# Comparison of Support Vector Machine, Bayesian Logistic Regression, and Alternating Decision Tree Algorithms for Shallow Landslide Susceptibility Mapping along a Mountainous Road in the West of Iran

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}and ranges in elevation from 1699 to 2500 m above sea level [19]. A road through the saddle, which connects Sanandaj City to Tehran, the capital of Iran, has strategic, economic, and socio-cultural importance. Much of Kurdistan province is located in the Zagros Mountains, a tectonically active range dominated by sedimentary and volcanic rocks [80].

## 3. Data Acquisition

#### 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. Distance to Road

#### 3.2.5. Topographic Wetness Index

#### 3.2.6. Normalized Difference Vegetation Index

#### 3.2.7. Lithology

#### 3.2.8. Land Cover/Land Use

#### 3.2.9. Rainfall

#### 3.2.10. Distance to Fault

#### 3.2.11. Plan Curvature

#### 3.2.12. Profile Curvature

#### 3.2.13. Slope Length-Angle Index (LS)

#### 3.2.14. Solar Radiation

#### 3.2.15. Stream Power Index (SPI)

#### 3.2.16. Distance to the River

#### 3.2.17. River Density

^{2}. Five categories were established based on the natural break classification method: 0–4, 4–8, 8–12, 12–16, and >16 km/km

^{2}(Figure 3q).

#### 3.2.18. Fault Density

## 4. Machine Learning Algorithms

#### 4.1. Support Vector Machine

_{i}, which includes linear training data i = (0, 2, 3, …, n), referred to as training vectors. The training vectors contain two classes denoted by y

_{i}= ±1. The support vector machine maximizes the two datasets by finding an n-dimensional hyperplane (Figure 4), expressed as follows,

#### 4.2. Bayesian Logistic Regression

- (1)
- Determine the prior probability of parameters
- (2)
- Determine the likelihood function for data
- (3)
- Create a posterior distribution function for parameters

_{i}are the effective factors, c is the prior log odds ratio ($\mathrm{c}=\mathrm{log}\frac{\mathrm{P}\left(\mathrm{class}=0\right)}{\mathrm{P}\left(\mathrm{class}=1\right)}$), and b is the bias. w

_{0}and w

_{i}are the weights trained by training data, and i

_{th}factors of xi are used to calculate the f(x

_{i}) function using $\mathrm{log}\frac{\mathrm{P}\left({\mathrm{x}}_{\mathrm{i}}|\mathrm{class}=0\right)}{\mathrm{P}\left({\mathrm{x}}_{\mathrm{i}}|\mathrm{class}=1\right)}$ (for binary variables). A prior univariate Gaussian function is used to calculate weights in Bayesian-logistic regression model,

_{i}’ are the data average, and variance, respectively [89].

#### 4.3. Alternating Decision Tree

- 1-
- Initialization

- 2-
- Pre-adjustment

- -
- Create a C group of rules by the weak algorithm using the weight-related to each training sample ${W}_{i,t}$.
- -
- For each main precondition ${c}_{1}\in {P}_{t}$ and each condition ${c}_{1}\in {P}_{t}$ calculate:$${Z}_{t}({c}_{1},{c}_{2})=2\left(\sqrt{W+({c}_{1}^{c}_{2})W-({c}_{1}^{c}_{2})}+\sqrt{W+({c}_{1}^{\stackrel{\u2322}{c}}_{2})W-({c}_{1}^{\stackrel{\u2322}{c}}_{2})}\right)+W({\stackrel{\u2322}{c}}_{1})$$
- -
- Select ${c}_{1},{c}_{2}$ with minima ${Z}_{t}({c}_{1},{c}_{2})$ and run ${R}_{t+1}$ and ${R}_{t}$ through the adding ${R}_{t}$ rule so that the precondition and condition are equal to, respectively, ${c}_{1}$ and ${c}_{2}$. Then predict the two prediction amounts:$$\alpha =\frac{1}{2}\mathrm{ln}\frac{{W}_{+}{(\mathrm{c}}_{1}{^\mathrm{c}}_{2})+\epsilon}{{W}_{-}{(\mathrm{c}}_{1}{^\mathrm{c}}_{2})+\epsilon}$$$$b=\frac{1}{2}\mathrm{ln}\frac{{W}_{+}{(\mathrm{c}}_{1}^{\stackrel{\u2322}{c}}_{2})+\epsilon}{{W}_{-}{(\mathrm{c}}_{1}^{\stackrel{\u2322}{c}}_{2})+\epsilon}$$
- -
- Establish ${P}_{t+1}$ and ${P}_{t}$ by adding ${c}_{1}^{c}_{2}$ and ${c}_{1}^{\stackrel{\u2322}{c}}_{2}$
- -
- Update the weights based on the following equation for each repeat:$${W}_{{}_{i,t+1}}={W}_{i,t{e}^{-{r}_{t}({x}_{i})yi}}$$

