# Performance Evaluation of Machine Learning Methods for Forest Fire Modeling and Prediction

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## Abstract

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## 1. Introduction

_{2}capture [5]. The susceptibility of the forests and their adjacent areas, i.e., human settlements and infrastructures, to fires is a major concern to the communities in many land ecosystems of the world [6,7,8,9,10,11,12]. Increased changes in socioeconomic processes and climate that induced extensive modification of natural environment [13,14] and prolonged drought periods [15,16,17,18,19] have placed strong demands on authorities and decision makers to temporally and spatially delineate the forested areas in terms of susceptibility to fires [6,11,20]. Identifying areas with high/very high fire susceptibility must be undertaken to successfully design fire management plans [21] and allocate firefighting resources [22,23,24,25,26]. To this end, robust approaches and tools are required to enable the managers and engineers to accurately estimate the time, location, and extent of future fires [8,10,12,27,28,29]. The improvements in techniques for predicting fire susceptibility and delineating the forested areas into different susceptibility levels can help forest managers and policy makers to achieve a better understanding of fires that facilitates the development of prevention measures for the fire-prone forests [4,30].

## 2. Study Area

## 3. Data Preparation

#### 3.1. Fire Inventory Map

#### 3.2. Explanatory Variables

## 4. Methods

#### 4.1. Relief-F Feature Selection Method

#### 4.2. Bayes Network (BN)

#### 4.3. Naïve Bayes (NB)

_{1}, x

_{2,}…x

_{n)}is a vector of n properties that are independent explanatory variables. Thus, the probability of fire occurrence (p(C

_{k}|x

_{1},…,x

_{n})) is represented as one of the states of the class of different events for different Ks:

#### 4.4. Decision Tree (DT)

#### 4.5. Multivariate Logistic Regression (MLR)

_{0}+ b

_{1 × 1}+ b

_{2 × 2}+ … + b

_{n × n}

_{0}is the intercept of the equation, bi (i = 0, 1, 2, …, n) are the model coefficients, and xi (i = 0, 1, 2, …, n) are the fire explanatory variables.

#### 4.6. Validation Metrics

#### 4.6.1. Receiver Operating Characteristics (ROC)

#### 4.6.2. Statistical Metrics

_{obs}is the observations (i.e., validation dataset), and X

_{est}is the estimated values by the forest fire predictive models.

## 5. Modeling Methodology

## 6. Results and Discussions

#### 6.1. Variable Importance

#### 6.2. Model Validation and Comparison

_{training}= 89.74% and PPV

_{validation}= 100% performed the best. In terms of the NPV metric that is the proportion of samples that were correctly classified as non-fire, the DT and MLR models with the values equal to 100% were identified as the best models. Regarding the SST metric that measured the models’ abilities to predict a proportion of all fire samples as fire (i.e., true positives), the DT and MLR models with the values equal to 100% were dominant over the other models. In terms of the SPF metric that measured the models’ abilities to predict a proportion of all non-fire samples as non-fire (i.e., true negatives), the BN model with PPVtraining = 89.47% and PPVvalidation = 100% was the best model. In terms of the ACC metric that measured the overall models’ efficiencies, the MLR (ACC = 92.31%) and BN (ACC = 94.12%) were the most efficient models in the training phase and validation phase, respectively. Regarding the Kappa index, the MLR (Kappa = 0.846) and BN (Kappa = 0.884) showed perfect agreement between observed fires and predicted fires in the training phase and validation phase, respectively. These variant training and validation performances that have been also previously observed in different models used for different applications [24,67,68,69,71,77,78,83,92] can be attributed to the specific nature and structure the models applied to different datasets. These results underscore the conclusion drawn by Bui, Khosravi, Tiefenbacher, Nguyen and Kazakis [84] that no model exists that always performs the best for all datasets from different sources.

#### 6.3. Robustness Analysis

#### 6.4. Forest Fire Susceptibility Maps

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Receiver operating characteristics (ROC) curves and area under the receiver operating characteristic curve (AUC) values of the models in the (

**a**) training and (

**b**) validation datasets.

**Figure 7.**Quantitative analysis of the fire susceptibility maps: (

**a**) Percentage of class pixels; (

**b**) Percentage of fire pixels; (

**c**) Frequency ratio analysis.

Variable | Source | Scale | Access Date |
---|---|---|---|

Slope degree | USGS DEM | 30 × 30 m | 2015 |

Elevation (m) | USGS DEM | 30 × 30 m | 2015 |

Aspect | USGS DEM | 30 × 30 m | 2015 |

River density | USGS DEM | 30 × 30 m | 2015 |

Land cover | Landsat ETM+ | 30 × 30 m | 2016 |

Annual temperature (°C) | VMO | - | 2016 |

Drought index | NDVI and LST | 30 × 30 m | 2016 |

Distance from roads (m) | NCGFV and GEI | 1:100,000 | 2015 |

Distance from residential areas (m) | NCGFV and GEI | 1:100,000 | 2015 |

Rank | Variable | AM |
---|---|---|

1 | Distance from roads | 85.9 |

2 | Distance from residential areas | 83.4 |

3 | Land cover | 79.5 |

4 | Elevation | 74.4 |

5 | Annual temperature | 71.8 |

6 | Aspect | 56.5 |

7 | River density | 55.1 |

8 | Slope degree | 53.8 |

9 | Drought index | 48.7 |

Metric | Training Dataset | Validation Dataset | ||||||
---|---|---|---|---|---|---|---|---|

