Intuitively, a ** Group** is a set of entities that travel together for a sufficiently long period of time.

From many formal definitions of a group, we compare four grouping definitions: The Convoys[1], Swarms[2], (Original) Groups[3] and Refined Groups[4].

All four definitions require three parameters to define a group:

- minimum number entities in a group:
**m** - minimum time duration of a group:
**δ** - minimum distance between entities:
**ε**(see [1][3][4] for details)

From the results, we visualize the trajectories and integrate them in the video from the same data set.

Our visualization program is based on the work of Maurice Marx .

Groups by a grouping definition: none

Groups by a grouping definition: {4,5}

Groups by grouping definition: {7,8,9}, {8,9}, {9,10}

Contains trajectories of 630 pedestrians tracked in the hallway.

Parameters: *m*=2,*ε*=0.963m,*δ*={17,38,58}

Pedestrian near a university building, contains 434 trajectories

Parameters: *m*=2,*ε*={1.22,1.52}m,*δ*={36,57,78}

There are 2592 trajectories in this 800 frames data set. We try different sampling rate of trajectories.

Parameters: *m*=2,*ε*=0.76m,*δ*={10,15,20}s

Sampling Rate: 100%, 50%, and 25%

Source: here

There are 3313 trajectories in this 800 frames data set. We try different sampling rate of trajectories.

Parameters: *m*=2,*ε*=0.76m,*δ*={10,15,20}s

Sampling Rate: 100%, 50%, and 25%

Source: here

Pedestrians entering and exiting a university building, contains of 360 trajectories

Parameters: *m*=2,*ε*=1.24m,*δ*={72,89,105}

Source: here

Pedestrians in the sidewalk near the tram stop, contains 389 trajectories

Parameters: *m*=2,*ε*=0.94m,*δ*={20,58,96}

Source: here

- [1] Hoyoung Jeung, Man Lung Yiu, Xiaofang Zhou, Christian S.J ensen, and Heng Tao Shen. 2008. Discovery of convoys in trajectory databases. PVLDB 1, 1 (2008), 1068–1080.
- [2] Zhenhui Li, Bolin Ding, Jiawei Han, and Roland Kays. 2010. Swarm: Mining Relaxed Temporal Moving Object Clusters. PVLDB 3, 1 (2010), 723–734.
- [3] Kevin Buchin, Maike Buchin, Marc van Kreveld, Bettina Speckmann, and Frank Staals. 2015. Trajectory grouping structure. Journal of Computational Geometry 6, 1 (2015), 75–98.
- [4] Marc van Kreveld, Maarten Löffler, Frank Staals, and Lionov Wiratma. 2018. A Refined Definition for Groups of Moving Entities and Its Computation. Int. J. Comput. Geometry Appl. 28, 2 (2018), 181–196.