# Hybrid Machine Learning-Statistical Method for Anomaly Detection in Flight Data
## 5 Conclusions  
This paper provides a hybrid statistical--local outlier factor for anomaly detection for flight data analysis by combining the local outlier factor technique with [PERSON]'s method of anomaly detection  
The paper shows that LOF quantifies the degree of an outlier by giving each flight a score. This is a development in machine learning techniques applied to flight data so far, which have produced a binary categorizing, as in the case of clustering algorithms. Thus, with LOF, for the first time, we demonstrated that in the aviation industry, anomalous flights can not only be identified but also be given an anomaly score to compare two anomalous flights in an unsupervised manner. Furthermore, LOF helps to track anomalous behavior in time during the flight and identifies the time window during the flight duration when a flight was anomalous. This is insightful when a flight is only abnormal for some seconds or a short duration.  
For the first time, we detected flight parameters responsible for anomalous behavior or at least gave direction to human experts looking for the cause of abnormal behavior. By combining the LOF algorithm with [PERSON]'s method, a dynamic threshold is fixed for the set of flights arriving at a given airport, which helps to identify real outliers and filters false positives given by the LOF algorithm. The paper also shows how the optimal value of \(k\) is decided for the implementation of the LOF algorithm. The analysis was conducted on real-life flight data in an unsupervised manner, as opposed to simulated data used in many works discussed earlier, thus giving an insight into the difficulties when applying such techniques to real data. The same methodology can be implemented on any time-series-based multidimensional dataset to detect anomalous data points.  
Figure 13: Changing LOF score of a flight during last 3 min before touchdown.  
**Author Contributions:** Conceptualization, S.K.J., G.V. and R.C.; data curation, A.M.; formal analysis, S.K.J., G.V. and R.C.; funding acquisition, R.C.; investigation, S.K.J., G.V. and R.C., methodology, S.K.J. and G.V.; project administration, R.C.; supervision, R.C. and G.V.; resources, R.C.; visualization, S.K.J.; validation, A.M.; writing--original draft preparation, S.K.J.; writing--review and editing, R.C. and G.V. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The findings presented in this paper are a result of the Project WAGE, financed by the Malta Council for Science and Technology, for and on behalf of the Foundation for Science and Technology, through the FUSION: R&I Technology Development Programme.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available in the public domain and can be accessed at [[https://c3.ndc.nasa.gov/dashlink/projects/85/](https://c3.ndc.nasa.gov/dashlink/projects/85/)]([https://c3.ndc.nasa.gov/dashlink/projects/85/](https://c3.ndc.nasa.gov/dashlink/projects/85/)) (accessed on 18 February 2018).  
**Acknowledgments:** The authors would like to thank all reviewers and editors for their helpful suggestions for the improvement of this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.