 | |

300–650 | 5047 | 67,801 | 20.02 | 17.07 | 0.230 | 0.598 | |

650–950 | 2259 | 47,096 | 8.96 | 11.85 | −0.404 | 0.402 | |

950–1550 | 1808 | 69,776 | 7.17 | 17.56 | −1.292 | 0.206 | |

>1550 | 481 | 135,453 | 1.91 | 34.09 | −4.160 | 0.01 | |

Distance to gully (m) | 0–150 | 15,036 | 194,536 | 59.64 | 48.97 | 0.284 | 0.99 |

150–350 | 7653 | 106,289 | 30.35 | 26.75 | 0.182 | 0.75 | |

350–500 | 1553 | 30,901 | 6.16 | 7.78 | −0.337 | 0.5 | |

500–900 | 962 | 36,022 | 3.82 | 9.07 | −1.249 | 0.26 | |

>900 | 8 | 29,541 | 0.03 | 7.44 | −7.872 | 0.01 | |

Distance to faults (m) | 0–450 | 14,652 | 154,959 | 58.12 | 39.00 | 0.575 | 0.99 |

450–900 | 7121 | 77,607 | 28.24 | 19.53 | 0.532 | 0.663 | |

900–1750 | 3155 | 75,914 | 12.51 | 19.11 | −0.611 | 0.337 | |

>1750 | 284 | 88,809 | 1.13 | 22.35 | −4.311 | 0.01 | |

Lithology (L) | L1 | 3890 | 47,612 | 15.43 | 11.98 | 0.365 | 0.598 |

L2 | 15,126 | 132,299 | 60.00 | 33.30 | 0.849 | 0.794 | |

L3 | 1316 | 20,209 | 5.22 | 5.09 | 0.037 | 0.402 | |

L4 | 2003 | 16,307 | 7.94 | 4.10 | 0.953 | 0.99 | |

L5 | 0 | 11,826 | 0.00 | 2.98 | −∞ | 0.01 | |

L6 | 2877 | 168,880 | 11.41 | 42.51 | −1.897 | 0.206 | |

L7 | 0 | 156 | 0.00 | 0.04 | −∞ | 0.01 | |

Bedding structure (BS) | BS1 | 206 | 509 | 0.82 | 0.13 | 2.673 | 0.99 |

BS2 | 1423 | 34,200 | 5.64 | 8.61 | −0.609 | 0.173 | |

BS4 | 3204 | 87,211 | 12.71 | 21.95 | −0.789 | 0.337 | |

BS5 | 4695 | 87,741 | 18.62 | 22.08 | −0.246 | 0.01 | |

BS6 | 8549 | 113,523 | 33.91 | 28.57 | 0.247 | 0.5 | |

BS7 | 3721 | 39,376 | 14.76 | 9.91 | 0.574 | 0.663 | |

BS8 | 3414 | 34,729 | 13.54 | 8.74 | 0.631 | 0.827 |

Category | Main Lithology | Geologic Group |
---|---|---|

A | Siltstone, silty mudstone | T_{2}b^{2} |

B | Siltstone, muddy limestone, dolostone with mudstone | T_{2}b^{3}, T_{2}b^{4} |

C | Mudstone, muddy limestone | T_{2}b^{1} |

D | Sandstone, silty shale | T_{3}xj^{1}, T_{3}e |

E | Muddy limestone with limestone | T_{1}d^{1}, T_{1}d^{2}, T_{1}d^{3}, T_{1}d^{4} |

F | Limestone with dolostone, muddy limestone, dolomitic limestone | T_{1}j^{1}, T_{1}j^{2}, T_{1}j^{3}, T_{1}j^{4} |

G | Limestone, silty shale with coal seam | P_{3}w, P_{3}d |

Category | $\mathbf{Definition}\text{}(\mathbf{slope}:\mathit{\theta}$$,\text{}\mathbf{aspect}:\mathit{\sigma}$$,\text{}\mathbf{bed}\text{}\mathbf{dip}\text{}\mathbf{angle}:\mathit{\alpha}$$,\text{}\mathbf{bed}\text{}\mathbf{dip}\text{}\mathbf{direction}:\mathit{\beta})$ |
---|---|

