Shape-based Similarity Query for Trajectory of Mobile Object

1. Shape-based Similarity Query forTrajectory of Mobile Object NTT Communication Science Laboratories, NTT Corporation, JAPAN. Yutaka Yanagisawa Jun-ichi Akahani Tetsuji Satoh “Rickshaw” (NARA/KYOTO)

2. / 31 Background • The Recent technologies allow us to track moving objects using highly accurate positioning devices. • There are many applications using such location information have been developed. • Navigation Systems, Location-based Information Systems, etc. Digital City Kyoto: A Location-based Information System A Navigation System

3. / 31 Motion Pattern Analysis • Motion pattern analysis is one of the most interesting technologies of these applications. • By analyzing their motion patterns, it is possible to extract the behavioral characteristics of moving objects. • The applications can predict the future behavior of the moving objects using extracted characteristics. • Single Motion Analysis • focuses on the statistical characteristics of a moving object. • Relative Motion Analysis • focuses on the similarity between motion patterns. We discuss the approach based on the similarity of trajectory shapes because it is a simple and intuitive approach.

4. B C It retrieves trajectories that are similar to A … A D It is possible to predict the future route of the new visitor. Entrance Exit / 31 Similarity of Trajectory Shapes • This approach is called shape-based approach. An example of an information providing system. Exhibition hall The trajectories of visitors are stored in a database. Show informationabout B, C, and D.

5. / 31 Problem • However, there are few database systems which can searchtrajectories based on shapes. • Many database systems retrieve moving objects based on only “distance”. The minimum distance between L and L2 is less than the distance between L and L1. However, L2 is more similar in shape to L than L1 intuitively. Y L L1 L2 D2 D1 Not appropriate for shape-based approach X

6. / 31 Our Approaches • We propose a shape-based similarity query for searching trajectories from moving object databases. • Moreover, we present an efficient indexing method for retrieving moving objects based on our proposed query.

7. Shape-based Similarity Query

8. / 31 Data Model for Trajectory • In real world, a trajectory of a moving object can be modeled as a continuous line in space. • However, positioning devices can not track a moving object continuously. • In our work, a trajectory is stored as a sequence of points (discrete line) in databases. • This model is used as a popular data model. In Real World In Databases

9. / 31 A Similarity of Time Series Data • The key idea have been proposed in the technique for time series database. • The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space. W = <w1, w2, …, w9> W’ = <w’1, w’2, …, w’9> x x (n=9) D(W, W’) w9 w2 w1 w’9 w’1 t8 t t1 t

10. Distance between W and W’ is 5 = 3 4 0 3 2 2 1 2 1 / 31 A Similarity of Time Series Data • The key idea have been proposed in the techniques for time series database. • The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space. W = <2, 3, 4, 3> W’ = <1, 1, 2, 3> 5 4 3 2 1

11. W = <2, 2, 2, 3> W’ = <2, 2, 2, 3> 5 4 3 2 1 Smaller distance means higher similarity / 31 A Similarity of Time Series Data • The key idea have been proposed in the techniques for time series database. • The similarity between two time series data is defined as the Euclidean distance between the points in n dimensional space. In this case, the distance is zero.

12. / 31 A Similarity of Time Series Data • The distance fits to intuitive similarity of line shapes. • There is aneffective search algorithm to calculate this distance. • We will extend the similarity for trajectory in 2 or more dimensional space.

13. Y p7 p’7 l l’ p1 p’1 X / 31 Our Proposed Similarity of Trajectories • The similarity of trajectories can be defined as an extension of the distance of time series data. • The distance can be given as the following expression.

14. ＋ Stored trajectories A given trajectory Answer trajectories / 31 Shape-based Similarity Queryfor Trajectories • We define a shape-based similarity query for trajectories as a subsequence matching query. • Because the length of trajectories are often difference. SSQ(L, l, q) L: A set of stored trajectories in database. l: A trajectory to be compared. q: The distance from l. Answer La: A set of sub-trajectories

15. A Given Trajectory / 31 Shape-based Similarity Queryfor Trajectories An Answer Sub-Trajectory • The database calculates the distance between the given trajectory l and each sub-trajectory. • If the distance is less than the given distance q, the database adds the sub-trajectory to the answer set of trajectories La.

16. Indexing

17. / 31 Approach • The existing spatial structures are appropriate for retrieving an object based on the distance. • However, these structures have no method for searching the data based on the similarity between trajectories. We extend the spatial data structure for our proposed query.

