Effectively Indexing Uncertain Moving Objects for Predictive Queries

1. Effectively Indexing Uncertain Moving Objects for Predictive Queries Meihui Zhang, Su Chen, Christian S. Jensen, Beng Chin Ooi, Zhenjie Zhang

2. Outline • Introduction • Uncertain Moving Object Model • Movement Inference Model • Indexing and Query Processing • Index structure • Probabilistic Range Query • k-PNN Query • Experiments • Conclusion

3. Outline • Introduction • Uncertain Moving Object Model • Movement Inference Model • Indexing and Query Processing • Index structure • Probabilistic Range Query • k-PNN Query • Experiments • Conclusion

4. Introduction • Trends and applications • Positioning Systems, Wireless Communication, etc. • Intelligent Transport Systems, Location-Based Services, etc.

5. Motivation • Existing work on moving object management Assumption: deterministic movement • Real world • Limited accuracy • Complex and stochastic movement • … School bus in Athens metropolitan

6. Motivation • Problem • Information gap between real movement and deterministic models • Solution • Introduce an uncertainty model

7. Our contributions • Uncertain moving object model • Take into account the uncertainties of both location and velocity • Movement inference model • Infer the location distribution at t • Ease of integration into existing index structures • Indexing • Query processing

8. Outline • Introduction • Uncertain Moving Object Model • Movement Inference Model • Indexing and Query Processing • Index structure • Probabilistic Range Query • k-PNN Query • Experiments • Conclusion

9. Uncertain Moving Object Model • Discrete timestamps • 2-D moving objects • Uncertain moving object representation • Distributions • Instead of exact values

10. Distribution Representation • Distribution • Domain discretization • Probability assigned to each cell • Uniform distribution assumption in each cell Cells with non-zero probabilities 1 0.2 0.75 0.1 0.2 0.5 0 0.1 0.5 0.25 -0.1 0.2 0 0.25 0.5 0.75 1 -0.2 -0.1 0 0.1 0.2 Location distribution Velocity distribution

11. Outline • Introduction • Uncertain Moving Object Model • Movement Inference Model • Indexing and Query Processing • Index structure • Probabilistic Range Query • k-PNN Query • Experiments • Conclusion

12. Movement Inference Model • Location distribution prediction • given the location and velocity distributions ofoi , update time tu, query time t • derive a new location distribution for object oiat near-future time t • Solutions • Rectangle inference • Monte Carlo simulation

13. Rectangle Inference 1 0.2 0.75 0.1 0.2 0.5 0 0.1 0.5 0.5 0.25 -0.1 0.2 0 0.25 0.5 0.75 1 -0.2 -0.1 0 0.1 0.2 Location distribution Velocity distribution

14. Rectangle Inference 1 0.2 0.75 0.1 0.5 0 0.5 0.25 -0.1 0 0.25 0.5 0.75 1 -0.2 -0.1 0 0.1 0.2 Location distribution Velocity distribution

15. Rectangle Inference tu tu+ 1 tu+ 2 1 1 1 0.75 0.75 0.75 IR3 0.245 IR4 0.105 IR5 0.105 IR6 0.045 0.5 0.5 0.5 IR1 0.35 IR2 0.15 0.5 0.25 0.25 0.25 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 0.6 0.6 0.25 0.25 0.25 0.35 0.6 0.7

16. Monte Carlo Simulation • Randomized method to simulate the motion • Error rate  , confidence , simulation number N • For each simulation • Initial step: selects a random location • following steps: pick up a velocity • final step: returns location • Estimate the location distribution with the simulation results

17. Outline • Introduction • Uncertain Moving Object Model • Movement Inference Model • Indexing and Query Processing • Index structure • Probabilistic Range Query • k-PNN Query • Experiments • Conclusion

18. Bx-Tree • Use B+-tree to index moving objects • Space filling curve • 2-D location 1-D key value • 2-D range query  Several 1-D range queries

19. Indexing Uncertain Moving Objects • Index structure • Time domain partition • Two sub-trees • Reference time • Sub-trees roll over • Index each location cell with non-zero probability along with the probability and velocity distribution info