BS1 | $\alpha <10\xb0$ |

BS2 | $\left(\left(\left|\alpha -\beta \right|\in \left(0,30\xb0\right]\right)\parallel \left(\left|\alpha -\beta \right|\in \left[330\xb0,360\xb0\right)\right)\right)\&\&\left(\alpha >10\xb0\right)\&\&\left(\theta >\alpha \right)$ |

BS3 | $\left(\left(\left|\alpha -\beta \right|\in \left(0,30\xb0\right]\right)\parallel \left(\left|\alpha -\beta \right|\in \left[330\xb0,360\xb0\right)\right)\right)\&\&\left(\alpha >10\xb0\right)\&\&\left(\theta =\alpha \right)$ |

BS4 | $\left(\left(\left|\alpha -\beta \right|\in \left(0,30\xb0\right]\right)\parallel \left(\left|\alpha -\beta \right|\in \left[330\xb0,360\xb0\right)\right)\right)\&\&\left(\alpha >10\xb0\right)\&\&\left(\theta <\alpha \right)$ |

BS5 | $\left(\left|\alpha -\beta \right|\in \left[30\xb0,60\xb0\right)\right)\parallel \left(\left|\alpha -\beta \right|\in \left[300\xb0,330\xb0\right)\right)$ |

BS6 | $\left(\left|\alpha -\beta \right|\in \left[60\xb0,120\xb0\right)\right)\parallel \left(\left|\alpha -\beta \right|\in \left[240\xb0,300\xb0\right)\right)$ |

BS7 | $\left(\left|\alpha -\beta \right|\in \left[90\xb0,150\xb0\right)\right)\parallel \left(\left|\alpha -\beta \right|\in \left[210\xb0,240\xb0\right)\right)$ |

BS8 | $\left(\left|\alpha -\beta \right|\in \left[120\xb0,180\xb0\right)\right)\parallel \left(\left|\alpha -\beta \right|\in \left[180\xb0,210\xb0\right)\right)$ |

Factor | Original Factor System | New Factor System | ||
---|---|---|---|---|

Tolerances | VIF | Tolerances | VIF | |

Altitude | 0.176 | 5.687 | / | / |

Slope | 0.535 | 1.870 | 0.536 | 1.867 |

Aspect | 0.979 | 1.021 | 0.980 | 1.021 |

Curvature | 0.846 | 1.183 | 0.849 | 1.178 |

Plan curvature | 0.926 | 1.080 | 0.927 | 1.079 |

Profile curvature | 0.876 | 1.142 | 0.876 | 1.142 |

TRI | 0.522 | 1.916 | 0.522 | 1.914 |

Lithology | 0.489 | 2.044 | 0.544 | 1.837 |

Bedding structure | 0.939 | 1.065 | 0.941 | 1.063 |

Distance to faults | 0.603 | 1.658 | 0.627 | 1.595 |

Distance to rivers | 0.235 | 4.259 | 0.751 | 1.332 |

Distance to gully | 0.769 | 1.300 | 0.802 | 1.247 |

Model | Eliminating Less Important Factors | Accuracy |
---|---|---|

Model 1 | Without eliminating any factor | 0.918 |

Model 2 | TWI | 0.918 |

Model 3 | TWI, profile curvature | 0.920 |

Model 4 | TWI, profile curvature, plan curvature | 0.919 |

Model 5 | TWI, profile curvature, plan curvature, curvature | 0.922 |

Model 6 | TWI, profile curvature, plan curvature, curvature, aspect | 0.908 |

Models | Parameters | Notes |
---|---|---|

SVM | c = 20, γ = 1.3 | c is the penalty factor, γ is the parameter of the kernel function |

ANN | n = 5, α = 0.9 | n is the neurons number, α is the momentum |

Susceptibility Level | Pixels in Landslide | Pixels in Domain | Proportion of LD | Proportion of LTL | Proportion of DTD | Frequency Ratios |
---|---|---|---|---|---|---|

