# Improved Shallow Landslide Susceptibility Prediction Based on Statistics and Ensemble Learning

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

^{2}, which is composed of mountainous areas (82.9%), cultivated land (8.3%), and reservoirs, roads, and villages (collectively 9.8%). The average annual precipitation is 663.1 mm (1981–2012) mainly concentrated in summer (76.4%) and it is a continental monsoon semi-arid climate.

#### 2.2. Data Preparation

#### 2.2.1. Landslide Inventory

^{2}to 300 m

^{2}while the depth of most landslides is less than 4 m, belonging to shallow landslides.

#### 2.2.2. Choice of Mapping Units

#### 2.2.3. Conditioning Factors

_{s}is the specific catchment area, $\mathsf{\beta}$ is the slop angle.

## 3. Methods

#### 3.1. Sampling Strategy

#### 3.1.1. K-Means Clustering

_{n+}

_{1}represents the sum of squares of distances from each point to the cluster center after the nth clustering; $\epsilon $ represents the precision value.

#### 3.1.2. FCM Algorithm

_{i}represents the cluster centers, C represents the number of centers, u

_{ij}represents the membership matrix; m represents the degree of fuzziness; J is the objective function and n is the number of objects in the database; d

^{2}is the Euclidean distance between the ith clustering center and the jth sample [35].

#### 3.1.3. Frequency Ratio

_{i}greater than 1 manifest that there exists a close relationship between landslide occurring and variable class, and if the values are less than 1 then a weak correlation is reflected. Continuous variables are required to be reclassified into classes before application, as Table 1 showed.

#### 3.2. Modeling Landslide Susceptibility

#### 3.2.1. LR Model

_{0}is the constant value, and b

_{1}, b

_{2}, …, b

_{n}refer to each significant input variable (x

_{1}, x

_{2},..., x

_{n}

_{)}causing the landslide.

