# A REM Update Methodology Based on Clustering and Random Forest

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## Abstract

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## 1. Introduction

#### 1.1. Related Work

#### 1.2. Main Contributions

- We propose an efficient methodology to update a REM based on clustering and RF in a timely manner. In the proposed scheme, the K-means algorithm is applied to divide the area of interest in K clusters, where one RF model is deployed per cluster. The REM is constructed to cover every point within the area of interest, where the prediction of the RSSI values for each location is obtained by the corresponding RF model in each cluster.
- The RSSI measurements were collected by a mobile robot, which can reduce the risk of human error because the robot can be programmed to move in a controlled manner. This can help ensure that RSSI measurements are taken at consistent intervals and under consistent conditions, while improving the accuracy and reliability of the measurements. Moreover, mobile robots can operate autonomously, which can save time and resources compared to manual data collection methods.
- In the REM construction, to avoid abrupt changes in the border areas between the clusters, we propose a methodology that utilizes the weighted average of the RF model predictions from the two nearest centroids to determine the RSSI value of the points within the border areas. Moreover, when new measurements are available, only the RF models for clusters that have enough measurement samples are updated.
- We extensively evaluate the proposed scheme for different scenarios, including the presence of obstacles and relocating the AP, and we consider several comparative ML methods, including the case without clusters. Moreover, the computational complexity of the proposed scheme is analyzed along with the comparative schemes. The simulation results demonstrated the superior performance of the proposed scheme compared to the baseline methods in effectively adapting to changes in the wireless environment. Moreover, the proposed approach requires only newly collected data in specific sectors to update a large area of interest.

## 2. Measurement Methodology

## 3. Proposed Approach for REM Updates

#### 3.1. Overview

#### 3.2. Random Forest

#### 3.3. REM Construction

## 4. Evaluation

#### 4.1. Historical Dataset and Comparative Models

#### 4.2. REM Update Evaluation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**REM for the initial measurements by considering four clusters. (

