# Feature Importances: A Tool to Explain Radio Propagation and Reduce Model Complexity

^{*}

## Abstract

**:**

## 1. Introduction

- ○
- Insight into the model’s behavior is gained through the association between the changes in feature importances and the emergence of different radio propagation mechanisms.
- ○
- Simpler and faster models are deployed through a feature selection procedure based on the ranked importances.

## 2. Propagation Mechanisms According to the Transmitter’s Height

## 3. Problem Description and Model Used

#### 3.1. Features and the Associated Propagation Mechanisms

#### 3.2. Models Used: XGBoost and Random Forest

#### 3.3. Relative Feature Importances in Tree-Based Models

_{j}takes on a value less than s.

_{i}in the region R

_{1}(j,s) and ${\widehat{y}}_{{R}_{2}}$ is the mean response for the training observations x

_{i}in the region R

_{2}(j,s). The actual output for the ith input pattern is denoted y

_{i}.

#### 3.4. Metrics of the Prediction Error

_{i}(p) is the actual path loss value, y

_{i,mean}(p) is the mean actual path loss value and y

_{o}(p) is the predicted path loss value. N

_{test}is the number of test patterns, while p represents the input according to which the prediction is made.

## 4. Numerical Results

#### 4.1. Path Loss Predictions for Both Models and Transmitter Heights

^{2}values for both models and transmitter heights. Each model was constructed with 700 trees.

#### 4.2. Feature Importances When the Transmitter is at 30 m

#### 4.3. Feature Importances When the Transmitter is at 35 m

#### 4.4. Gradual Addition of Features with Reverse Order of Importance

#### 4.5. Model Reduction

## 5. Discussion

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The first 10 features [18].

**Figure 3.**Features 19 to 23 refer only to the positions of the transmitter and the receiver, and the distance between them. They do not depend on the built-up profile of the area in question. Table 1 summarizes and describes all features.

**Figure 4.**Feature importances, as estimated when the transmitter is placed at 30 m, via two machine learning models: (

**a**) XGBoost; (

**b**) Random Forest. The feature called Buildings is ranked as the most important.

**Figure 5.**Feature importances, as estimated when the transmitter is placed at 35 m, via two machine learning models: (

**a**) XGBoost; (

**b**) Random Forest. The feature called LOS_3b is ranked as the most important.

**Figure 6.**Gradual addition of features with reverse order of importance. The improvement is negligible as features of low importance are added.

**Figure 7.**The XGBoost model obtains the minimum MAE value with a smaller number of trees for an optimum input subset of 18 features (for the 30 m case).

Number | Name | Description |
---|---|---|

1 | LOS_1a | The distance (h_{1}) of the top of the tallest building of the first segment, from the point at which the building intersects the LOS ray, between Tr and R |

2 | LOS_1b | The distance d_{1} of the tallest building of the first segment from the transmitter |

3 | LOS_1c | The length, l_{1}, of the tallest building of the first segment |

4 | LOS_2a | The distance (h_{2}) of the top of the tallest building of the second segment, from the point at which the building intersects the LOS ray, between Tr and R |

5 | LOS_2b | The distance d_{2} of the tallest building of the second segment from the transmitter |

6 | LOS_2c | The length, l_{2}, of the tallest building of the second segment |

7 | LOS_3a | The distance (h_{3}) of the top of the tallest building of the third segment, from the point at which the building intersects the LOS ray, between Tr and R |

8 | LOS_3b | The distance d_{3} of the tallest building of the first segment from the transmitter |

9 | LOS_3c | The length, l_{3}, of the tallest building of the third segment |

10 | Buildings: | The total number of the buildings which interrupt the LOS path. |

11 | SSI_1 | The height of the building (or the existence of a street) 10m right from the receiver |

12 | SSI_2 | The height of the building (or the existence of a street) 10 m left from the receiver |

13 | SSI_3 | The height of the building (or the existence of a street) 10 m above the receiver |

14 | SSI_4 | The height of the building (or the existence of a street) 10 m below the receiver |

15 | SSI_5 | The height of the building (or the existence of a street) 10 m left and above the receiver |

16 | SSI_6 | The height of the building (or the existence of a street) 10 m left and below the receiver |

17 | SSI_7 | The height of the building (or the existence of a street) 10 m right and above the receiver |

18 | SSI_8 | The height of the building (or the existence of a street) 10 m right and below the receiver |

19 | Tr_x | X_coordinate of the transmitter |

20 | Tr_y | Y_coordinate of the transmitter |

21 | R_x | X_coordinate of the receiver |

22 | R_y | Y_coordinate of the receiver |

23 | Distance | The distance between transmitter and receiver in the xy plane |

Transmitter Height (m) | XGBoost | Random Forest | ||
---|---|---|---|---|

MAE (dB) | R^{2} | MAE (dB) | R^{2} | |

30 | 3.54 | 0.89 | 3.97 | 0.87 |

35 | 3.17 | 0.91 | 3.35 | 0.90 |

**Table 3.**Time comparison of XGBoost models with the same MAE, for the 30 m case. (Data in bold font indicates the smaller values.)

Model No | MAE (dB) | Trees | Features | Training Time (s) | Response Time (ms) |
---|---|---|---|---|---|

1 | 3.54 | 700 | 23 | 68.34 | 382.51 |

2 | 3.54 | 700 | 18 | 58.46 | 354.79 |

3 | 3.54 | 300 | 18 | 32.02 | 147.88 |

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**MDPI and ACS Style**

Sotiroudis, S.P.; Goudos, S.K.; Siakavara, K.
Feature Importances: A Tool to Explain Radio Propagation and Reduce Model Complexity. *Telecom* **2020**, *1*, 114-125.
https://doi.org/10.3390/telecom1020009

**AMA Style**

Sotiroudis SP, Goudos SK, Siakavara K.
Feature Importances: A Tool to Explain Radio Propagation and Reduce Model Complexity. *Telecom*. 2020; 1(2):114-125.
https://doi.org/10.3390/telecom1020009

**Chicago/Turabian Style**

Sotiroudis, Sotirios P., Sotirios K. Goudos, and Katherine Siakavara.
2020. "Feature Importances: A Tool to Explain Radio Propagation and Reduce Model Complexity" *Telecom* 1, no. 2: 114-125.
https://doi.org/10.3390/telecom1020009