1. On-Line Discovery of Flock Patterns in Spatio-Temporal Data * Marcos Vieira Petko Bakalov Vassilis Tsotras UC-Riverside ESRI UC-Riverside mvieira@cs.ucr.edu pbakalov@esri.com tsotras@cs.ucr.edu * This research was partially supported by NSF and CAPES/Fulbright

2. Introduction Informal definition of a flock pattern identifying all groups of trajectories that stay “together” for the duration of a given time interval Capture “collaborative” or “group” behavior between moving objects. t=1 t=2 t=3t=4

3. Definition Formal definition of a Flock Patterns: Find groups of at least  trajectories contained in a disk of diameter  for at least  consecutive timestamps Example: Flock(  =3, ,  =3) Answer: f 1 ={T 1,T 2,T 3 }[t 1 :t 3 ] f 2 ={T 4,T 5,T 6 }[t 2 :t 4 ]

4. Solution The solution for this problem goes through two steps. Step 1 Identifying the clusters of moving objects which can be covered by a disk of diameter  for each specific time instance. Step 2 Combining the identified clusters into a flock with length at least  consecutive timestamps.

5. Solution: Step 1 The Problem: There are infinite number of possible centers of the flock cluster centers to test. The Solution: Use a simple heuristic that limits the number of possible flock cluster centers that we have to test. The number of such possible locations is polynomial on the total number of moving objects.

6. Step 1: The Eristic If there is a disk with diameter  that covers all objects in the flock at given time instance then there exists another disk with the same diameter but with different center that also covers all objects covered by the first one and has at least two points on its circumference. Total number of disks to test - |T| 2

7. Solution: Step 2 Brute force solution – perform join between all the flock clusters for all the time instances. Use filter-and-refinement paradigm with the purpose of reducing the total number of candidates and thus the overall computation cost of the algorithm.  TDE: Top Down Evaluation  PFE: Pipe Filter Evaluation  CRE: Continuous Refinement Evaluation  CFE: Clustering Filtering Evaluation