#### 3.2.2. RF

#### 3.2.3. GBDT

#### 3.2.4. AdaBoost-DT

#### 3.2.5. Gini Index

#### 3.2.6. Stacking

#### 3.3. Evaluating Model Performance

## 4. Results and Verification

#### 4.1. Non-Landslide Samples Selected by FCM and K-Means

#### 4.2. Evaluation and Comparison of Different Models

#### 4.3. Application of Stacking Method for LSM

#### 4.4. Analysis of Major Conditioning Factors

## 5. Discussion

#### 5.1. Ensuring the Reliability of Models

#### 5.1.1. Internal and External Cross-Validation

#### 5.1.2. The Selection of Non-Landslide Samples

#### 5.2. Increasing the Accuracy of LSM

#### 5.3. Maintain the Integrity of Geological Hazard Assessment

## 6. Conclusions

- The performance of different ensemble techniques varies, but achieved satisfactory results as a whole. Stacking was considered the most suitable model with obvious improvement in terms of accuracy compared to the basic classifiers.
- The combination of the bivariate statistical method and Gini index helps better explore the major conditioning factors and improve the integrity of ensemble techniques.
- The non-landslide samples selected by FCM are more representative and improved the quality of samples. Overall, improvement of sample quality and selection of advanced methods help improve the practicability of LSM.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Huang, X.; Guo, F.; Deng, M.; Yi, W.; Huang, H. Understanding the deformation mechanism and threshold reservoir level of the floating weight-reducing landslide in the Three Gorges Reservoir Area, China. Landslides
**2020**, 17, 2879–2894. [Google Scholar] [CrossRef] - Sun, X.; Chen, J.; Li, Y.; Rene, N.N. Landslide Susceptibility mapping along a rapidly uplifting river valley of the Upper Jinsha River, Southeastern Tibetan Plateau, China. Remote Sens.
**2022**, 14, 1730. [Google Scholar] [CrossRef] - Kim, J.C.; Lee, S.; Jung, H.S.; Lee, S. Landslide susceptibility mapping using random forest and boosted tree models in Pyeong-Chang, Korea. Geocarto Int.
**2018**, 33, 1000–1015. [Google Scholar] [CrossRef] - Safran, E.B.; O’Connor, J.E.; Ely, L.L.; House, P.K.; Grant, G.; Harrity, K.; Jones, E. Plugs or flood-makers? The unstable landslide dams of eastern Oregon. Geomorphology
**2015**, 248, 237–251. [Google Scholar] [CrossRef] [Green Version] - Zhu, A.X.; Miao, Y.; Wang, R.; Zhu, T.; Deng, Y.; Liu, J.; Hong, H. A comparative study of an expert knowledge-based model and two data-driven models for landslide susceptibility mapping. Catena
**2018**, 166, 317–327. [Google Scholar] [CrossRef] - Ayalew, L.; Yamagishi, H. The application of GIS-based logistic regression for landslide susceptibility mapping in the Kaku-da-Yahiko Mountains, Central Japan. Geomorphology
**2005**, 65, 15–31. [Google Scholar] [CrossRef] - Jiao, Y.; Zhao, D.; Ding, Y.; Liu, Y.; Xu, Q.; Qiu, Y.; Liu, C.; Liu, Z.; Zha, Z.; Li, R. Performance evaluation for four GIS-based models purposed to predict and map landslide susceptibility: A case study at a World Heritage site in Southwest China. Catena
**2019**, 183, 104221. [Google Scholar] [CrossRef] - Shi, M.; Chen, J.; Song, Y.; Zhang, W.; Song, S.; Zhang, X. Assessing debris flow susceptibility in Heshigten Banner, Inner Mongolia, China, using principal component analysis and an improved fuzzy C-means algorithm. Bull. Eng. Geol. Environ.
**2016**, 75, 909–922. [Google Scholar] [CrossRef] - Liang, Z.; Wang, C.M.; Zhang, Z.M.; Khan, K.U.J. A comparison of statistical and machine learning methods for debris flow susceptibility mapping. Stoch. Environ. Res. Risk Assess.
