# Evaluating the Efficiency of Different Regression, Decision Tree, and Bayesian Machine Learning Algorithms in Spatial Piping Erosion Susceptibility Using ALOS/PALSAR Data

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of the Study Area

^{2}, with an average elevation of 1974 m and an average slope of 3.2%. According to the climatic classification of the Zarandieh watershed, it is located in the arid and cold arid climates of the desert, with an average rainfall of 343 mm, with the highest rainfall occurring in winter. Land uses in the area include agricultural, bare land, rangeland, and residential land; most of the study area is rangeland. Most of the piping affected land is located in the eastern and center regions of the watershed, which are mainly agricultural and bare land. The soil of the Zarandieh watershed is deep, saline, and alkaline and, at the surface, saline. The most important limitations in this area are soil texture, salinity, alkalinity, and lack of drainage. The soils are generally deep and sometimes semi-shallow to calcareous and calcareous and articular (Administration of Natural Resources, Markazi Province https://markazi.frw.ir/00/Fa/default.aspx). The soils of the Zarandieh watershed are prone to erosion due to climatic conditions and the presence of highly saline soils, especially piping erosion due to the low slope of the region, and this erosion is one of the main problems in the region. Examples of piping erosion in the study area are shown in Figure 2.

#### 2.2. Methods

#### 2.3. Dataset Preparation for Spatial Modeling

#### 2.4. Multi-Collinearity Analysis

^{2}J

^{2}J represents the regression coefficient of determination of explanatory variable J on all the other explanatory variables.

#### 2.5. Machine Learning Method Used in Modeling the Piping Erosion

#### 2.5.1. Random Forest (RF)

#### 2.5.2. Support Vector Machine (SVM)

#### 2.5.3. Bayesian Generalized Linear Models (Bayesian GLM)

#### 2.6. Methods of Validation and Accuracy Assessment

## 3. Results

#### 3.1. Multi-Collinearity Analysis

#### 3.2. Piping Erosion Susceptibility Modeling

#### 3.3. Validation of the Models

## 4. Discussion

#### 4.1. Comparison of the Models

#### 4.2. Variable Importance Analysis

#### 4.3. Implications and Soil Erosion Control

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Methodological flow chart: topographic position index (TWI), cation exchange capacity (CEC), stream power index (SPI), precision predictive value (PPV), negative predictive value (NPV), receiver operating characteristic (ROC)

**Figure 4.**Piping erosion conditioning factors: (

**a**) aspect, (

**b**) land use, (

**c**) lithology, (

**d**) altitude, (

**e**) rainfall, (

**f**) TWI, (

**g**) profile curvature, (

**h**) distance from river, (

**i**) drainage density, (

**j**) clay content, (

**k**) CEC, (

**l**) sand content, (

**m**) pH, (

**n**) bulk density, (

**o**) silt content, (

**p**) SPI, (

**q**) plan curvature.

Parameters | Equations | Kernel Function |
---|---|---|

- | $K\left({x}_{i},{x}_{j}\right)={x}_{i}\xb7{x}_{j}$ | Linear kernel |

$\gamma $ and $d$ | $K\left({x}_{i},{x}_{j}\right)={\left(\gamma {x}_{i}\xb7{x}_{j}+r\right)}^{d}$ | Polynomial kernel |

$\gamma $ | $K\left({x}_{i},{x}_{j}\right)=\mathrm{exp}\left(-\gamma {\parallel {x}_{i}-{x}_{j}\parallel}^{2}\right)$ | Radial basis function kernel |

Row | Variables | VIF |
---|---|---|

1 | Aspect | 1.13 |

2 | Altitude | 2.52 |

3 | Plan | 1.73 |

4 | Profile | 1.62 |

5 | Distance from river | 1.28 |

6 | Slope | 1.79 |

7 | TWI | 1.40 |

8 | Lithology | 1.49 |

9 | Land use | 1.41 |

10 | Rainfall | 3.62 |

11 | TPI | 1.51 |

12 | Silt | 2.58 |

13 | Sand | 1.89 |

14 | Clay | 3.93 |

15 | CEC | 1.88 |

16 | Bulk density | 2.96 |

17 | pH | 2.57 |

Susceptibility Class | GLM Bayesian | SVM | RF | |||
---|---|---|---|---|---|---|

Area (Km^{2}) | Area (%) | Area (Km^{2}) | Area (%) | Area (Km^{2}) | Area (%) | |

Very Low | 196.67 | 5.48 | 904.50 | 25.18 | 1542.10 | 42.93 |

Low | 510.74 | 14.22 | 1055.98 | 29.40 | 680.66 | 18.95 |

Moderate | 876.75 | 24.41 | 694.27 | 19.33 | 537.86 | 14.97 |

High | 1196.65 | 33.32 | 523.98 | 14.59 | 428.56 | 11.93 |

Very High | 811.04 | 22.58 | 413.11 | 11.50 | 402.64 | 11.21 |

Models | SVM | RF | GLM Bayesian | |||
---|---|---|---|---|---|---|

Evaluation Parameter | Test | Train | Test | Train | Test | Train |

Sensitivity | 0.918 | 0.891 | 0.89 | 0.95 | 0.91 | 0.80 |

Specificity | 0.702 | 0.893 | 0.74 | 0.97 | 0.70 | 0.89 |

NPV | 0.891 | 0.893 | 0.87 | 0.95 | 0.89 | 0.82 |

PPV | 0.762 | 0.891 | 0.78 | 0.97 | 0.76 | 0.88 |

AUC | 0.88 | 0.96 | 0.90 | 0.98 | 0.87 | 0.93 |

Variables | Importance |
---|---|

Aspect | 1.59 |

Altitude | 9.29 |

Plan curvature | 0.51 |

Profile curvature | 0.84 |

Distance from river | 4.47 |

Slope | 1.76 |

TWI | 2.76 |

Lithology | 0.78 |

Land use | 1.29 |

Rain | 0.18 |

TPI | 1.00 |

Silt | 1.46 |

Sand | 1.65 |

Clay | 0.90 |

CEC | 3.99 |

Bulk density | 6.81 |

pH | 8.80 |

© 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**

Band, S.S.; Janizadeh, S.; Saha, S.; Mukherjee, K.; Bozchaloei, S.K.; Cerdà, A.; Shokri, M.; Mosavi, A.
Evaluating the Efficiency of Different Regression, Decision Tree, and Bayesian Machine Learning Algorithms in Spatial Piping Erosion Susceptibility Using ALOS/PALSAR Data. *Land* **2020**, *9*, 346.
https://doi.org/10.3390/land9100346

**AMA Style**

Band SS, Janizadeh S, Saha S, Mukherjee K, Bozchaloei SK, Cerdà A, Shokri M, Mosavi A.
Evaluating the Efficiency of Different Regression, Decision Tree, and Bayesian Machine Learning Algorithms in Spatial Piping Erosion Susceptibility Using ALOS/PALSAR Data. *Land*. 2020; 9(10):346.
https://doi.org/10.3390/land9100346

**Chicago/Turabian Style**

Band, Shahab S., Saeid Janizadeh, Sunil Saha, Kaustuv Mukherjee, Saeid Khosrobeigi Bozchaloei, Artemi Cerdà, Manouchehr Shokri, and Amirhosein Mosavi.
2020. "Evaluating the Efficiency of Different Regression, Decision Tree, and Bayesian Machine Learning Algorithms in Spatial Piping Erosion Susceptibility Using ALOS/PALSAR Data" *Land* 9, no. 10: 346.
https://doi.org/10.3390/land9100346