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

Table 1

Applying our model to the formation in Figure 9.

Characteristic line	Entities that make up the characteristic line	Characteristic line equation	Pearson’s coefficient	Entity coordinates: original and calculated using the characteristic line equation
𝑙1	𝐴={𝑒1,𝑒2,𝑒3,𝑒4}	𝑦=2.1+0.85𝑥	0.99	𝑒1: (−4, −1) and (−4, −1.3); 𝑒2: (−2, −0) and (−2, 0.4); 𝑒3: (0, 2) and (0, 2.1); 𝑒4: (2, 4) and (2, 3.8)
𝑙2	𝐵={𝑒4,𝑒5,𝑒6,𝑒7}	𝑦=8.7−2.2𝑥	0.97	𝑒4: (2, 4) and (2, 4.3); 𝑒5: (3, 2) and (3, 2.1); 𝑒6: (4, 1) and (4, 0.1); 𝑒7: (5, −3) and (5, −2.3)