**2020**, 34, 1887–1907. [Google Scholar] [CrossRef] - Lian, C.; Zeng, Z.; Yao, W.; Tang, H. Extreme learning machine for the displacement prediction of landslide under rainfall and reservoir level. Stoch. Environ. Res. Risk Assess.
**2014**, 28, 1957–1972. [Google Scholar] [CrossRef] - Merghadi, A.; Abderrahmane, B.; Tien Bui, D. Landslide susceptibility assessment at Mila Basin (Algeria): A comparative as-sessment of prediction capability of advanced machine learning methods. ISPRS Int. J. Geo-Inf.
**2018**, 7, 268. [Google Scholar] [CrossRef] [Green Version] - Tien Bui, D.; Ho, T.C.; Revhaug, I.; Pradhan, B.; Nguyen, D.B. Landslide Susceptibility Mapping Along the National Road 32 of Vietnam Using GIS-Based J48 Decision Tree Classifier and Its Ensembles[M]//Cartography from Pole to Pole; Springer: Berlin/Heidelberg, Germany, 2014; pp. 303–317. [Google Scholar]
- Hu, X.; Zhang, H.; Mei, H.; Xiao, D.; Li, Y.; Li, M. Landslide susceptibility mapping using the stacking ensemble machine learning method in Lushui, Southwest China. Appl. Sci.
**2020**, 10, 4016. [Google Scholar] [CrossRef] - Bennett, G.L.; Miller, S.R.; Roering, J.J.; Schmidt, D.A. Landslides, threshold slopes, and the survival of relict terrain in the wake of the Mendocino Triple Junction. Geology
**2016**, 44, 363–366. [Google Scholar] [CrossRef] [Green Version] - Du, J.; Glade, T.; Woldai, T.; Chai, B.; Zeng, B. Landslide susceptibility assessment based on an incomplete landslide in-ventory in the Jilong Valley, Tibet, Chinese Himalayas. Eng. Geol.
**2020**, 270, 105572. [Google Scholar] [CrossRef] - Lee, S.; Min, K. Statistical analysis of landslide susceptibility at Yongin, Korea. Environ. Earth Sci.
**2001**, 40, 1095–1113. [Google Scholar] [CrossRef] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef] [Green Version] - Varnes, D.J. Landslide types and processes. Landslides Eng. Pract.
**1958**, 24, 20–47. [Google Scholar] - Furlani, S.; Ninfo, A. Is the present the key to the future? Earth-Sci. Rev.
**2015**, 142, 38–46. [Google Scholar] [CrossRef] - Guzzetti, F.; Galli, M.; Reichenbach, P.; Ardizzone, F.; Cardinali, M.; Galli, M. Estimating the quality of landslide susceptibility models. Geomorphology
**2006**, 81, 166–184. [Google Scholar] [CrossRef] - Guzzetti, F.; Galli, M.; Reichenbach, P.; Ardizzone, F.; Cardinali, M. Landslide hazard assessment in the Collazzone area, Umbria, Central Italy. Nat. Hazards Earth Syst. Sci.
**2006**, 6, 115–131. [Google Scholar] [CrossRef] - Sun, X.L.; Zhao, Y.G.; Wang, H.L.; Yang, L.; Qin, C.Z.; Zhu, A.X.; Li, B. Sensitivity of digital soil maps based on FCM to the fuzzy exponent and the number of clusters. Geoderma
**2012**, 171, 24–34. [Google Scholar] [CrossRef] - Van Westen, C.J.; Castellanos, E.; Kuriakose, S.L. Spatial data for landslide susceptibility, hazard, and vulnerability assessment: An overview. Eng. Geol.
**2008**, 102, 112–131. [Google Scholar] [CrossRef] - Feizizadeh, B.; Blaschke, T.; Nazmfar, H. GIS-based ordered weighted averaging and dempster—Shafer methods for landslide susceptibility mapping in the Urmia Lake Basin, Iran. Int. J. Digit. Earth
**2012**, 7, 688–708. [Google Scholar] [CrossRef] - Hong, H.; Pradhan, B.; Xu, C.; Bui, D.T. Spatial prediction of landslide hazard at the Yihuang area (China) using two-class kernel logistic regression, alternating decision tree and support vector machines. Catena
**2015**, 133, 266–281. [Google Scholar] [CrossRef] - Magliulo, P.; Di Lisio, A.; Russo, F.; Zelano, A. Geomorphology and landslide susceptibility assessment using GIS and bivariate statistics: A case study in southern Italy. Nat. Hazards
**2008**, 47, 411–435. [Google Scholar] [CrossRef] - Liang, Z.; Wang, C.; Han, S.; Khan, K.U.J.; Liu, Y. Classification and susceptibility assessment of debris flow based on a semi-quantitative method combination of the fuzzy C-means algorithm, factor analysis and efficacy coefficient. Nat. Hazards Earth Syst. Sci.
