Continual Neighborhood Tracking for Moving Objects

1. Continual Neighborhood Tracking for Moving Objects Using Adaptive Distances Yoshiharu Ishikawa Hiroyuki Kitagawa Tooru Kawashima University of Tsukuba, Japan {ishikawa,kitagawa}@is.tsukuba.ac.jp

2. Organization • Background and Overview • Our Approach • Experiments • Query Processing with Spatial Indexes • Incremental Query Update • Conclusions and Future Work

3. Background • Progress of Digital Cartography • Development of GPS Technologies • Wide Use of PDA and Hand-held Devices New Types of Information Services: Providing neighborhood information to moving objects (people with PDAs, cars with navigation systems) considering their locations and trajectories

4. Motivating Example (1) Neighborhood Query: A user at point x wants to find nearby gas stations Typical Approach: retrieve gas stations with their distances less than 200 meters from x x A spatial query based on the Euclidean distance

5. past trajectory future trajectory Motivating Example (2) What’s Wrong? If we know user’s past and future trajectories, we can provide more appropriate information A

6. Our Idea (1) • Use of an ellipsoid region to represent a neighborhood query • An ellipsoid region is computed based on the past/future trajectories • A neighborhood query is specified as a spatial query with an ellipsoid distance A

7. At each sample position, a spatial query is generated initial query parameters start point destination : sampled estimated positions of the moving object destination start point Our Idea (2) Neighborhood Info Retrieval System : Data objects • Sample positions are taken by unit-time basis • The system perform queries continuously

8. Problems and Solutions • How can we generate appropriate spatial queries? • Introduction of influence model of trajectory points • Proposal of query derivation models • How about efficiency? • Use of spatial indexes for efficient query processing • Low-cost query update procedure for continuous queries

9. Organization • Background and Overview • Our Approach • Influence model of trajectory points • Query derivation model • Experiments • Query Processing with Spatial Indexes • Incremental Query Update • Conclusions and Future Work

10. Representation of LocationInformation (1) • Object locations are represented by d-D vectors : no. of dimensions

11. Representation of LocationInformation (2) • Locations of a moving object: : departure time : current time : estimated arrival time destination current point start point Assumption: past/future trajectory points are given in unit-time basis

12. current position Influence Model of Trajectory Points (1) • We usually set high importance on current neighborhood points

13. current position Influence Model of Trajectory Points (2) • A user may be interested in near future neighborhood where he or she will arrive soon

14. Influence Model of Trajectory Points (3) • The influence model sets the highest weight “1” on location information at time t =  + s(s unit times after the current time ) • The influence values decay exponentially towards past and future with parameters m and n, respectively Influence Value time τ+σ－2 τ+σ τ+σ+2 τ+σ－1 τ+σ+1

15. Influence Model of Trajectory Points (4) • Influence value for each point when s = 1 nt’-1 nt’-2 m m2 1 n destination mt mt+1 current point n2 highest weight point since s = 1 start point

16. Organization • Background and Overview • Our Approach • Influence model of trajectory points • Query derivation model • Experiments • Query Processing with Spatial Indexes • Incremental Query Update • Conclusions and Future Work

17. D q Query Derivation Model • Neighborhood queries for moving objects are issued to a spatial database • A spatial query is fixed specifying • query center q • two models (cur, avg) • distance function D • three models (EU, OV, HB) • query task • range query and k-nn query

18. query center q Derivation of Query Centers (1) • Model cur: set the point with the highest importance to the query center current position

19. Derivation of Query Centers (2) • Model avg: weighted average based on influence values Setting of parameters m and n changes the query center current position query center q

20. D q Query Derivation Model • Neighborhood queries for moving objects are issued to a spatial database • A spatial query is fixed specifying • query center q • two models (cur, avg) • distance function D • three models (EU, OV, HB) • query task • range query and k-nn query

21. Distance Function Derivation Models (1) • Model EU: Euclid distance-based model • Pros • - simple and intuitive • - easy to compute • Cons • - do not consider past/future • - trajectory information

22. Ellipsoid Distance Appropriate setting of the distance matrix A allows flexible tuning of distances We derive an appropriate matrix A using past/future trajectory information

23. Distance Function Derivation Models (2) • Model OV: ellipsoid distance-based model derive a distance matrix M that reflects the sample point distribution nearby the query point [19] C is the weighted covariance matrix

24. Distance Function Derivation Models (3) • Model OV: ellipsoid distance-based model • pros • allows retrieval along the trajectory since the derived distance is an extended version of the Mahalanobis distance [8, 20] • cons: not robust compared to the Euclidean distance • When an object is moving along a straight line or staying in some place, the matrix C becomes an ill-conditioned matrix: therefore, we cannot derive the distance matrix M!