18. x t / 31 An Efficient Calculation Processfor the Shape-based Similarity: 1 • The essential idea was presented as a PAA: Piecewise Aggregate Approximation [Keogh01]． • PAA is an efficient method of approximating the time series data for a similarity search. Using the `average sequences’ of a sub-sequences. x (N=3) W W ‘ t

19. / 31 An Efficient Calculation Processfor the Shape-based Similarity: 2 • The distance between the average sequences is the lower bound of the distance between the original two sequences. x D( W, W’) D( W, W’) W W’ By comparing average sequences, we can know the lower bound of the distance between original sequences. t t

20. The distance between thesecenter points is the lower bound of the original distance. Y Calculating center points X / 31 An Efficient Calculation Processfor the Shape-based Similarity: 3 • In the case of trajectories, the distance between the center points of trajectories is the lower bound of the distance between the original trajectories. v1 Y L v’1 L’ v7 v’7 X

21. The center point offrom p5 to p8 The center point offrom p1 to p4 / 31 Combination of PAA and Spatial Data Structure: 1 • For making indexes, the database calculates the center points of sub-trajectories. • The length of each sub-trajectory must be fixed to the system parameter N. • In this example, N is four. l Y Y p8 l p7 p6 p5 p3 p4 p2 p1 X X

22. Y Y Y X X X / 31 Combination of PAA and Spatial Data Structure: 2 • Next, the database makes indexes to the points using a traditional spatial data structure. • Our implemented system makes an index to every center point using R+-Tree. The database can search objects based on the similarity of trajectories using the spatial data structure. Normal R+-Tree Our Proposed Index Structure

23. / 31 Query Processing: 1 • When a SSQ(L,lQ,q) is given, the database calculates the center point of lQ at first. • Suppose that the length of stored center points is fixed to 4 (N=4) in the following example. If a query SSQ(L,lQ,q) is given.. pQ is the center point of a given trajectory. Y Y lQ pQ X X

24. / 31 Query Processing: 2 • Next, the database searches stored points within the distance q from the calculated point pQ using the spatial data structure. Y An index tree (R+-Tree) A A Candidate points C B B C pQ X The region within the distance q from pQ

25. If , l1 is added to La / 31 Query Processing: 3 • Finally, the database checks the distance between a given trajectory lQand each candidate trajectory. • If the distance is less than a given threshold q, the candidate trajectory is added to the answer set La. Y p2 Y lQ pQ l1 p1 X l1 is the original trajectory of p1.

26. Performance Study

27. / 31 Performance Study • We conducted an experiment for evaluating our proposed query and indexing method. • Measuring the processing time for retrieving trajectories required by a shape-based similarity query. • For this evaluation, two types of trajectories are stored in a database. • tracked by GPS and generated by a simulator. We compared the processing time using both methods: • Our indexing method, • A spatial data structure (R+-Tree).

28. / 31 Trajectory Data: 1 • This is an example of trajectory data captured by GPS receivers on rickshaws (in Nara city). • Rickshaw is tour guide, they work in Nara / Kyoto. A trajectory of a rickshaw in all day A GPS Receiver (eTrex/GARMIN) Rickshaw

29. / 31 Trajectory Data: 2 • This figure displays trajectories generated by our implemented simulator. The simulator can generate trajectoriessuch that people walk on a plane freely. Velocity and direction of each object are given as random values. But the changes of these values are slow and continuous.

30. Length of lQ (=N) / 31 The Result of the Experiment The processing time to calculate 10 random queries is displayed: Using our index structure Using R+-Tree Amount of Stored Points For retrieving longer trajectories from stored data, our proposed method has high advantages to existing methods.

31. / 31 Conclusions • We have proposed a shape-based similarity query to find moving objects. • Database users can find moving objects for analyzing their motion patterns. • Moreover, we have presented an effective indexing method to search for the trajectories required by our proposed queries. • We demonstrated the advantage of our proposed method to existing spatial data structures.

32. / 31 Future Work • We will evaluate our proposed method using these data. • [Human Tracking by using Laser Scanners] • University of Tokyo(Dr. Zhao and Prof. Shibasaki) • Captured at Geoinformation Forum Japan 2002 (32.096 people visited) [Motion Capture Data] • Tokyo University of Technology (Creative Labo) • 76 moving points on bodies (120fps) • Playing football and judo