**2020**, 20, 1287–1304. [Google Scholar] [CrossRef] - Evans, I.S. An integrated system of terrain analysis and slope mapping. Z. Geomorphol.
**1980**, 36, 274–295. [Google Scholar] - Camilo, D.C.; Lombardo, L.; Mai, P.M.; Dou, J.; Huser, R. Handling high predictor dimensionality in slope-unit-based landslide susceptibility models through LASSO-penalized generalized linear model. Environ. Model. Softw.
**2017**, 97, 145–156. [Google Scholar] [CrossRef] [Green Version] - Dou, J.; Yamagishi, H.; Xu, Y.; Zhu, Z.; Yunus, A.P. Characteristics of the Torrential Rainfall-Induced Shallow Landslides by Typhoon Bilis, in July 2006, Using Remote Sensing and GIS[M]//GIS Landslide; Springer: Tokyo, Japan, 2017; pp. 221–230. [Google Scholar]
- Anil, K. Data clustering: 50 years beyond K-Means. Pattern Recogn. Lett.
**2010**, 31, 651–666. [Google Scholar] - Hartigan, J.; Wong, M. Algorithm AS 136: A K-means clustering algorithm. J. R. Stat. Soc. C.
**1979**, 28, 100–108. [Google Scholar] [CrossRef] - Dunn, J.C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybern.
**1973**, 3, 32–57. [Google Scholar] [CrossRef] - Bezdek, J.C. Pattern Recognition with Fuzzy Objective Function Algorithms; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013. [Google Scholar]
- Wang, J.; Chen, J.; Yang, J. Application of distance discriminant analysis method in classification of surrounding rock mass in highway tunnel. J. Jilin Univ.
**2008**, 38, 999–1004. [Google Scholar] - Chen, J.; Pi, D. A cluster validity index for fuzzy clustering based on non-distance. In Proceedings of the 2013 International Conference on Computational and Information Sciences, Yongzhou, China, 21–23 June 2013; pp. 880–883. [Google Scholar]
- Neter, J.; Wasserman, W.; Kutner, M.H. Applied Linear Statistical Models; Irwin: Chicago, IL, USA, 1996. [Google Scholar]
- Fernández-Delgado, M.; Cernadas, E.; Barro, S.; Amorim, D. Do we need hundreds of classifiers to solve real world classification problems? J. Mach. Learn. Res.
**2014**, 15, 3133–3181. [Google Scholar] - Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine learning in Python. J. Mach. Learn. Res.
**2011**, 12, 2825–2830. [Google Scholar] - Youssef, A.M.; Pradhan, B.; Jebur, M.N.; El-Harbi, H.M. Landslide susceptibility mapping using ensemble bivariate and multivariate statistical models in Fayfa area, Saudi Arabia. Environ. Earth Sci.
**2014**, 73, 3745–3761. [Google Scholar] [CrossRef] - Wang, Y.; Feng, L.; Li, S.; Ren, F.; Du, Q. A hybrid model considering spatial heterogeneity for landslide susceptibility mapping in Zhejiang Province, China. Catena
**2020**, 188, 104425. [Google Scholar] [CrossRef] - Freund, Y.; Schapire, R.E. A decision-theoretic generalization of online learning and an application to boosting. J. Comput. Syst. Sci.
**1997**, 55, 119–139. [Google Scholar] [CrossRef] [Green Version] - Džeroski, S.; Ženko, B. Is combining classifiers with stacking better than selecting the best one? Mach. Learn.
**2004**, 54, 255–273. [Google Scholar] [CrossRef] [Green Version] - Chung, C.J.F.; Fabbri, A.G. Validation of spatial prediction models for landslide hazard mapping. Nat. Hazards
**2003**, 30, 451–472. [Google Scholar] [CrossRef] - James, G.; Witten, D.; Hastie, T.; Tibshirani, R. An Introduction to Statistical Learning; Springer: New York, NY, USA, 2013. [Google Scholar]
- Green, D.M.; Swets, J.A. Signal Detection Theory and Psychophysics; Wiley: New York, NY, USA, 1966. [Google Scholar]