20. Indexing Uncertain Moving Objects • Index update • Insertion • Identify the sub-tree in which to insert • Infer the location distribution at tref • Insert the spatial cells with non-zero probabilities • Deletion • Locate the record in data file • Identify the sub-tree • Infer the location distribution • Delete from the index

21. Velocity-Based Partitioning • Uncertain  larger query expansion • Tighten velocity bound s.t. decrease query expansion • Velocity Minimal Bounding Rectangle (VMBR) • Partition each sub-tree into K logical sub-trees • reduce VMBRs recorded at each sub-tree root 0.2 0.1 0 -0.1 -0.2 -0.1 0 0.1 0.2

22. Query Processing • Probabilistic Range Query • Given a spatial range R, a query time t, and a threshold θ, the probabilistic range query returns all uncertain moving objects falling into R with probability no smaller than θ at time t • Top-k Probabilistic NN Query(k-PNN) • Given a query location q and a query time t, the k-PNN query returns k uncertain moving objects with the highest probabilities of being the nearest neighbor of q

23. Probabilistic Range Query • Growing step • Issue range query on index • Construct a candidate object list • Verification step • Rectangle inference works as a filter • Monte Carlo Simulation verifies

24. k-PNN Query • Issue a series of circular region range queries • Maintain • lower bound • upper bound • accumulated probability • Terminate • kth highest lower bound > any other upper bound • accumulated probability = 1 q 

25. k-PNN Query PC(o1,q,3) = 0.8 PR(o1,q,,2) = 0.2 PR(o1,q,2,3) = 0.6 • PC(oi,q,r) • Probability of oi belonging to circle centered at q with radius r • PR(oi,q,r1,r2) (r1< r2) • Probability of oi belonging to ring centered at q with radius between r1and r2 o1 q 

26. k-PNN Query PR(o1,q,2,3) = 0.6 0 + 0.8  1  1 PC(o2,q,2) = 0 0  0.8  1 PR(o1,q,,2) = 0.2 PR(o1,q,3,4) = 0.2 PC(o1,q,2) = 0.2 0.2  1  1 0.2 + 0.8  1  1 PC(o1,q,3) = 0.2 + 0.6 1-PC(o1,q,3) = 0.2 1-PC(o1,q,2) = 0.8 PR(o2,q,2,3) = 0.6 o1 q  PR(o3,q,2,3) = 0.1 o2 o3 1-PC(o2,q,2) = 1 1-PC(o2,q,3) = 0.4 1-PC(o3,q,2) = 1 1-PC(o3,q,3) = 0.9 PR(o2,q,3,4) = 0.3 PR(o3,q,3,4) = 0.7 0.2 + 0.6  0.4  0.9 0.416 + 0.2  0.4  0.9

27. Outline • Introduction • Uncertain Moving Object Model • Movement Inference Model • Indexing and Query Processing • Index structure • Probabilistic Range Query • k-PNN Query • Experiments • Conclusion

28. Experiments • Synthetic data • Uniformly distribute locations • Randomly select directions and speeds • Model uncertainty by Gaussian distribution • Performance study • Certain model vs. uncertain model • Efficiency tests

29. Certain Model vs. Uncertain Model • Certain model • Simple linear motion function • Average velocity and location • Measurement • Recall • Precision

30. Certain Model vs. Uncertain Model • Varying probability threshold (a) Recall (b) Precision

31. Efficiency Tests • Range query size • NP-tree: index w./o. velocity partition • VP-tree: index w. velocity partition (a) I/O cost (b) CPU cost

32. Efficiency Tests • Range query time • NP-tree: index w./o. velocity partition • VP-tree: index w. velocity partition (a) I/O cost (b) CPU cost

33. Conclusion • Inferring current/near-future uncertain locations from past uncertain velocity and location information • Indexing the uncertain moving objects by means of an adapted Bx-tree • Processing probabilistic range and nearest neighbor queries

34. Thank You!