Towards efficient prospective detection of multiple spatio -temporal clusters

1. XIV Brazilian Symposium on GeoInformatics Towards efficient prospective detection of multiple spatio-temporal clusters BráulioVeloso, Andréa Iabrudi and Thais Correa. Universidade Federal de OuroPreto – UFOP November, 2013, Campos do Jordão, SP – Brazil

2. Content • Introduction • Method • STCD • Problem • STCD-Sim • Metrics • Simulated Datasets • Results • Final Considerations

3. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process

4. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Surveillance Systems; • On-line; • Prospective;

5. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Surveillance Systems; • Applications:

6. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Surveillance Systems; • Applications: • Epidemic surveillance;

7. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Surveillance Systems; • Applications: • Epidemic surveillance; • Criminology behavior;

8. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Surveillance Systems; • Applications: • Epidemic surveillance; • Criminology behavior; • Traffic control;

9. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Surveillance Systems; • Applications: • Epidemic surveillance; • Criminology behavior; • Traffic control; • Social networks behavior;

10. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Spatio-temporal data are more available;

11. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Spatio-temporal data are more available; • Process with more then one cluster;

12. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • Technique to efficiently detect multiple emergent clusters in a space-time point process • Spatio-temporal data are more available; • Process with more then one cluster; • Need of computationally efficient approaches.

13. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • STCD • Point Process;

14. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • STCD • Point Process; • Earlier identification;

15. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • STCD • Point Process; • Earlier identification; • Fast Execution;

16. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • STCD • Point Process; • Earlier identification; • Fast Execution; • Efficient detection;

17. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | Introduction • STCD • Point Process; • Earlier identification; • Fast Execution; • Efficient detection; • But identifies only one cluster.

18. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | The Space-Time Cluster Detection

19. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Renato Assunção and Thais Correa. Surveillance to detect emerging space-time clusters. Computational Statistics and Data Analysis, 53(8):2817-2830, 2009.

20. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems

21. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems • Process: Under Control vs. Out of Control; • System: try to detected earlier a change in the process

22. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems; • Spatio-Temporal Events • Tuple: (id, x, y, t); • Order by time.

23. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems; • Spatio-Temporal Events; • Alarm • Evidence that the process changed from in control to out of control.

24. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems; • Spatio-Temporal Events; • Alarm; • Space-Time Cluster • Cylindrical shape • Circular base in space • Temporal Height Space Time

25. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems; • Spatio-Temporal Events; • Alarm; • Space-Time Cluster ; • Prospective Detection • Live Cluster Space Time

26. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems; • Spatio-Temporal Events; • Alarm; • Space-Time Cluster ; • Prospective Detection • Live Cluster Space Time

27. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Surveillance Systems; • Spatio-Temporal Events; • Alarm; • Space-Time Cluster ; • Prospective Detection • Live Cluster Space Time

28. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Ck,n: candidate cylinder to be a cluster, beginning (centered) in event k and ending in the last event

29. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Ck,n: candidate cylinder to be a cluster, beginning (centered) in event k and ending in the last event; • Lk : likelihood of the space-time Poisson process when there is a cluster Ck,n; • L ∞: likelihood of the space-time Poisson process when there is no cluster. • a

30. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Cumulative Sum Statistic

31. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Cumulative Sum Statistic

32. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Each parcel k is related to a candidate cluster.

33. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Each parcel k is related to a candidate cluster. • ε: increase in the intensity inside the cluster Ck,n;

34. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Each parcel k is related to a candidate cluster. • ε: increase in the intensity inside the cluster Ck,n; • N(Ck,n): number of events inside Ck,n;

35. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Each parcel k is related to a candidate cluster. • ε: increase in the intensity inside the cluster Ck,n; • N(Ck,n): number of events inside Ck,n; • μ(Ck,n): expectednumber of events inside Ck,n. • non parametric estimate forμ(Ck,n).

36. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Each parcel k is related to a candidate cluster. • ε: increase in the intensity inside the cluster Ck,n; • N(Ck,n): number of events inside Ck,n; • μ(Ck,n): expectednumber of events inside Ck,n. • non parametric estimate forμ(Ck,n).

37. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection • Alarm or not? • A and ‘

38. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

39. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

40. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

41. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

42. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

43. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

44. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

45. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

46. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

47. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

48. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

49. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual

50. | Introduction| STCD | Problem | STCD-Sim | Metrics | Datasets | Results | Final Considerations | STCD – Space Time Cluster Detection Space Time tactual