1. The Tornado Model: Uncertainty Model for Continuously Changing Data Byunggu Yu 1, Seon Ho Kim 2, Shayma Alkobaisi 2, Wan Bae 2, Thomas Bailey 3 Department of Computer Science National University 1 byu@nu.edu University of Denver 2 {seonkim, salkobai, wbae}@cs.du.edu University of Wyoming 3 tbailey@uwyo.edu

2. Outline Introduction Motivation Definition of CCDO Uncertainty Models –Cylinder Model (CM) – Revised Ellipse Model (REM) Tornado Uncertainty Model (TUM) Experiments Conclusion

3. Introduction An increasing number of emerging applications deal with a large number of continuously changing data objects (CCDOs) Efficient support for CCDO applications will offer significant benefit in: –mobile databases –sensor networks –environmental control To support large-scale CCDO applications, a data management system needs to: –store CCDOs –update CCDOs –retrieve CCDOs

4. Introduction Cont. Each CCDOs has: –Non-spatiotemporal properties such as ID, name, type –Spatiotemporal properties such as location, velocity Each object reports its spatiotemporal data and a database stores them

5. Introduction Cont. Challenges for CCDOs data management systems: –CCDOs spatiotemporal properties continuously change over time –Databases can only manage discrete records Missing states (in between records) form the uncertainty of the object’s history

6. Motivation As technology advances More sophisticated location reporting devices become able to report: –Locations –Higher derivatives (velocities, acceleration) Existing models utilize only some of these inputs So, why not utilize higher derivatives inputs to devise more efficient models? Approach: a 2 nd degree uncertainty model to reduce the uncertainty improve efficiency (reduce false-drop rate)

7. Definition of CCDO CCDO: data object consisting of non-temporal properties and trajectories (temporal property) Trajectory segment: connects two consecutively reported states (positions) P 1 and P 2 of the object Uncertainty region: all possible states between two reported states Uncertainty model: computational approach to manage (quantify) in-between states Snapshot: all possible states at a specific time t

8. Snapshot Definition dimension i t2t2 t1t1 time (i.e., dimension d+1) ee e ee P1P1 P2P2 P2P2 P1P1 eee Snapshot t

9. Cylinder Model (CM) CM (Trajcevski et al.) models the uncertainty region as a cylindrical body: –End points P 1 and P 2 of a trajectory segment are associated with a circle –Radius of the circle r is called the uncertainty threshold; –Using the maximum velocity M v, CM calculates the maximum displacement

10. CM Cont. time (i.e., dimension d+1) ee ee r r dimension i r r t2t2 t1t1 P2P2 P1P1

11. Revised Ellipse Model (REM) REM models the uncertainty region as the intersections of two funnels: –End points P 1 and P 2 of a trajectory segment are associated with a circle –Radius of the circle r is the instrument and measurement error e –Using the maximum velocity M v, REM calculates the maximum displacement as a linear function of time

12. REM Cont. time (i.e., dimension d+1) ee ee P1P1 P2P2 dimension i t2t2 t1t1

13. Snapshot of REM Given: –P 1 reported at t 1 –P 2 reported at t 2 –Measurement and instrument error e –Maximum velocity M v Snapshot of REM at time t is:

14. Tornado Uncertainty Model (TUM) TUM models the uncertainty region as the intersections of two funnels of degree 2: –End points P 1 and P 2 of a trajectory segment are associated with a circle –Radius of the circle r is the instrument and measurement error e –Using the maximum velocity M v, and maximum acceleration M a, TUM calculates the maximum displacement as a non-linear function of time

15. Definitions for TUM Given a velocity v, acceleration a and time t, TUM defines a 1 st degree and 2 nd degree displacement as follows:

16. TUM Cont. t2t2 t1t1

17. Snapshot of TUM Snapshot of TUM at time t is:

18. Domain of Acceleration All possible accelerations is defined by a hyper circle with a constant radius M a MaMa Set of possible actual acceleration

19. Example A car moving in 2D space from P 1 at time t 1 to P 2 at time t 2, calculate the uncertainty region (area) at a given time t = 6 between t 1 and t 2 : P1P1 P2P2 E(P 1,6) E(P 2,6)

20. Experiments (settings and data set) Using a portable GPS device that records every second A car with GPS drove from north of Denver to Loveland in Colorado, USA Collected (longitude, latitude, time) every second: –Straight movement on highway –Winding movement in a city area Settings: –Maximum velocity: M v = 50 m/s –Maximum acceleration: M a = 2.78 m/s 2

21. Experiments Cont. Percentage Reduction Comparison of TUM and REM with 20 sec fixed interval (TI=20) Uncertainty Volume

22. Experiments Cont. Percentage Reduction Comparison of TUM and REM with random interval (5<TI<35) Uncertainty Volume

23. Experiments Cont. TI Range in Seconds Average % Reduction 5-1099.25 11-1598.41 16-2096.40 21-2593.94 26-3088.22 30-3587.71 Varying time interval (TI)Varying maximum acceleration M a The average percentage reduction of uncertainty volume Max. Acceleration (M a ) Average % Reduction 1094.30 2081.79 3069.26 4058.90 5051.66 6046.30

24. Conclusion Proposed a 2 nd degree uncertainty model, The Tornado Uncertainty Model (TUM) that: –Used Maximum Velocity and Maximum Acceleration to calculate the maximum displacement as a non-linear function of time –Minimized the Uncertainty Region Experimental results showed: –TUM reduced the uncertainty volumes by more than an order of magnitude compared to REM Expected future results: –TUM model combined with an efficient MBR indexing will reduce the rate of false drops in the filtering-refinement steps of query processing

25. Thank You!