# Shallow Landslide Susceptibility Mapping: A Comparison between Logistic Model Tree, Logistic Regression, Naïve Bayes Tree, Artificial Neural Network, and Support Vector Machine Algorithms

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## Abstract

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## 1. Introduction

## 2. Description of the Study Area

^{2}; 35°48′25″ N to 35°09′50″ N and 47°28′50″ E to 47°46′44″ E) is located around Bijar City in the eastern part of the Kurdistan Province in Iran (Figure 1). The regional climate is cool, with annual average temperatures ranging from 4.4 °C to 13.4 °C. Mean annual rainfall recorded between 1987 and 2010 at Bijar City was about 338 mm. Although annual precipitation is low, short-duration storms can produce large amounts of rain. Intensities of about 34 mm/h have a return period of about 20 years. The area is hilly, with elevations ranging from 250 to 1573 m asl (above sea level) and slopes up to 60°. There are four types of land cover in the Bijar region: (1) barren lands (0.07%), (2) cultivated lands (53.62%), (3) residential areas (1.26%), and (4) grasslands (45.05%). Geologically, 94% of the area is underlain by conglomerate, siltstone, shale, and marl, and 6% is underlain by volcanic rocks [17,65,69].

## 3. Data Preparation

#### 3.1. Landslide Inventory Map

#### 3.2. Landslide Conditioning Factors

#### 3.2.1. Slope Angle

#### 3.2.2. Slope Aspect

#### 3.2.3. Elevation

#### 3.2.4. Curvature

#### 3.2.5. Plan Curvature

#### 3.2.6. Profile Curvature

#### 3.2.7. Slope Length

#### 3.2.8. Rainfall

#### 3.2.9. Annual Solar Radiation

#### 3.2.10. Stream Power Index

#### 3.2.11. Topographic Wetness Index

#### 3.2.12. Distance to Rivers

#### 3.2.13. River Density

^{2}(Figure 2m).

#### 3.2.14. Lithology

#### 3.2.15. Distance to Faults

#### 3.2.16. Fault Density

^{2}(Figure 2p).

#### 3.2.17. Land Use

#### 3.2.18. NDVI

#### 3.2.19. Distance to Roads

#### 3.2.20. Road Density

^{2}(Figure 2t).

## 4. Methods

#### 4.1. Naïve Bayes Tree

#### 4.2. Logistic Regression

#### 4.3. Logistic Model Tree

#### 4.4. Support Vector Machine

#### 4.5. Artificial Neutral Network

_{1}, u

_{2}, …, u

_{n}denote n input neurons, and v = v

_{1}, v

_{2}denote output neurons. For the classification, the activation function used in hidden neurons is computed as:

#### 4.6. Model Comparison and Validation

#### 4.6.1. Statistical Metrics

#### 4.6.2. ROC Curve and AUC Metric

#### 4.6.3. Friedman and Wilcoxon Sign Rank Statistical Tests

#### 4.7. Factor Selection Using One-R Attribute Evaluation Technique

#### 4.8. Summary of the Methodology Used in This Study

## 5. Results and Analysis

#### 5.1. Most Important Landslide Conditioning Factors

#### 5.2. Model Performance and Analysis

#### 5.3. Development of Landslide Susceptibility Maps

#### 5.4. Model Comparison and Validation

#### 5.4.1. ROC Curve

#### 5.4.2. Wilcoxon Sign Rank Test

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Location of shallow landslides in the study area. The blue circles denote landslides for training the algorithms, and the red circles denote landslides for validating the algorithms.

**Figure 2.**Landslide conditioning factors used in this study: (

**a**) slope, (

**b**) aspect, (

**c**) elevation, (

**d**) curvature, (

**e**) plan curvature, (

**f**) profile curvature, (

**g**) slope length (SL), (

**h**) rainfall, (

**i**) annual solar radiation (

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

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

**l**) distance to rivers, (

**m**) river density, (

**n**) lithology, (

**o**) distance to fault, (

**p**) fault density, (

**q**) land use, (

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

**s**) distance to road, (

**t**) road density.

**Figure 6.**Average merit of shallow landslide factors calculated by the One Rule Attribute Evaluation (ORAE) method.

**Figure 7.**Landslide susceptibility maps: (

**a**) Logistic Model Tree (LMT), (

**b**) Logistic Regression (LR), (

**c**) Naïve Bayes Tree (NBT), (

**d**) ANN, and (

**e**) SVM.

**Figure 8.**Receiver operating characteristic (ROC) curves and area under the receiver operatic characteristic curve (AUC) for the (

**a**) training dataset and (

**b**) validation dataset.

**Table 1.**Model performances of the applied data-mining approaches for the training and validation datasets.

Parameters | LMT | NBT | LR | ANN | SVM | |||||
---|---|---|---|---|---|---|---|---|---|---|