BN | DT | MLR | NB | BN | DT | MLR | NB | |

PPV (%) | 89.74 | 82.05 | 84.62 | 87.18 | 100.00 | 64.71 | 76.47 | 94.12 |

NPV (%) | 87.18 | 100.00 | 100.00 | 87.18 | 88.24 | 100.00 | 100.00 | 94.12 |

SST (%) | 87.50 | 100.00 | 100.00 | 87.18 | 89.47 | 100.00 | 100.00 | 94.12 |

SPF (%) | 89.47 | 84.78 | 86.67 | 87.18 | 100.00 | 73.91 | 80.95 | 94.12 |

ACC (%) | 88.46 | 91.03 | 92.31 | 87.18 | 94.12 | 82.35 | 88.24 | 94.12 |

Kappa | 0.769 | 0.821 | 0.846 | 0.744 | 0.884 | 0.647 | 0.765 | 0.882 |

Model | Phase | Metric | Fold | Mean | SD | ||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | |||||

BN | Training | ACC | 88.46 | 87.18 | 87.18 | 87.18 | 87.18 | 87.44 | 0.57 |

RMSE | 0.279 | 0.287 | 0.285 | 0.299 | 0.301 | 0.29 | 0.01 | ||

AUC | 0.99 | 0.984 | 0.98 | 0.98 | 0.98 | 0.98 | 0.00 | ||

Validation | ACC | 100 | 99.88 | 99.88 | 99.88 | 99.85 | 99.90 | 0.06 | |

RMSE | 0.192 | 0.31 | 0.291 | 0.296 | 0.286 | 0.28 | 0.05 | ||

AUC | 0.96 | 0.954 | 0.965 | 0.941 | 0.956 | 0.96 | 0.01 | ||

DT | Training | ACC | 91.03 | 89.99 | 90.87 | 89.62 | 89.9 | 90.28 | 0.63 |

RMSE | 0.272 | 0.306 | 0.267 | 0.325 | 0.321 | 0.30 | 0.03 | ||

AUC | 0.969 | 0.953 | 0.958 | 0.947 | 0.949 | 0.96 | 0.01 | ||

Validation | ACC | 94.12 | 94.12 | 93.18 | 93.01 | 93.18 | 93.52 | 0.55 | |

RMSE | 0.306 | 0.307 | 0.296 | 0.302 | 0.298 | 0.30 | 0.00 | ||

AUC | 0.94 | 0.94 | 0.94 | 0.934 | 0.94 | 0.94 | 0.00 | ||

MLR | Training | ACC | 92.31 | 91.9 | 92.9 | 89.9 | 89.18 | 91.24 | 1.61 |

RMSE | 0.255 | 0.35 | 0.344 | 0.352 | 0.34 | 0.33 | 0.04 | ||

AUC | 0.986 | 0.96 | 0.97 | 0.974 | 0.959 | 0.97 | 0.01 | ||

Validation | ACC | 88.24 | 87.06 | 90.18 | 88.14 | 88.14 | 88.35 | 1.13 | |

RMSE | 0.274 | 0.203 | 0.295 | 0.306 | 0.299 | 0.28 | 0.04 | ||

AUC | 0.937 | 0.935 | 0.93 | 0.933 | 0.938 | 0.93 | 0.00 | ||

NB | Training | ACC | 87.18 | 87.18 | 87.18 | 87.18 | 87.18 | 87.18 | 0.00 |

RMSE | 0.339 | 0.339 | 0.335 | 0.351 | 0.347 | 0.34 | 0.01 | ||

AUC | 0.983 | 0.983 | 0.979 | 0.979 | 0.979 | 0.98 | 0.00 | ||

Validation | ACC | 94.12 | 93.18 | 93.24 | 93.18 | 93.18 | 93.38 | 0.41 | |

RMSE | 0.274 | 0.299 | 0.315 | 0.297 | 0.256 | 0.29 | 0.02 | ||

AUC | 0.939 | 0.937 | 0.932 | 0.933 | 0.932 | 0.93 | 0.00 |

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## Share and Cite

**MDPI and ACS Style**

Pham, B.T.; Jaafari, A.; Avand, M.; Al-Ansari, N.; Dinh Du, T.; Yen, H.P.H.; Phong, T.V.; Nguyen, D.H.; Le, H.V.; Mafi-Gholami, D.;
et al. Performance Evaluation of Machine Learning Methods for Forest Fire Modeling and Prediction. *Symmetry* **2020**, *12*, 1022.
https://doi.org/10.3390/sym12061022

**AMA Style**

Pham BT, Jaafari A, Avand M, Al-Ansari N, Dinh Du T, Yen HPH, Phong TV, Nguyen DH, Le HV, Mafi-Gholami D,
et al. Performance Evaluation of Machine Learning Methods for Forest Fire Modeling and Prediction. *Symmetry*. 2020; 12(6):1022.
https://doi.org/10.3390/sym12061022

**Chicago/Turabian Style**

Pham, Binh Thai, Abolfazl Jaafari, Mohammadtaghi Avand, Nadhir Al-Ansari, Tran Dinh Du, Hoang Phan Hai Yen, Tran Van Phong, Duy Huu Nguyen, Hiep Van Le, Davood Mafi-Gholami,
and et al. 2020. "Performance Evaluation of Machine Learning Methods for Forest Fire Modeling and Prediction" *Symmetry* 12, no. 6: 1022.
https://doi.org/10.3390/sym12061022