# Performance Estimation in V2X Networks Using Deep Learning-Based M-Estimator Loss Functions in the Presence of Outliers

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

- Network monitoring improves security and efficiency, where network monitoring that identifies and fixes problems in applications is much more valuable to an organization to prevent unwanted system failures.
- Detect intrusions, errors, and anomalies to monitor raw data, such as user records, devices, networks, and servers. Quickly detect attacks and unclear security risks.
- Improving QoS requirements can be achieved by monitoring the control and management of network resources, reducing interference such as packet loss, latency, and jitter in the network. Network resources are managed through QoS by providing advantages for particular classes of data on the network. Prediction of quality Characteristics such as throughput, resource allocation, or timing issues. Model enabled accuracy prediction is a kind of prediction that applies a model as input for the prediction.Enterprise networks should provide expected and measured services for video conferencing that use real-time audio and video communications. Both are delay-sensitive and bandwidth-intensive forms of communication. Enterprises use QoS to efficiently manage sensitive applications, such as real-time voice, video, and critical data, and to avoid degradation of QoS parameters. Enterprises can achieve QoS by using certain features, such as jitter buffers and bandwidth management. For many enterprises, QoS is part of SLA with their NSP to ensure a specific stage of network performance.
- Health applications. Recently, medical IoT systems have become one of the most essential modern medical advancements. This technique can reach a critical benefit by improving the distance control of healthcare. It can also support detecting medical problems rapidly, therefore protecting patients’ lives and health.Nevertheless, many networked medical devices in the IoT healthcare space have security flaws that make them susceptible to malicious threats. The above challenges can cause serious consequences that influence patients’ lives by disrupting medical equipment. Therefore, it is necessary to overcome these challenges to maintain the efficiency and accuracy of medical IoT systems.At the same time, the wide distribution of sensitive medical information in IoT healthcare systems leaves them vulnerable to complex attacks that aim at main security aspects such as privacy and safety. This will harm the reliability, acquisition, and widespread use of IoT healthcare systems.
- Smart cities are becoming more and more of a reality, thanks to the enormous technological research enabling the development of IoT, which offers a wide range of applications around different types of sensors. More sustainable, environmentally friendly, and economical smart cities and technologies are needed to cope with the growing population in cities.For smart-city management, numerous sensors, cameras, and actuators are installed everywhere. These sensors collect and send a bulk of data in actual time. The analysis and processing of the collected data should be almost instantaneous for efficient management of city operations. Additionally, for instant processing, high-speed internet connectivity is essential.With the advent of smart-city devices, internet-connected devices will transmit large amounts of data in real time. While this data contributes to the efficiency of city functions, it also poses serious security risks that cannot be ignored. Data from parking lots, security cameras, electric vehicle charging stations, and GPS systems contain citizens’ confidential information. Not every networked device is already cyber-resistant. If it is, criminals can easily access the data and use it for illegal purposes. Therefore, governments and IT professionals should strengthen the security perimeters of smart devices and supporting infrastructure. Identifying and solving smart-city challenges is a collaborative approach. Governments and IT professionals, private organizations, and citizens should join together to work for a common goal—the success of the smart city
- Smart farming. With the world’s population growing and climatic changes resulting in unpredictable weather in the world’s food chains, the race for the sustainability of farming and the efficient use of dwindling resources such as water is a global challenge for countries worldwide. Smart farming uses sensors implanted in plants and fields to take measurements that assist make decisions and plant protection. Precision farming is an essential part of the smart-farming paradigm, in which sensors are implanted in plants to take a certain measure to allow targeted care measurement. Precision farming will be needed to ensure food protection in the future; therefore, it is essential for farming sustainability. The primary use cases of AI in IoT for farming are plant health and disease identification and data-based crop protection.

- Optimize quality of service (QoS) requirements and network monitoring to manage resources and ensure security.
- Monitor network availability and activity to identify and eliminate outliers (anomalies), including security and operational issues.
- One of the primary approaches to obtain a robust learning algorithm that is more robust to outliers is to replace the traditional loss function of the performance measure MSE with another robust function, to improve performance in the presence of outliers. In this approach, robustness against outliers has been satisfied by minimizing the effect of significant training errors due to outliers.
- The lack of accurate machine-learning analysis to achieve adequate performance.
- The computational complexity of challenging problems in optimizing QoS measures.