SVM | ||||||

Very low | 6 | 154,275 | 0.00% | 0.02% | 38.83% | 0.001 |

Low | 210 | 83,697 | 0.25% | 0.83% | 21.07% | 0.040 |

Moderate | 2636 | 79,817 | 3.30% | 10.46% | 20.09% | 0.520 |

High | 22,360 | 79,500 | 28.13% | 88.69% | 20.01% | 4.432 |

ANN | ||||||

Very low | 409 | 160,378 | 0.26% | 1.62% | 40.37% | 0.040 |

Low | 1741 | 79,155 | 2.20% | 6.91% | 19.92% | 0.347 |

Moderate | 5479 | 78,975 | 6.94% | 21.73% | 19.88% | 1.093 |

High | 17,583 | 78,781 | 22.32% | 69.79% | 19.83% | 3.517 |

LR | ||||||

Very low | 393 | 161,746 | 0.24% | 1.56% | 40.71% | 0.038 |

Low | 1838 | 79,127 | 2.32% | 7.29% | 19.92% | 0.366 |

Moderate | 5640 | 78,411 | 7.19% | 22.37% | 19.74% | 1.133 |

High | 17,341 | 78,005 | 22.23% | 68.78% | 19.63% | 3.503 |

CART | ||||||

Very low | 491 | 160,378 | 0.31% | 1.95% | 40.37% | 0.048 |

Low | 1341 | 79,419 | 1.69% | 5.32% | 19.99% | 0.266 |

Moderate | 7621 | 82,440 | 9.24% | 30.23% | 20.75% | 1.457 |

High | 15,759 | 75,052 | 21.00% | 62.51% | 18.89% | 3.309 |

Models | Area Under the ROC Curve (AUC) | Standard Error | 95% Confidence Interval | |
---|---|---|---|---|

Lower Limit | Upper Limit | |||

Training group | ||||

SVM | 0.927 | 0.002 | 0.923 | 0.930 |

ANN | 0.866 | 0.002 | 0.962 | 0.871 |

LR | 0.860 | 0.002 | 0.855 | 0.864 |

CART | 0.842 | 0.003 | 0.837 | 0.847 |

Prediction group | ||||

SVM | 0.922 | 0.001 | 0.920 | 0.923 |

ANN | 0.875 | 0.001 | 0.873 | 0.877 |

LR | 0.863 | 0.001 | 0.860 | 0.865 |

CART | 0.837 | 0.001 | 0.835 | 0.840 |

Authors | Study Area | Accuracy of SVM |
---|---|---|

An et al. [38] | The Wangzhou segment of the TGRA | 0.814 |

Marjanovic et al. [20] | The Fruška Gora Mountain (Serbia) | 0.842 |

Marjanovic et al. [39] | NW (Northwest) slopes of Fruška Gora Mountain, Serbia | 0.880 |

Chen et al. [40] | Hanyuan county, China | 0.875 |

Bui et al. [10] | The Son La hydropower basin (Vietnam) | 0.887 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yu, L.; Cao, Y.; Zhou, C.; Wang, Y.; Huo, Z. Landslide Susceptibility Mapping Combining Information Gain Ratio and Support Vector Machines: A Case Study from Wushan Segment in the Three Gorges Reservoir Area, China. *Appl. Sci.* **2019**, *9*, 4756.
https://doi.org/10.3390/app9224756

**AMA Style**

Yu L, Cao Y, Zhou C, Wang Y, Huo Z. Landslide Susceptibility Mapping Combining Information Gain Ratio and Support Vector Machines: A Case Study from Wushan Segment in the Three Gorges Reservoir Area, China. *Applied Sciences*. 2019; 9(22):4756.
https://doi.org/10.3390/app9224756

**Chicago/Turabian Style**

Yu, Lanbing, Ying Cao, Chao Zhou, Yang Wang, and Zhitao Huo. 2019. "Landslide Susceptibility Mapping Combining Information Gain Ratio and Support Vector Machines: A Case Study from Wushan Segment in the Three Gorges Reservoir Area, China" *Applied Sciences* 9, no. 22: 4756.
https://doi.org/10.3390/app9224756