- 3-
- Output

#### 4.4. Multicollinearity Tests

^{2}) and variance inflation factor (VIF) (VIF = 1/TOL), have been used in the multicollinearity test [93,94]. If TOL > 0.1 and VIF < 10, there is a correlation among the factors and the factor with having such information should be removed from the modeling process [48,75].

#### 4.5. Selecting the Most Important Conditioning Factors by IGR

#### 4.6. Validation and Comparison of the Models

## 5. Results and Analysis

#### 5.1. Correlation between the Conditioning Factors

#### 5.2. The Most Important Landslide Conditioning Factors in the Study Area

#### 5.3. Landslide Modeling and Evaluation Process

#### 5.4. Development of Landslide Susceptibility Maps

#### 5.5. Evaluation of Landslide Susceptibility Maps

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The study area and its location in Kurdistan province (upper right) in northwest Iran (lower right).

**Figure 3.**Spatial database for landslide susceptibility analysis: (

**a**) slope, (

**b**) aspect, (

**c**) elevation, (

**d**) distance to road, (

**e**) TWI, (

**f**) NDVI, (

**g**) lithology, (

**h**) land cover, (

**i**) rainfall, (

**j**) distance to fault, (

**k**) plan curvature, (

**l**) profile curvature, (

**m**) LS, (

**n**) solar radiation, (

**o**) SPI, (

**p**) distance to river, (

**q**) river density, (

**r**) fault density.

**Figure 5.**Histograms used to prepare the landslide susceptibility maps for three classification methods (natural break, quantile, and geometrical interval): (

**a**) SVM, (

**b**) BLR, (

**c**) ADTree.

**Figure 6.**Landslide susceptibility maps generated by (

**a**) SVM with the quantile method, (

**b**) SVM with the natural break method, (

**c**) SVM classified with the geometrical interval method, (

**d**) BLR with the quantile method, (

**e**) BLR with the natural break method, (

**f**) BLR with the geometrical interval method, (

**g**) ADTree with the quantile method, (

**h**) ADTree with the natural break method, and (

**i**) ADTree with the geometrical interval method.

**Figure 7.**ROC curve and AUC for the SVM, BLR, and ADTree models: (

**a**) training and (

**b**) validation datasets.

Lithological Unit | Description | Age Era | Age Period | |
---|---|---|---|---|

1 | Kll1 | Gray and light gray, thick-bedded to massive, fetid orbitolina bearing limestone. | MESOZOIC | Early Cretaceous |

2 | Kll2 | Thick-bedded, gray to dark gray, rudist and orbitolina bearing limestone. | MESOZOIC | Early Cretaceous |

3 | Klv,12 | Basaltic and andesitic volcanics, tuff, volcanic breccia and calcareous shale with intercalations of limestone. | MESOZOIC | Early Cretaceous |

4 | K213 | Gray and light gray micritic limestone and radioarian limestone with calcschiste structure. | MESOZOIC | Late Cretaceous |

5 | K2v | Basalt, andesite, spilitic basalte and pyroclastic rocks with developed layering and climbing. | MESOZOIC | Late Cretaceous |

6 | Klv,13 | Spilitic basalt, basalt and andesite lava with intercalation of red, blue, gray limestone, red shale and sandstone. | MESOZOIC | Early Cretaceous |

7 | Klv,14 | Tuff, green tuff, andesite and andesitic dacite, shale, limestone and sandstone. | MESOZOIC | Early Cretaceous |

8 | Kls | Purpel to red medium to thick-bedded sandstone with intercalation of polymictic conglomerate and silty shale. | MESOZOIC | Early Cretaceous |

9 | K2sh | Black, dark gray, yellow shale, silty shale and phillitic shale with minor sandstone and micritic limestone intercalations. (Sanandaj shale) | MESOZOIC | Late Cretaceous |

