Identification of V-Formations and Circular and Doughnut Formations in a Set of Moving Entities with Outliers

Listing 1

Outlier detection algorithm.

ALGORITHM: Outlier detection on a characteristic line

INPUT:  lineMembers = [𝑒₁,𝑒₂,…,𝑒_𝑚] //Array of 𝑚 entities

     𝜇_𝑝 //Threshold for Pearson’s coefficient

     percentageOutliers //Maximum percentage of outliers permitted on lineMembers

OUTPUT:  outliers = [] // Array of outliers

BEGIN

 (1) Obtain the equation of the line 𝑙 which most suits the positions (𝑥,𝑦) of the entities in lineMembers, see (2).

 (2) Get the maximum number of outliers permitted on lineMembers: nbrOutliers = 𝑚∗𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒𝑂𝑢𝑡𝑙𝑖𝑒𝑟𝑠/100.

 (3) Find the nbrOutliers entities in lineMembers which have the maximum distance to 𝑙.

 (4) Remove from lineMembers the entities found in Step  3.

 (5) Calculate Pearson’s coefficient using positions (𝑥,𝑦) of each entity in lineMembers:

    Pearson = PearsonCoefficient(lineMembers).

 (6) If Pearson ≥𝜇_𝑝 then return in outliers the entities found in Step  3.

END