- Schratz, P.; Muenchow, J.; Iturritxa, E.; Richter, J.; Brenning, A. Hyperparameter tuning and performance assessment of statistical and machine-learning algorithms using spatial data. Ecol. Model.
**2019**, 406, 109–120. [Google Scholar] [CrossRef] [Green Version] - Duarte, E.; Wainer, J. Empirical comparison of cross-validation and internal metrics for tuning SVM hyperparameters. Pattern Recognit. Lett.
**2017**, 88, 6–11. [Google Scholar] [CrossRef] - Bengio, Y. Gradient-based optimization of hyperparameters. Neural Comput.
**2000**, 12, 1889–1900. [Google Scholar] [CrossRef] [PubMed] - Reichenbach, P.; Rossi, M.; Malamud, B.D.; Mihir, M.; Guzzetti, F. A review of statistically-based landslide susceptibility models. Earth-Sci. Rev.
**2018**, 180, 60–91. [Google Scholar] [CrossRef] - Ciurleo, M.; Cascini, L.; Calvello, M. A comparison of statistical and deterministic methods for shallow landslide susceptibility zoning in clayey soils. Eng. Geol.
**2017**, 223, 71–81. [Google Scholar] [CrossRef] - Liu, R.; Yang, X.; Xu, C.; Wei, L.; Zeng, X. Comparative study of convolutional neural network and conventional machine learning methods for landslide susceptibility mapping. Remote Sens.
**2022**, 14, 321. [Google Scholar] [CrossRef] - Dou, J.; Yunus, A.P.; Bui, D.T.; Merghadi, A.; Sahana, M.; Zhu, Z.; Chen, C.; Han, Z.; Pham, B.T. Improved landslide assessment using support vector machine with bagging, boosting, and stacking ensemble machine learning framework in a mountainous watershed, Japan. Landslides
**2020**, 17, 641–658. [Google Scholar] [CrossRef] - Di Napoli, M.; Carotenuto, F.; Cevasco, A.; Confuorto, P.; Di Martire, D.; Firpo, M.; Pepe, G.; Raso, E.; Calcaterra, D. Machine learning ensemble modelling as a tool to improve landslide susceptibility mapping reliability. Landslides
**2020**, 17, 1897–1914. [Google Scholar] [CrossRef] - Arabameri, A.; Chandra Pal, S.; Rezaie, F.; Chakrabortty, R.; Saha, A.; Blaschke, T.; Thi Ngo, P.T. Decision tree based ensemble machine learning approaches for landslide susceptibility mapping. Geocarto Int.
**2021**, 1–35. [Google Scholar] [CrossRef] - Li, W.; Fang, Z.; Wang, Y. Stacking ensemble of deep learning methods for landslide susceptibility mapping in the Three Gorges Reservoir area. China. Stoch. Environ. Res. Risk Assess.
**2021**, 1–22. [Google Scholar] [CrossRef] - Chen, W.; Xie, X.; Wang, J.; Pradhan, B.; Hong, H.; Bui, D.T.; Ma, J. A comparative study of logistic model tree, random forest, and classification and regression tree models for spatial prediction of landslide susceptibility. Catena
**2017**, 151, 147–160. [Google Scholar] [CrossRef] [Green Version] - Dietterich, T.G. An experimental comparison of three methods for constructing ensembles of decision trees: Bagging, boosting, and randomization. Mach. Learn.
**2000**, 40, 139–157. [Google Scholar] [CrossRef] - Youssef, A.M.; Pourghasemi, H.R. Landslide susceptibility mapping using machine learning algorithms and comparison of their performance at Abha Basin, Asir Region, Saudi Arabia. Geosci. Front.
**2021**, 12, 639–655. [Google Scholar] [CrossRef]