- A novel DL algorithm has been proposed to estimate the performance of V2X using robust M-estimator loss functions instead of the standard MSE loss function.
- A new comparison of the M-estimator approach and the conventional MSE loss function has been applied in terms of RMSE and MAPE, and under different sets of outliers on V2X traffic datasets used to verify the efficiency of the proposed method.
- Finally, the results of the simulation-based tests show that:
- ✓
- The robust M-estimator loss functions have the best performance in all cases and outperform the conventional MSE loss function when data is clean or contains Gaussian noise or outliers.
- ✓
- When using noise-free data, the robust Fair loss function performs well and has the best performance compared to its peers.
- ✓
- When using data corrupted by Gaussian noise, the robust Cauchy loss function shows the best performance compared to the others.
- ✓
- Even on training data contaminated with outliers, the robust Fair loss function performs better than its competitors.

## 2. Relevant Works

## 3. Proposed Work

## 4. Robust Learning and Outliers

## 5. M-Estimators Loss Function

- ρ(e) is a positive-definite symmetric function, where ρ(e) = ρ(−e) for all e.
- ρ(e) ≥ 0 for all e and has a unique minimum at e = 0.
- ρ(e) increases when e increases from 0 but does not become too large when e increases and is selected to be less increasing than square.

## 6. V2X Simulation Environment

## 7. Deep Neural Network Learning

^{−3}, and a performance goal (minimum loss) of 1 × 10

^{−3}. The model DL was trained several times with different configurations. We created different combinations of the input dataset with minor changes to the network parameters and ran them with all possible topologies. However, this is only the initial phase; once the input dataset is prepared, only this dataset is used, and the number of data type values is fixed.

## 8. Simulation Results

- (1)
- Set A: The DNN is trained with noise-free, high-quality, clean data.
- (2)
- Set B: The network is trained with perfect data contaminated with slight Gaussian noise (GN): G2~N (0, 0.1).
- (3)
- Set C: DNN is trained with data contaminated with GN, G2~N (0,0.1), in addition to very good, randomized outliers of the form:H
_{1}~N (+15, 2), H_{2}~N (−20, 3), H_{3}~N (+30, 1.5), H_{4}~N (−12, 3).

_{2}, H

_{1}, H

_{2}, H

_{3}, and H

_{4}are probability distributions occurring on probability $1-\epsilon $ and $\epsilon $, respectively, where $\epsilon $ is fixed and H random. In this case, the outliers were included in the training data with a percentage $\epsilon $= 10% of the data. We assigned the outliers randomly to the desired percentage of data (percent outliers) (25% of this percentage will have outlier H

_{1}type, the other 25% will have H

_{2}type, and so on … H

_{3}and H

_{4}). The dataset used for this experiment was generated from the V2X network. The dataset is then contaminated in the x–y axis by Gaussian noise with a mean of zero and a standard deviation of 0.1, G2~N (0, 0.1). A variable percentage, ε, of data was randomly selected and then replaced with probability, ε, by background noise uniformly distributed in the specific range [24,26,29,31,32].

^{−3}. The normalization of the input data must be in the interval [−1, 1], which is compatible with the actual maximum to minimum values. DNN can estimate the optimal performance of a V2X network based on the collected V2X dataset; it used V2X throughput as input and packet loss rate as output (desired output). The goal is to develop a robust DNN that can estimate V2X performance when the data contains outliers. We conducted a comparative study between robust and traditional DNN performances regarding RMSE and MAPE, to prove which algorithm gives excellent results for the considered application.