**a**) RF; (

**b**) SVR; (

**c**) AdaBoost.

**Figure 6.**The three areas considered for newly collected measurements. (

**a**) Data collected at time ${\mathbf{t}}_{1}$; (

**b**) Data collected at time ${\mathbf{t}}_{2}$; (

**c**) Data collected at time ${\mathbf{t}}_{3}$.

**Figure 7.**The proposed REM update mechanism considering four clusters. (

**a**) The REM at time ${\mathbf{t}}_{1}$; (

**b**) The REM at time ${\mathbf{t}}_{2}$; (

**c**) The REM at time ${\mathbf{t}}_{3}$.

**Figure 8.**The baseline REM update mechanism without clustering. (

**a**) The REM at time ${\mathbf{t}}_{1}$; (

**b**) The REM at time ${\mathbf{t}}_{2}$; (

**c**) The REM at time ${\mathbf{t}}_{3}$.

**Figure 10.**The three areas considered for newly collected measurements after the relocation of the AP. (

**a**) Data collected at time ${\mathbf{t}}_{1}$; (

**b**) Data collected at time ${\mathbf{t}}_{2}$; (

**c**) Data collected at time ${\mathbf{t}}_{3}$.

**Figure 11.**REMs obtained with the proposed update mechanism after the relocation of the AP. (

**a**) The REM at time ${\mathbf{t}}_{1}$; (

**b**) The REM at time ${\mathbf{t}}_{2}$; (

**c**) The REM at time ${\mathbf{t}}_{3}$.

MAPE | ||||
---|---|---|---|---|

Model for Prediction | 4 Clusters | 3 Clusters | 2 Clusters | 1 Cluster |

RF | 1.511% | 1.513% | 1.507% | 1.515% |

SVR | 3.565% | 3.718% | 3.828% | 4.504% |

MLP | 4.325% | 4.174% | 4.254% | 4.835% |

AdaBoost | 3.001% | 3.178% | 3.603% | 4.064% |

RMSE | ||||

Model for Prediction | 4 Clusters | 3 Clusters | 2 Clusters | 1 Cluster |

RF | 1.295 | 1.290 | 1.290 | 1.285 |

SVR | 2.418 | 2.486 | 2.537 | 2.793 |

MLP | 2.648 | 2.556 | 2.602 | 2.977 |

AdaBoost | 1.810 | 1.912 | 2.150 | 2.409 |

R2 Score | ||||

Model for Prediction | 4 Clusters | 3 Clusters | 2 Clusters | 1 Cluster |

RF | 0.948 | 0.949 | 0.949 | 0.949 |

SVR | 0.819 | 0.809 | 0.801 | 0.760 |

MLP | 0.783 | 0.799 | 0.791 | 0.727 |

AdaBoost | 0.899 | 0.887 | 0.857 | 0.821 |

MAPE | 4 Clusters | Without Clustering | ||||
---|---|---|---|---|---|---|

Model for Prediction | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ |

RF | 6.10% | 5.03% | 1.92% | 10.52% | 6.60% | 12.40% |

SVR | 7.90% | 6.01% | 4.90% | 15.89% | 8.74% | 15.54% |

MLP | 12.98% | 5.76% | 4.55% | 27.27% | 18.56% | 7.97% |

AdaBoost | 6.40% | 5.49% | 3.82% | 13.37% | 6.78% | 9.03% |

RMSE | 4 Clusters | Without Clustering | ||||

Model for Prediction | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ |

RF | 3.731 | 3.401 | 2.069 | 6.100 | 4.019 | 8.167 |

SVR | 4.952 | 3.823 | 3.439 | 8.996 | 5.174 | 9.514 |

MLP | 9.959 | 3.538 | 3.018 | 15.811 | 11.235 | 5.193 |

AdaBoost | 3.952 | 3.422 | 2.527 | 7.513 | 3.960 | 6.064 |

R2 Score | 4 Clusters | Without Clustering | ||||

Model for prediction | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ |

RF | 0.646 | 0.735 | 0.842 | 0.055 | 0.630 | −1.463 |

SVR | 0.563 | 0.598 | 0.440 | −1.056 | 0.387 | −2.342 |

MLP | −1.520 | 0.714 | 0.664 | −5.351 | -1.888 | 0.004 |

AdaBoost | 0.603 | 0.732 | 0.764 | −0.434 | 0.641 | −0.358 |

Training Time (s) | ||||
---|---|---|---|---|

Model for Prediction | Historical Data ${D}_{H}$ | Data at ${\mathbf{t}}_{1}$ | Data at ${\mathbf{t}}_{2}$ | Data at ${\mathbf{t}}_{3}$ |

RF 4 clusters | 0.539 | 0.366 | 0.375 | 0.418 |

RF without clusters | 0.213 | 0.215 | 0.234 | 0.341 |

SVR 4 clusters | 0.111 | 0.205 | 0.231 | 0.374 |

MLP 4 clusters | 1.14 | 0.669 | 1.48 | 1.13 |

AdaBoost 4 clusters | 0.502 | 0.234 | 0.369 | 0.301 |

Grid Prediction Time (s) | ||||

Model for Prediction | 100 × 100 grid | 300 × 300 grid | ||

RF 4 clusters | 0.112 | 0.285 | ||

RF without clusters | 0.04 | 0.251 | ||

SVR 4 clusters | 0.195 | 1.25 | ||

MLP 4 clusters | 0.038 | 0.218 | ||

AdaBoost 4 clusters | 0.134 | 0.625 |

4 Clusters | Without Clustering | |||||
---|---|---|---|---|---|---|

Error metric | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ | ${\mathbf{t}}_{1}$ | ${\mathbf{t}}_{2}$ | ${\mathbf{t}}_{3}$ |

MAPE | 7.11% | 4.24% | 2.19% | 8.61% | 7.45% | 5.96% |

RMSE | 5.806 | 4.018 | 2.346 | 6.317 | 6.422 | 4.749 |

R2 score | 0.044 | 0.255 | 0.826 | −0.132 | −0.902 | 0.288 |

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## Share and Cite

**MDPI and ACS Style**

Camana, M.R.; Garcia, C.E.; Hwang, T.; Koo, I.
A REM Update Methodology Based on Clustering and Random Forest. *Appl. Sci.* **2023**, *13*, 5362.
https://doi.org/10.3390/app13095362

**AMA Style**

Camana MR, Garcia CE, Hwang T, Koo I.
A REM Update Methodology Based on Clustering and Random Forest. *Applied Sciences*. 2023; 13(9):5362.
https://doi.org/10.3390/app13095362

**Chicago/Turabian Style**

Camana, Mario R., Carla E. Garcia, Taewoong Hwang, and Insoo Koo.
2023. "A REM Update Methodology Based on Clustering and Random Forest" *Applied Sciences* 13, no. 9: 5362.
https://doi.org/10.3390/app13095362