**Figure 2.**Field investigation photos. (

**a**) shallow landslide in Lama Gate South gully; (

**b**) falls in Lama Gate South gully.

**Figure 3.**Field investigation photos. (

**a**) early debris-flow deposits in Dawa gully; (

**b**) Partial enlargement.

**Figure 5.**Study area thematic maps: (

**a**) Elevation; (

**b**) Plan curvature; (

**c**) Profile curvature; (

**d**) TWI; (

**e**) MED; (

**f**) Slope; (

**g**) Aspect; (

**h**) DTR; (

**i**) DTF; (

**j**) DTS; (

**k**) Lithology; (

**l**) Maximum 24 h Rainfall; (

**m**) Maximum seven days Rainfall.

**Figure 9.**Analysis of ROC curve for the landslide susceptibility map: (

**a**) Success rate curve of landslide using the training dataset; (

**b**) Prediction rate curve of landslide using the validation dataset.

Category | Conditioning Factors | Type | Data Source | Values |
---|---|---|---|---|

Topographical | Elevation (m) | Continuous | SRTM | (1) <200; (2) 200–400; (3) 400–600; (4) 600–800; |

(5) >800 | ||||

Plan curvature | Continuous | SRTM | (1) <0; (2) 0–0.01; (3) 0.01–0.02; (4) 0.02–0.03; | |

(5) >0.03 | ||||

Profile curvature | Continuous | SRTM | (1) <0; (2) 0–0.01; (3) 0.01–0.02; (4) 0.02–0.03; | |

(5) >0.03 | ||||

Slope angle (°) | Continuous | SRTM | (1) <10; (2) 10–20; (3) 20–30; (4) >30 | |

TWI | Continuous | SRTM | (1) <6.5; (2) 6.5–7; (3) 7–7.5; (4) 7.5–8; | |

(5) 8–8.5; (6) >8.5 | ||||

MED (m) | Continuous | SRTM | (1) <100; (2) 100–200; (3)200–300; (4) 300–400; | |

(5) 400–500; (6) >500 | ||||

Slope aspect | Categorical | SRTM | (1) north; (2) northeast; (3) east; (4) southeast; (5) south; (6) southwest; (7) west; (8) northwest | |

Geological and Geomorphological | Distance to faults (m) | Continuous | Geological map | (1) <1000; (2) 1000–2000; (3) 2000–3000; (4)3000–4000; (5) >4000 |

Distance to streams (m) | Continuous | DNRB | (1) <1000; (2) 1000–2000; (3) 2000–3000; (4)3000–4000; (5) >4000 | |

Lithology | Categorical | Geological map | (1) Gneiss; (2) Dolomites; (3) Siltstone (4) Granite;(5) Limestone; (6) Conglomerate | |

Triggering factors | Maximum 24 h rainfall (mm) | Continuous | BHM | (1) <270; (2) 270–280; (3) 280–290; (4) >290 |

Maximum 7 days rainfall (mm) | Continuous | BHM | (1) <320; (2) 320–330; (3) 330–340; (4) >340 | |

Distance to roads (m) | Continuous | DNRB | (1) <1000; (2) 1000–2000; (3) 2000–3000; (4)3000–4000; (5) >4000 |

Methods | Parameters |
---|---|

DT | Criterion = ‘gini’; max_features = None; max_depth = 20; min_samples_split = 2; min_samples_leaf = 1; max_leaf_nodes = None; class_weight = None |

RF | n_estimators = 500; criterion = ‘gini’; max_depth = None; max_features = ‘sqrt’; |

GBDT | n_estimators = 100; learning_rate = 0.1; max_depth = 2; verbose = 1; subsample = 0.7; max_leaf_nodes = None |

AdaBoost-DT | base_estimator = None; n_estimators = 100; learning_rate = 1.0; algorithm = ‘SAMME.R’; random_state = None |

Method | Class | Landslide Ratio (%) | Area Ratio (%) | FR |
---|---|---|---|---|