## 9. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

M-estimators | Maximum-likelihood estimators |

LMedS | Least Median of Squares |

L-estimators | Linear combination of order statistics |

R-estimators | Estimates based on rank transformations |

MSE | Mean square error |

DNN | Deep neural networks |

DL | Deep Learning |

BP | Backpropagation |

RMSE | Root Mean square error |

MAPE | Mean absolute percentage of error |

LTS | Least Trimmed Squares |

LMLS | Least mean log square |

QoS | Quality of service |

ITS | Intelligent Transportation Systems |

AI | Artificial Intelligence |

IoT | Internet of Things |

ML | Machine Learning |

ANN | Artificial Neural Networks |

MFNNs | Multilayer feedforward neural networks |

V2X | Vehicle to Everything |

WANET | Wireless ad hoc network |

MANET | Mobile ad hoc network |

VANETs | Vehicular ad hoc networks |

FANETs | Flying ad hoc networks |

LMLS | The least mean log squares |

Traincgf | Conjugate gradient backpropagation with Fletcher-Reeves updates |

SLA | Service level agreement |

NSP | Network service provider |

## References

- Morocho-Cayamcela, M.E.; Haeyoung, L.; Wansu, L. Machine Learning for 5G/B5G Mobile and Wireless Communications: Potential, Limitations, and Future Directions. IEEE Access
**2019**, 7, 137184–137206. [Google Scholar] [CrossRef] - Sumalee, A.; Ho, H. Smarter and more connected: Future intelligent transportation system. IATSS Res.
**2018**, 42, 67–71. [Google Scholar] [CrossRef] - Sarker, I.H. Machine Learning: Algorithms, Real-World Applications and Research Directions. SN Comput. Sci.
**2021**, 2, 160. [Google Scholar] [CrossRef] [PubMed] - Sun, Y.; Peng, M.; Zhou, Y.; Huang, Y.; Mao, S. Application of Machine Learning in Wireless Networks: Key Techniques and Open Issues. IEEE Commun. Surv. Tutor.
**2019**, 21, 3072–3108. [Google Scholar] [CrossRef] [Green Version] - Ali, E.S.; Hasan, M.K.; Hassan, R.; Saeed, R.A.; Hassan, M.B.; Islam, S.; Nafi, N.S.; Bevinakoppa, S. Machine Learning Technologies for Secure Vehicular Communication in Internet of Vehicles: Recent Advances and Applications. Secur. Commun. Netw.
**2021**, 2021, 8868355. [Google Scholar] [CrossRef] - Tong, W.; Hussain, A.; Bo, W.X.; Maharjan, S. Artificial Intelligence for Vehicle-to-Everything: A Survey. IEEE Access
**2019**, 7, 10823–10843. [Google Scholar] [CrossRef] - Alsharif, M.H.; Kelechi, A.H.; Yahya, K.; Chaudhry, S.A. Machine Learning Algorithms for Smart Data Analysis in Internet of Things Environment: Taxonomies and Research Trends. Symmetry
**2020**, 12, 88. [Google Scholar] [CrossRef] [Green Version] - Jagannath, J.; Polosky, N.; Jagannath, A.; Restuccia, F.; Melodia, T. Machine learning for wireless communications in the Internet of Things: A comprehensive survey. Ad Hoc Networks
**2019**, 93, 101913. [Google Scholar] [CrossRef] [Green Version] - Zhu, J.; Xu, W. Real-Time Data Filling and Automatic Retrieval Algorithm of Road Traffic Based on Deep-Learning Method. Symmetry
**2020**, 13, 1. [Google Scholar] [CrossRef] - Hassan, R.; Qamar, F.; Hasan, M.K.; Aman, A.H.M.; Ahmed, A.S. Internet of Things and Its Applications: A Comprehensive Survey. Symmetry
**2020**, 12, 1674. [Google Scholar] [CrossRef] - Martin, T.; Geneiatakis, D.; Kounelis, I.; Kerckhof, S.; Fovino, I.N. Towards a Formal IoT Security Model. Symmetry
**2020**, 12, 1305. [Google Scholar] [CrossRef] - Khedkar, S.P.; Canessane, R.A.; Najafi, M.L. Prediction of Traffic Generated by IoT Devices Using Statistical Learning Time Series Algorithms. Wirel. Commun. Mob. Comput.
**2021**, 2021, 5366222. [Google Scholar] [CrossRef] - Boutaba, R.; Salahuddin, M.A.; Limam, N.; Ayoubi, S.; Shahriar, N.; Estrada-Solano, F.; Caicedo, O.M. A comprehensive survey on machine learning for networking: Evolution, applications and research opportunities. J. Internet Serv. Appl.
**2018**, 9, 16. [Google Scholar] [CrossRef] [Green Version] - Kaur, J.; Khan, M.A.; Iftikhar, M.; Imran, M.; Haq, Q.E.U. Machine Learning Techniques for 5G and Beyond. IEEE Access
**2021**, 9, 23472–23488. [Google Scholar] [CrossRef] - Singh, D.P.; Sharma, D. Traffic Prediction Using Machine Learning and IoT. In Integration of Cloud Computing with Internet of Things; Wiley: Hoboken, NJ, USA, 2021; pp. 111–129. [Google Scholar] [CrossRef]
- Cayamcela, M.E.M.; Lim, W. Artificial Intelligence in 5G Technology: A Survey. In Proceedings of the 2018 International Conference on Information and Communication Technology Convergence (ICTC), Jeju, Korea, 17–19 October 2018. [Google Scholar]
- Arena, F.; Pau, G. An Overview of Vehicular Communications. Futur. Internet