10 | Qal | Recent alluvium (alluvial channel deposits). | CENOZOIC | Quaternary |

11 | Residential area | Salavat Saddle |

Factors | TOL | VIF |
---|---|---|

Slope angle | 0.520 | 1.587 |

Aspect | 0.322 | 2.184 |

Elevation | 0.212 | 1.135 |

Profile curvature | 0.825 | 2.381 |

Plan curvature | 0.705 | 1.843 |

Distance to road | 0.553 | 2.529 |

NDVI | 0.498 | 1.814 |

Land use | 0.340 | 2.321 |

Lithology | 0.263 | 1.311 |

LS | 0.541 | 1.849 |

Rainfall | 0.887 | 1.552 |

Solar radiation | 0.670 | 2.698 |

TWI | 0.776 | 1.541 |

SPI | 0.732 | 1.873 |

Distance to river | 0.820 | 2.987 |

River density | 0.922 | 1.784 |

Distance to fault | 0.712 | 2.835 |

Fault density | 0.825 | 2.781 |

**Table 3.**Ranks of significant landslide conditioning factors based on the IGR technique and the training dataset.

Conditioning Factor | Rank | AMIGR |
---|---|---|

Distance to road | 1 | 0.1434 |

NDVI | 2 | 0.0725 |

Land use | 3 | 0.0187 |

Aspect | 4 | 0.0139 |

Lithology | 5 | 0.0097 |

Slope angle | 6 | 0.0091 |

Rainfall | 7 | 0.0090 |

Distance to fault | 8 | 0.0087 |

Elevation | 9 | 0.0078 |

TWI | 10 | 0.0040 |

Parameter | SVM | BLR | ADTree |
---|---|---|---|

TP | 50 | 48 | 47 |

TN | 52 | 52 | 50 |

FP | 1 | 1 | 3 |

FN | 3 | 5 | 6 |

Sensitivity | 0.943 | 0.906 | 0.887 |

Specificity | 0.981 | 0.981 | 0.943 |

Accuracy | 0.962 | 0.943 | 0.915 |

Kappa | 0.924 | 0.886 | 0.846 |

RMSE | 0.192 | 0.237 | 0.245 |

AUC | 0.986 | 0.943 | 0.912 |

Parameter | SVM | BLR | ADTree |
---|---|---|---|

TP | 12 | 11 | 11 |

TN | 11 | 10 | 9 |

FP | 1 | 2 | 2 |

FN | 2 | 3 | 4 |

Sensitivity | 0.857 | 0.786 | 0.714 |

Specificity | 0.917 | 0.833 | 0.818 |

Accuracy | 0.885 | 0.808 | 0.760 |

Kappa | 0.869 | 0.846 | 0.751 |

RMSE | 0.251 | 0.277 | 0.343 |

AUC | 0.976 | 0.923 | 0.910 |

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**MDPI and ACS Style**

Nhu, V.-H.; Zandi, D.; Shahabi, H.; Chapi, K.; Shirzadi, A.; Al-Ansari, N.; Singh, S.K.; Dou, J.; Nguyen, H.
Comparison of Support Vector Machine, Bayesian Logistic Regression, and Alternating Decision Tree Algorithms for Shallow Landslide Susceptibility Mapping along a Mountainous Road in the West of Iran. *Appl. Sci.* **2020**, *10*, 5047.
https://doi.org/10.3390/app10155047

**AMA Style**

Nhu V-H, Zandi D, Shahabi H, Chapi K, Shirzadi A, Al-Ansari N, Singh SK, Dou J, Nguyen H.
Comparison of Support Vector Machine, Bayesian Logistic Regression, and Alternating Decision Tree Algorithms for Shallow Landslide Susceptibility Mapping along a Mountainous Road in the West of Iran. *Applied Sciences*. 2020; 10(15):5047.
https://doi.org/10.3390/app10155047

**Chicago/Turabian Style**

Nhu, Viet-Ha, Danesh Zandi, Himan Shahabi, Kamran Chapi, Ataollah Shirzadi, Nadhir Al-Ansari, Sushant K. Singh, Jie Dou, and Hoang Nguyen.
2020. "Comparison of Support Vector Machine, Bayesian Logistic Regression, and Alternating Decision Tree Algorithms for Shallow Landslide Susceptibility Mapping along a Mountainous Road in the West of Iran" *Applied Sciences* 10, no. 15: 5047.
https://doi.org/10.3390/app10155047