FCM | Very low | 3.24 | 15.97 | 0.20 |

Low | 19.73 | 23.25 | 0.85 | |

Moderate | 21.35 | 19.29 | 1.11 | |

High | 40.00 | 33.50 | 1.19 | |

Very high | 15.68 | 8.00 | 1.96 | |

k-means | Very low | 1.62 | 11.66 | 0.14 |

Low | 15.41 | 22.30 | 0.69 | |

Moderate | 15.57 | 18.71 | 0.83 | |

High | 48.11 | 39.16 | 1.22 | |

Very high | 17.30 | 8.17 | 2.11 |

Metrics | RF | GBDT | Ada-DT | Stacking |
---|---|---|---|---|

TP (%) | 82.46 | 84.88 | 81.29 | 91.22 |

TN (%) | 76.80 | 87.67 | 86.44 | 92.20 |

FP (%) | 17.54 | 15.12 | 18.71 | 8.78 |

FN (%) | 23.2 | 12.37 | 13.56 | 7.80 |

Sensitivity (%) | 79.93 | 86.97 | 85.66 | 91.89 |

Specificity (%) | 83.16 | 85.67 | 82.26 | 91.78 |

Accuracy (%) | 81.56 | 86.29 | 83.87 | 91.84 |

Models | AUC | Standard Error | 95% Confidence Interval |
---|---|---|---|

RF | 0.920 | 0.011 | 0.899–0.941 |

GBDT | 0.957 | 0.008 | 0.942–0.973 |

Ada-DT | 0.959 | 0.009 | 0.942–0.976 |

Stacking | 0.963 | 0.006 | 0.950–0.975 |

Metrics | RF | GBDT | Ada-DT | Stacking |
---|---|---|---|---|

TP (%) | 77.22 | 86.30 | 83.54 | 90.54 |

TN (%) | 79.71 | 83.78 | 86.96 | 91.78 |

FP (%) | 22.78 | 13.70 | 16.46 | 9.46 |

FN (%) | 20.29 | 16.22 | 13.04 | 8.22 |

Sensitivity (%) | 81.33 | 86.11 | 86.96 | 91.78 |

Specificity (%) | 75.34 | 84.00 | 82.19 | 90.54 |

Accuracy (%) | 78.38 | 85.03 | 85.13 | 91.16 |

Models | AUC | Standard Error | 95% Confidence Interval |
---|---|---|---|

RF | 0.906 | 0.027 | 0.853–0.959 |

GBDT | 0.910 | 0.026 | 0.859–0.962 |

Ada-DT | 0.917 | 0.021 | 0.877–0.958 |

Stacking | 0.944 | 0.018 | 0.908–0.980 |

Method | DTS | DTR | Elevation | Slope Angel | TWI | Maximum 24 h Rainfall | Lithology | MED | Maximum 7 Days Rainfall | Profile Curvature |
---|---|---|---|---|---|---|---|---|---|---|

GBDT | 0.37 | 0.34 | 0.16 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | 0.01 | 0.01 |

**Table 9.**Spatial relationship between landslide conditioning factors and landslides using frequency ratio.

Conditioning Factor | Zone | Landslide (%) | Non-Landslide (%) | FR |
---|---|---|---|---|

DTS(m) | <1000 | 46.99% | 0.95% | 49.30 |

1000–2000 | 24.43% | 0.14% | 173.29 | |

2000–3000 | 14.33% | 6.63% | 2.16 | |

3000–4000 | 5.33% | 15.72% | 0.34 | |

>4000 | 8.91% | 76.69% | 0.12 | |

DTR(m) | <1000 | 56.06% | 7.13% | 7.87 |

1000–2000 | 23.02% | 7.13% | 3.23 | |

2000–3000 | 15.59% | 9.29% | 1.68 | |

3000–4000 | 3.95% | 11.51% | 0.34 | |

>4000 | 1.37% | 66.79% | 0.02 | |

Elevation(m) | <200 | 4.36% | 2.08% | 2.09 |

200–400 | 53.76% | 12.29% | 4.37 | |

300–600 | 30.36% | 23.70% | 1.28 | |

400–800 | 10.06% | 34.52% | 0.29 | |

>800 | 1.46% | 27.41% | 0.05 |

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## Share and Cite

**MDPI and ACS Style**

Liang, Z.; Liu, W.; Peng, W.; Chen, L.; Wang, C.
Improved Shallow Landslide Susceptibility Prediction Based on Statistics and Ensemble Learning. *Sustainability* **2022**, *14*, 6110.
https://doi.org/10.3390/su14106110

**AMA Style**

Liang Z, Liu W, Peng W, Chen L, Wang C.
Improved Shallow Landslide Susceptibility Prediction Based on Statistics and Ensemble Learning. *Sustainability*. 2022; 14(10):6110.
https://doi.org/10.3390/su14106110

**Chicago/Turabian Style**

Liang, Zhu, Wei Liu, Weiping Peng, Lingwei Chen, and Changming Wang.
2022. "Improved Shallow Landslide Susceptibility Prediction Based on Statistics and Ensemble Learning" *Sustainability* 14, no. 10: 6110.
https://doi.org/10.3390/su14106110