**2019**, 11, 27. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.; Meratnia, N.; Havinga, P. Outlier Detection Techniques for Wireless Sensor Networks: A Survey. IEEE Commun. Surv. Tutor.
**2010**, 12, 159–170. [Google Scholar] [CrossRef] [Green Version] - Rassam, M.; Zainal, A.; Maarof, M.A. Advancements of Data Anomaly Detection Research in Wireless Sensor Networks: A Survey and Open Issues. Sensors
**2013**, 13, 10087–10122. [Google Scholar] [CrossRef] [Green Version] - Abdellah, A.R.; Muthanna, A.; Koucheryavy, A. Robust Estimation of VANET Performance-Based Robust Neural Networks Learning. In Internet of Things, Smart Spaces, and Next Generation Networks and Systems; NEW2AN 2019, ruSMART 2019. Lecture Notes in Computer Science; Galinina, O., Andreev, S., Balandin, S., Koucheryavy, Y., Eds.; Springer: Cham, Switzerland, 2019; Volume 11660. [Google Scholar] [CrossRef]
- Abdellah, A.R.; Muthanna, A.; Koucheryavy, A. Energy Estimation for VANET Performance Based Robust Neural Networks Learning. In Distributed Computer and Communication Networks; DCCN Communications in Computer and Information Science; Vishnevskiy, V., Samouylov, K., Kozyrev, D., Eds.; Springer: Cham, Switzerland, 2019; Volume 1141. [Google Scholar] [CrossRef]
- Liang, L.; Ye, H.; Li, G. Toward Intelligent Vehicular Networks: A Machine Learning Framework. IEEE Internet Things J.
**2019**, 6, 124–135. [Google Scholar] [CrossRef] [Green Version] - Zahra, M.M.; Essai, M.H.; Abd Ellah, A.R. Performance Functions Alternatives of Mse for Neural Networks Learning. Int. J. Eng. Res. Technol. (IJERT)
**2014**, 3, 967–970. [Google Scholar] - Essai, M.H.; Abd Ellah, A.R. M-Estimators Based Activation Functions for Robust Neural Network Learning. In Proceedings of the IEEE 10th International Computer Engineering Conference (ICENCO2014), Cairo, Egypt, 29–30 December 2014; pp. 76–81. [Google Scholar]
- Doan, M.; Zhang, Z. Deep Learning in 5G Wireless Networks—Anomaly Detections. In Proceedings of the 29th Wireless and Optical Communications Conference (WOCC2020), Newark, NJ, USA, 1–2 May 2020; pp. 1–6. [Google Scholar] [CrossRef]
- Abd Ellah, A.R.; Essai, M.H.; Yahya, A. Comparison of Different Backpropagation Training Algorithms Using Robust M-Estimators Performance Functions. In Proceedings of the IEEE 2015 Tenth International Conference on Computer Engineering & Systems (ICCES), Cairo, Egypt, 23–24 December 2015; pp. 384–388. [Google Scholar]
- Maimo, L.F.; Clemente, F.J.G.; Gil Perez, M.; Perez, G.M. On the performance of a deep learning-based anomaly detection system for 5G networks. In Proceedings of the 2017 IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computed, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI), San Francisco, CA, USA, 4–8 August 2017; Institute of Electrical and Electronics Engineers (IEEE): Piscataway, NJ, USA, 2017; pp. 1–8. [Google Scholar]
- Reddy, D.K.; Behera, H.S.; Nayak, J.; Vijayakumar, P.; Naik, B.; Singh, P.K. Deep neural network based anomaly detection in Internet of Things network traffic tracking for the applications of future smart cities. Trans. Emerg. Telecommun. Technol.
**2020**, 32, 2161–3915. [Google Scholar] [CrossRef] - Ellah, A.R.A.; Essai, M.H.; Yahya, A. Robust Backpropagation Learning Algorithm Study for Feed Forward Neural Networks. Master’s Thesis, Al-Azhar University, Cairo Governorate, Egypt, 2016. [Google Scholar]
- Rusiecki, A. Trimmed Robust Loss Function for Training Deep Neural Networks with Label Noise. In Artificial Intelligence and Soft Computing. ICAISC 2019; Lecture Notes in Computer Science; Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J., Eds.; Springer: Cham, Switzerland, 2019; Volume 11508. [Google Scholar] [CrossRef]
- Mohamed, M.Z.; Mohamed, H.; Essai Ali, R.; Abd, E. Robust Neural Network Classifier. Int. J. Eng. Dev. Res. (IJEDR)
**2013**, 1, 326–331. [Google Scholar] - Pernia-Espinoza, A.; Ordieres-Meré, J.; Martínez-De-Pisón, F.; González-Marcos, A. TAO-robust backpropagation learning algorithm. Neural Netw.
**2005**, 18, 191–204. [Google Scholar] [CrossRef] [PubMed] - Bagheri, H.; Rahim, N.A.; Liu, Z.; Lee, H.; Pesch, D.; Moessner, K.; Xiao, P. 5G NR-V2X: Toward Connected and Cooperative Autonomous Driving. IEEE Commun. Stand. Mag.
**2021**, 5, 48–54. [Google Scholar] [CrossRef] - Liu, Z.; Lee, H.; Khyam, M.O.; He, J.; Pesch, D.; Moessner, K.; Poor, H.V. 6g for vehicle-to-everything (v2x) communications: Enabling technologies, challenges, and opportunities. arXiv
**2020**, arXiv:2012.07753. [Google Scholar] - Peter, J.H.; Elvezio, M.R. Robust Statistics, 2nd ed.; John Wiley and Sons: New York, NY, USA, 2009. [Google Scholar]
- Peter, J.R.; Annick, M.L. Robust Regression and Outlier Detection; John Wiley and Sons: New York, NY, USA, 2005. [Google Scholar]
- Rusiecki, A.; Kordos, M.; Kamiński, T.; Greń, K. Training Neural Networks on Noisy Data. In Artificial Intelligence and Soft Computing. ICAISC 2014; Lecture Notes in Computer Science; Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., Eds.; Springer: Cham, Switzerland, 2014; Volume 8467. [Google Scholar] [CrossRef]
- Zhang, Z. Parameter estimation techniques: A tutorial with application to conic fitting. Image Vis. Comput.
**1997**, 15, 59–76. [Google Scholar] [CrossRef] [Green Version]