25. regularization : unit matrix Distance Function Derivation Models (4) • Model HB: hybrid model • integrates the benefits of EU and OV models becomes an regular matrix

26. D q Query Derivation Model • Neighborhood queries for moving objects are issued to a spatial database • A spatial query is fixed specifying • query center q • two models (cur, avg) • distance function D • three models (EU, OV, HB) • query task • range query and k-nn query

27. Query Task (1) • Range Query: At each point, retrieve objects within distance e

28. Query Task (2) • k-Nearest Neighbor Query: At each point retrieve nearest k objects when k = 3

29. Organization • Background and Overview • Our Approach • Experiments • Query Processing with Spatial Indexes • Incremental Query Update • Conclusions and Future Work

30. Experiment 1: Observation of Behaviors • Query generation example for the trajectory (blue line) • Target points are shown in green points • Queries are generated based on the hybrid model

31. x Experiment 1 (1) • Comparison of Euclidean distance and ellipsoid distance

32. y modified parameters σ= 5 , μ=0.4 ν=0.4, λ= 1.0 Experiment 1 (2) • Set the “near future” point as query center initial parameters σ= 0 , μ=0.5 ν=0.5, λ= 1.0 x

33. refined parameters σ= 0 , μ=0.4 ν=0.9, λ= 1.0 Experiment 1 (3) • Set high weights on future trajectory initial parameters σ= 0 , μ=0.4 ν=0.4, λ= 1.0 x

34. refined parameters σ= 0 , μ=0.4 ν=0.4, λ= 0.7 Experiment 1 (4) • Use of the regularization parameter l initial parameters σ= 0 , μ=0.4 ν=0.4, λ= 1.0 x

35. Experiment 2: Simulation Based on Trace Data (1) • Car driving trace data is used to compute queries

36. Experiment 2: Simulation Based on Trace Data (2) • Each isosurface represents the query generated at the point

37. Organization • Background and Overview • Our Approach • Experiments • Query Processing with Spatial Indexes • Incremental Query Update • Conclusions and Future Work

38. Query Processing Based on Spatial Indexes • Most of spatial indexes do not support ellipsoid distance-based queries • We extend the approach of Seidl & Kriegel [30] to support ellipsoid distance-based queries with conventional spatial indexes • Assumptions: only three generic retrieval functions are supported by the underlying spatial indexes

39. r Generic Retrieval Functions (1) • rect_search(r): retrieve objects within the specified rectangle region r

40.  Generic Retrieval Functions (2) • dist_search(q, ):retrieve objects within distance e from q using the Euclidean distance

41. Generic Retrieval Functions (3) • knn_search(q, k): retrieve nearest k objects from the query center q using the Euclidean distance

42. Minimal Bounding Box (MBB) for Ellipsoid Isosurface [30] • MBB that tightly encloses the ellipsoid ellip(M, q, e) ellip(M, q, e) j-th dimension : (i, i) element of the inverse of M i-th dimension

43. Minimal Bounding Sphere (MBS) for Ellipsoid Isosuraface [30] • MBS that tightly encloses the ellipsoid ellip(M, q, e) ellip(M, q, e) : the smallest eigenvalue of M

44. e Query Processing (1) • Range query processing with MBB approximation

45. e Query Processing (1) • Range query processing with MBB approximation

46. Query Processing (2) • k-NN query (k = 3)

47. Query Processing (2) • k-NN query (k = 3) • Perform k-NN query • based on the Euclidean • distance 2. Derive an ellipsoid that tightly encloses k-NN objects 3. Perform a range query with MBS (or MBB) that tightly encloses the ellipsoid region 4. Select nearest k objects from the retrieved objects using the ellipsoid distance

48. Experiment: Retrieval I/O Cost with Spatial Indexes (1) • I/O cost evaluation using R-tree (GiST) • Target dataset (green points): 39,226 crossroad points of Maryland County in U.S. • Query: 62 blue points along the road • I/O costs are compared for • sequential scan • ellipsoid distance query with the support of spatial indexes • k-NN (k = 1, 10, …, 150) results are shown

49. Experiment: Retrieval I/O Cost with Spatial Indexes (2) • Average page I/O cost per query

50. Organization • Background and Overview • Our Approach • Examples • Query Processing with Spatial Indexes • Incremental Query Update • Conclusions and Future Work