T * | V * | T | V | T | V | T | V | T | V | |

True positive | 78 | 19 | 77 | 18 | 80 | 19 | 76 | 16 | 77 | 18 |

True negative | 81 | 19 | 83 | 20 | 81 | 19 | 73 | 17 | 83 | 20 |

False positive | 11 | 3 | 12 | 4 | 9 | 3 | 13 | 6 | 12 | 4 |

False negative | 8 | 3 | 6 | 2 | 8 | 3 | 16 | 5 | 6 | 2 |

Sensitivity (%) | 0.907 | 0.864 | 0.928 | 0.900 | 0.909 | 0.864 | 0.826 | 0.762 | 0.928 | 0.900 |

Specificity (%) | 0.880 | 0.864 | 0.874 | 0.833 | 0.900 | 0.864 | 0.849 | 0.739 | 0.874 | 0.833 |

Accuracy (%) | 0.893 | 0.864 | 0.899 | 0.864 | 0.904 | 0.864 | 0.837 | 0.750 | 0.899 | 0.864 |

MAE | 0.207 | 0.216 | 0.225 | 0.225 | 0.213 | 0.216 | 0.241 | 0.235 | 0.223 | 0.246 |

RMSE | 0.304 | 0.313 | 0.319 | 0.341 | 0.311 | 0.314 | 0.349 | 0.358 | 0.318 | 0.369 |

AUC | 0.944 | 0.936 | 0.918 | 0.874 | 0.939 | 0.936 | 0.911 | 0.871 | 0.899 | 0.864 |

**Table 2.**Performance of the five landslide machine learning models using Wilcoxon signed-rank test (two-tailed).

No. | Landslide Model | Mean Rank | χ2 | p-Value |
---|---|---|---|---|

1 | LMT | 2.80 | 557.912 | 0.000 |

2 | LR | 2.93 | ||

3 | NBT | 2.88 | ||

4 | ANN | 3.07 | ||

5 | SVM | 2.32 |

**Table 3.**Performance of the five landslide machine learning models using the Wilcoxon signed-rank test (two-tailed).

No. | Pairwise Comparison | Number of Positive Differences | Number of Negative Differences | z-Value | p-Value | Significance |
---|---|---|---|---|---|---|

1 | LMT vs. LR | 60 | 50 | −1.536 | 0.125 | No |

2 | LMT vs. NBT | 83 | 27 | −5.590 | 0.000 | Yes |

3 | LMT vs. ANN | 62 | 46 | −0.878 | 0.080 | Yes |

4 | LMT vs. SVM | 36 | 74 | −3.677 | 0.000 | Yes |

5 | LR vs. NBT | 82 | 29 | −5.589 | 0.000 | Yes |

6 | LR vs. ANN | 61 | 49 | −0.605 | 0.015 | Yes |

7 | LR vs. SVM | 35 | 75 | −4.081 | 0.000 | Yes |

8 | NBT vs. ANN | 36 | 73 | −3.958 | 0.000 | Yes |

9 | NBT vs. SVM | 30 | 80 | −5.711 | 0.000 | Yes |

10 | ANN vs. SVM | 43 | 67 | −3.140 | 0.002 | Yes |

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Nhu, V.-H.; Shirzadi, A.; Shahabi, H.; Singh, S.K.; Al-Ansari, N.; Clague, J.J.; Jaafari, A.; Chen, W.; Miraki, S.; Dou, J.;
et al. Shallow Landslide Susceptibility Mapping: A Comparison between Logistic Model Tree, Logistic Regression, Naïve Bayes Tree, Artificial Neural Network, and Support Vector Machine Algorithms. *Int. J. Environ. Res. Public Health* **2020**, *17*, 2749.
https://doi.org/10.3390/ijerph17082749

**AMA Style**

Nhu V-H, Shirzadi A, Shahabi H, Singh SK, Al-Ansari N, Clague JJ, Jaafari A, Chen W, Miraki S, Dou J,
et al. Shallow Landslide Susceptibility Mapping: A Comparison between Logistic Model Tree, Logistic Regression, Naïve Bayes Tree, Artificial Neural Network, and Support Vector Machine Algorithms. *International Journal of Environmental Research and Public Health*. 2020; 17(8):2749.
https://doi.org/10.3390/ijerph17082749

**Chicago/Turabian Style**

Nhu, Viet-Ha, Ataollah Shirzadi, Himan Shahabi, Sushant K. Singh, Nadhir Al-Ansari, John J. Clague, Abolfazl Jaafari, Wei Chen, Shaghayegh Miraki, Jie Dou,
and et al. 2020. "Shallow Landslide Susceptibility Mapping: A Comparison between Logistic Model Tree, Logistic Regression, Naïve Bayes Tree, Artificial Neural Network, and Support Vector Machine Algorithms" *International Journal of Environmental Research and Public Health* 17, no. 8: 2749.
https://doi.org/10.3390/ijerph17082749