**Figure 4.**The predicted models in the robust loss functions Cauchy and Fair and the traditional loss function MSE in Set A.

**Figure 6.**The predicted models in robust loss functions Cauchy and Fair and traditional loss function MSE in set B.

**Figure 8.**Predicted models in the robust loss functions Cauchy and Fair and the traditional loss function MSE in the set C case.

Type | Ρ (e) | Ψ (e) | $\mathit{\omega}\left(\mathit{e}\right)$ |
---|---|---|---|

L2 | ${e}^{2}/2$ | $e$ | 1 |

Fair | ${c}^{2}\left[\frac{\left|e\right|}{c}-\mathrm{log}\left(1+\frac{\left|e\right|}{c}\right)\right]$ | $\frac{e}{1+\left|e\right|/c}$ | $\frac{1}{1+\left|e\right|/c}$ |

Cauchy | $\frac{{c}^{2}}{2}\mathrm{log}\left(1+{(e/c)}^{2}\right)$ | $\frac{e}{1+{(e/c)}^{2}}$ | $\frac{1}{1+{(e/c)}^{2}}$ |

**Table 2.**Performance scores for networks trained with MSE, Fair, and Cauchy loss functions for estimating V2X traffic.

Loss Function | Set A | Set B | Set C | |||
---|---|---|---|---|---|---|

RMSE | MAPE% | RMSE | MAPE% | RMSE | MAPE% | |

MSE | 0.0156 | 1.3 | 0.1786 | 10.6 | 0.5179 | 16.7 |

Cauchy | 0.0194 | 1.5 | 0.0630 | 5.4 | 0.0923 | 9.8 |

Fair | 0.0132 | 1.1 | 0.0740 | 6.2 | 0.0756 | 8.6 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Abdellah, A.R.; Alshahrani, A.; Muthanna, A.; Koucheryavy, A.
Performance Estimation in V2X Networks Using Deep Learning-Based M-Estimator Loss Functions in the Presence of Outliers. *Symmetry* **2021**, *13*, 2207.
https://doi.org/10.3390/sym13112207

**AMA Style**

Abdellah AR, Alshahrani A, Muthanna A, Koucheryavy A.
Performance Estimation in V2X Networks Using Deep Learning-Based M-Estimator Loss Functions in the Presence of Outliers. *Symmetry*. 2021; 13(11):2207.
https://doi.org/10.3390/sym13112207

**Chicago/Turabian Style**

Abdellah, Ali R., Abdullah Alshahrani, Ammar Muthanna, and Andrey Koucheryavy.
2021. "Performance Estimation in V2X Networks Using Deep Learning-Based M-Estimator Loss Functions in the Presence of Outliers" *Symmetry* 13, no. 11: 2207.
https://doi.org/10.3390/sym13112207