scholarly journals Trajectory Clustering within the Terminal Airspace Utilizing a Weighted Distance Function

Proceedings ◽  
2020 ◽  
Vol 59 (1) ◽  
pp. 7
Author(s):  
Samantha J. Corrado ◽  
Tejas G. Puranik ◽  
Oliva J. Pinon ◽  
Dimitri N. Mavris
Keyword(s):  
Anomaly Detection ◽  
Distance Function ◽  
Euclidean Distance ◽  
Air Traffic ◽  
Detection Methods ◽  
Traffic Flows ◽  
Trajectory Clustering ◽  
Trajectory Prediction ◽  
Euclidean Distance Function ◽  
Definition Of

To support efforts to modernize aviation systems to be safer and more efficient, high-precision trajectory prediction and robust anomaly detection methods are required. The terminal airspace is identified as the most critical airspace for individual flight-level and system-level safety and efficiency. To support successful trajectory prediction and anomaly detection methods within the terminal airspace, accurate identification of air traffic flows is paramount. Typically, air traffic flows are identified utilizing clustering algorithms, where performance relies on the definition of an appropriate distance function. The convergent/divergent nature of flows within the terminal airspace makes the definition of an appropriate distance function challenging. Utilization of the Euclidean distance is standard in aviation literature due to little computational expense and ability to cluster entire trajectories or trajectory segments at once. However, a primary limitation in the utilization of the Euclidean distance is the uneven distribution of distances as aircraft arrive at or depart from the airport, which may result in skewed classification and inadequate identification of air traffic flows. Therefore, a weighted Euclidean distance function is proposed to improve trajectory clustering within the terminal airspace. In this work, various weighting schemes are evaluated, applying the HDBSCAN algorithm to cluster the trajectories. This work demonstrates the promise of utilizing a weighted Euclidean distance function to improve the identification of terminal airspace air traffic flows. In particular, for the selected terminal airspace, if trajectory points closer to the border of the terminal airspace, but not necessarily at the border, are weighted highest, then a more accurate clustering is computed.

scholarly journals Geometric applications of critical point theory to submanifolds of complex projective space

1974 ◽  
Vol 55 ◽  
pp. 5-31 ◽  
Author(s):  
Thomas E. Cecil
Keyword(s):  
Projective Space ◽  
Critical Point ◽  
Distance Function ◽  
Complex Projective Space ◽  
Euclidean Distance ◽  
Point Theory ◽  
Euclidean Distance Function ◽  
Complex Projective ◽  
Class Of Functions

In a recent paper, [6], Nomizu and Rodriguez found a geometric characterization of umbilical submanifolds Mn ⊂ Rn+p in terms of the critical point behavior of a certain class of functions Lp, p ⊂ Rn+p, on Mn. In that case, if p ⊂ Rn+p, x ⊂ Mn, then Lp(x) = (d(x,p))2, where d is the Euclidean distance function.

Trajectory Clustering and Classification for Characterization of Air Traffic Flows

2016 ◽  
Author(s):  
Mayara Conde Rocha Murca ◽  
Richard DeLaura ◽  
R John Hansman ◽  
Richard Jordan ◽  
Tom Reynolds ◽  
...  
Keyword(s):  
Air Traffic ◽  
Traffic Flows ◽  
Trajectory Clustering ◽  
Clustering And Classification

scholarly journals Selective Image Segmentation Models Using Three Distance Functions

2021 ◽  
Vol 21 (No.1) ◽  
pp. 95-116
Author(s):  
Abdul Kadir Jumaat ◽  
Siti Aminah Abdullah
Keyword(s):  
Image Segmentation ◽  
Distance Function ◽  
Execution Time ◽  
Euclidean Distance ◽  
Operator Splitting ◽  
Splitting Method ◽  
Distance Functions ◽  
Similarity Coefficients ◽  
City Block ◽  
Euclidean Distance Function

