# Hybrid Computational Intelligence Methods for Landslide Susceptibility Mapping

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## Abstract

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## 1. Introduction

## 2. Study Area and Data

## 3. Modeling Approach

#### 3.1. Credal Decision Tree

#### 3.2. Radial Basis Function Network

_{i}represents the center of the i

_{th}hidden node, x is the input vector, w

_{ih}is the weight of the i

_{th}node of the hidden layer, w

_{0h}is the offset of the h node of the output layer, and ${\mathsf{\varphi}}_{\mathrm{i}}$ is the radial basis function centered on c

_{i}. In general, the Gaussian function is often used as a basis function in RBFN. The Gaussian function can be expressed as in Equation (5) [86]:

_{i}indicates the center vector of the i

_{th}hidden node of the RBFN.

#### 3.3. MultiBoosting

_{i}, y

_{i}), where x

_{i}∈ R, y

_{i}∈ (landslide, non-landslide), the final classifier can be obtained from the following equations [46]:

_{t}is the weighted error on the training dataset.

## 4. Results

#### 4.1. Optimization of the Dataset

#### 4.2. Model Performances and Validation

#### 4.3. Generation of Landslide Susceptibility Maps

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Landslide conditioning factors: (

**a**) altitude, (

**b**) profile curvature, (

**c**) plan curvature, (

**d**) slope aspect, (

**e**) slope angle, (

**f**) stream power index (SPI), (

**g**) topographic wetness index (TWI), (

**h**) sediment transport index (STI), (

**i**) distance to rivers, (

**j**) distance to roads, (

**k**) distance to faults, (

**l**) rainfall, (

**m**) normalized difference vegetation index (NDVI), (

**n**) soil, (

**o**) land use, and (

**p**) lithology.

**Figure 8.**Landslide susceptibility maps: (

**a**) credal decision tree (CDT) model; (

**b**) radial basis function network (RBFN) model; (

**c**) multiboosting-credal decision tree (MCDT) model; (

**d**) multiboosting- radial basis function network (MRBFN) model.

Conditioning Factors | Classes |
---|---|

Altitude (m) | 312–500; 500–700; 700–900; 900–1100; 1100–1300; 1300–1500; 1500–1700; 1700–1900; 1900–2228 |

Slope angle (°) | <10; 10–20; 20–30; 30–40; 40–50; 50–60; 60–70; >70 |

Slope aspect | F (−1); N (0–22.5; 337.5–360); NE (22.5–67.5); E (67.5–112.5); SE (112.5–157.5); S (157.5–202.5); SW (202.5–247.5); W (247.5–292.5); NW (292.5–337.5) |

Plan curvature | (−23.95)–(−0.05); (−0.05)–0.05; 0.05–19.49 |

Profile curvature | (−27.51)–(−0.05); (−0.05)–0.05; 0.05–21.58 |

SPI | 0–5; 5–10; 10–15; 15–20; >20 |

TWI | 0.24–1; 1–1.5; 1.5–2; 2–2.5; >2.5 |

STI | 0–5; 5–10; 10–15; 15–20; >20 |

NDVI | (−0.05)–0.2; 02–0.26; 0.26–0.32; 0.32–0.38; 0.38–0.56 |

Land use | Farmland; forestland; grassland; water; residential areas |

Rainfall (mm/yr) | 333.62–1221.86; 1221.86–1502.36; 1502.36–1954.28; 1954.28–2639.96; 2639.95–4307.36 |

Distance to roads (m) | 0–200; 200–400; 400–600; 600–800; >800 |

Distance to faults (m) | 0–1000; 1000–2000; 2000–3000; 3000–4000; >4000 |

Distance to rivers (m) | 0–200; 200–400; 400–600; 600–800; >800 |

Lithology | Type 1; Type 2; Type 3; Type 4; Type 5; Type 6; Type 7 |

Soil | Haplic Alisol; Cumulic Anthrosol; Dystric Cambisol; Rendzic Leptosol; Haplic Luvisol; Chromic Luvisol; Dystric Regosol |

Test Variables | CDT Model | RBFN Model | MCDT Model | MRBFN Model |
---|---|---|---|---|

ROC curve area | 0.86 | 0.75 | 0.9 | 0.76 |

Standard error | 0.018 | 0.024 | 0.015 | 0.024 |

95% confidence interval | 0.82 to 0.89 | 0.70 to 0.79 | 0.87 to 0.93 | 0.71 to 0.81 |

p-value | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

Test Variables | CDT Model | RBFN Model | MCDT Model | MRBFN Model |
---|---|---|---|---|

ROC curve area | 0.75 | 0.67 | 0.77 | 0.73 |

Standard error | 0.037 | 0.041 | 0.035 | 0.038 |

95% confidence interval | 0.68 to 0.82 | 0.60 to 0.75 | 0.71 to 0.84 | 0.65 to 0.80 |

p-value | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

Pair | CDT Model, RBFN Model | CDT Model, MCDT Model | CDT Model, MRBFN Model | RBFN Model, MCDT Model | RBFN Model, MRBFN Model | MCDT Model, MRBFN Model |
---|---|---|---|---|---|---|

Chi-square | 21.15 | 10.06 | 18.19 | 47.69 | 0.62 | 47.21 |

p-value | <0.0001 | 0.001512 | <0.0001 | <0.0001 | 0.431685 | <0.0001 |

© 2020 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**

Wang, G.; Lei, X.; Chen, W.; Shahabi, H.; Shirzadi, A.
Hybrid Computational Intelligence Methods for Landslide Susceptibility Mapping. *Symmetry* **2020**, *12*, 325.
https://doi.org/10.3390/sym12030325

**AMA Style**

Wang G, Lei X, Chen W, Shahabi H, Shirzadi A.
Hybrid Computational Intelligence Methods for Landslide Susceptibility Mapping. *Symmetry*. 2020; 12(3):325.
https://doi.org/10.3390/sym12030325

**Chicago/Turabian Style**

Wang, Guirong, Xinxiang Lei, Wei Chen, Himan Shahabi, and Ataollah Shirzadi.
2020. "Hybrid Computational Intelligence Methods for Landslide Susceptibility Mapping" *Symmetry* 12, no. 3: 325.
https://doi.org/10.3390/sym12030325