1. Effectively Indexing Uncertain Moving Objects for Predictive Queries School of Computing National University of Singapore Department of Computer Science Aalborg University 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 0.1 0.2 0.5 00.250.50.751 0.25 0.5 0.75 1 -0.2-0.1 00.10.2 -0.1 0 0.1 0.2 Location distributionVelocity distribution  Cells with non-zero probabilities

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 of o i, update time t u, query time t –derive a new location distribution for object o i at near- future time t Solutions –Rectangle inference –Monte Carlo simulation

13. Rectangle Inference 0.5 00.250.50.751 0.25 0.5 0.75 1 -0.2-0.1 00.10.2 -0.1 0 0.1 0.2 Location distributionVelocity distribution 0.1 0.2 0.5

14. Rectangle Inference 0.5 00.250.50.751 0.25 0.5 0.75 1 -0.2-0.1 00.10.2 -0.1 0 0.1 0.2 Location distributionVelocity distribution

15. Rectangle Inference 00.250.50.75 0.25 0.5 0.75 1 tutu 00.250.50.75 0.25 0.5 0.75 1 t u + 1 00.250.50.75 0.25 0.5 0.75 1 t u + 2 0.5 111 IR 1 0.35 IR 2 0.15 0.25 0.6 0.25 0.6 0.7 0.35 IR 3 0.245 IR 4 0.105 IR 5 0.105 IR 6 0.045

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. B x -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 t ref 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 00.10.2 -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 –k th highest lower bound > any other upper bound –accumulated probability = 1 q 

25. k-PNN Query q  PC(o 1,q,3  ) = 0.8 PC(o i,q,r) Probability of o i belonging to circle centered at q with radius r PR(o i,q,r 1,r 2 ) (r 1 < r 2 ) Probability of o i belonging to ring centered at q with radius between r 1 and r 2 o1o1 PR(o 1,q, ,2  ) = 0.2 PR(o 1,q,2 ,3  ) = 0.6

26. k-PNN Query q  iterationobjectacc i low i up i iterationobjectacc i low i up i iteration 2 iterationobjectacc i low i up i iteration 2 o1o1 0.2 1 iterationobjectacc i low i up i iteration 2 o1o1 0.2 1 o2o2 000.8 iterationobjectacc i low i up i iteration 2 o1o1 0.2 1 o2o2 000.8 o3o3 00 iterationobjectacc i low i up i iteration 2 o1o1 0.2 1 o2o2 000.8 o3o3 00 iteration 3 o1o1 0.80.4160.488 o2o2 0.60.1080.18 o3o3 0.10.0080.08 iterationobjectacc i low i up i iteration 2 o1o1 0.2 1 o2o2 000.8 o3o3 00 iteration 3 o1o1 0.80.4160.488 o2o2 0.60.1080.18 o3o3 0.10.0080.08 iteration 4 o1o1 10.42 o2o2 0.90.108 o3o3 0.80.008 PC(o 1,q,2  ) = 0.2 PC(o 2,q,2  ) = 0 0.2  1  10.2 + 0.8  1  1 0  0.8  1 0 + 0.8  1  1 PR(o 1,q,3 ,4  ) = 0.2 PC(o 1,q,3  ) = 0.2 + 0.6 0.2 + 0.6  0.4  0.90.416 + 0.2  0.4  0.9 1-PC(o 1,q,2  ) = 0.81-PC(o 1,q,3  ) = 0.2 PR(o 1,q, ,2  ) = 0.2 o1o1 PR(o 1,q,2 ,3  ) = 0.6 PR(o 2,q,2 ,3  ) = 0.6 1-PC(o 2,q,2  ) = 11-PC(o 3,q,2  ) = 1 o3o3 PR(o 3,q,2 ,3  ) = 0.1 1-PC(o 2,q,3  ) = 0.41-PC(o 3,q,3  ) = 0.9 o2o2 PR(o 2,q,3 ,4  ) = 0.3PR(o 3,q,3 ,4  ) = 0.7

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 B x -tree Processing probabilistic range and nearest neighbor queries

34. Thank You!