Image segmentation can be defined as partitioning an image that contains multiple segments of meaningful parts for further processing. Global segmentation is concerned with segmenting the whole object of an observed image. Meanwhile, the selective segmentation model is focused on segmenting a specific object required to be extracted. The Convex Distance Selective Segmentation (CDSS) model, which uses the Euclidean distance function as the fitting term, was proposed in 2015. However, the Euclidean distance function takes time to compute. This paper proposed the reformulation of the CDSS minimization problem by changing the fitting term with three popular distance functions, namely Chessboard, City Block, and Quasi-Euclidean. The proposed models were CDSSNEW1, CDSSNEW2, and CDSSNEW3, which applied the Chessboard, City Block, and Quasi-Euclidean distance functions, respectively. In this study, the Euler-Lagrange (EL) equations of the proposed models were derived and solved using the Additive Operator Splitting method. Then, MATLAB coding was developed to implement the proposed models. The accuracy of the segmented image was evaluated using the Jaccard and Dice Similarity Coefficients. The execution time was recorded to measure the efficiency of the models. Numerical results showed that the proposed CDSSNEW1 model based on the Chessboard distance function could segment specific objects successfully for all grayscale images with the fastest execution time as compared to other models.

Identifying the Mastery Concepts in Linear Algebra by Using FCM-CM Algorithm

2010 ◽  
Vol 44-47 ◽  
pp. 3897-3901
Author(s):  
Hsiang Chuan Liu ◽  
Yen Kuei Yu ◽  
Jeng Ming Yih ◽  
Chin Chun Chen
Keyword(s):  
Objective Function ◽  
Linear Algebra ◽  
Fuzzy Clustering ◽  
Distance Function ◽  
Mahalanobis Distance ◽  
Euclidean Distance ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Euclidean Distance Function ◽  
Fuzzy C Means Algorithm

Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters by employing Mahalanobis distance in objective function, however, both of them need to add some constrains for Mahalanobis distance. In this paper, the authors’ improved Fuzzy C-Means algorithm based on common Mahalanobis distance (FCM-CM) is used to identify the mastery concepts in linear algebra, for comparing the performances with other four partition algorithms; FCM-M, GG, GK, and FCM. The result shows that FCM-CM has better performance than others.

scholarly journals Spatio-temporal Anomaly Detection, Diagnostics, and Prediction of the Air-traffic Trajectory Deviation using the Convective Weather

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Xinyu Zhao ◽  
Hao Yan ◽  
Jing Li ◽  
Yutian Pang ◽  
Yongming Liu
Keyword(s):  
Anomaly Detection ◽  
Large Deviation ◽  
Air Traffic ◽  
Weather Data ◽  
Impact Factors ◽  
Cusum Chart ◽  
Trajectory Prediction ◽  
Flight Plan ◽  
Spatio Temporal ◽  
Convective Weather

With ahead-of-time aircraft management, we are able to reduce aircraft collision and improve air traffic capacity. However, there are various impact factors which will cause a large deviation between the actual flight and the original flight plan. Such uncertainty will result in an inappropriate decision for flight management. In order to solve this problem, most of the existing research attempt to build up a stochastic trajectory prediction model to capture the influence of the weather. However, the complexity of the weather information and various human factors make it hard to build up an accurate trajectory prediction framework. Our approach considers the problem of trajectory deviation as the "anomaly" and builds up an analytics pipeline for anomaly detection, anomaly diagnostics, and anomaly prediction. For anomaly detection, we propose to apply the CUSUM chart to detect the abnormal trajectory point which differs from the flight plan. For anomaly diagnostics, we would like to link the entire anomalous trajectory sequences with the convective weather data and identify the important weather impact factors base on XGBoost and time-series feature engineering. For anomaly prediction, we will build up a point-wise prediction framework based on the Hidden Markov Model and Convectional LSTM to predict the probability that the pilot would deviate from the flight plan. Finally, we demonstrate the significance of the proposed method using real flight data from JFK to LAX.

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