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Algorithms for Movement Patterns

Joachim Gudmundsson. Algorithms for Movement Patterns. This talk. Focus on algorithms (with a provable bounds) and various models. Other communities: Data mining Data bases GIS Visualization Geography. Input.

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Algorithms for Movement Patterns

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  1. Joachim Gudmundsson Algorithms for Movement Patterns

  2. This talk • Focus on algorithms (with a provable bounds) and various models. • Other communities: • Data mining • Data bases • GIS • Visualization • Geography

  3. Input Data: a sequence of (x, y, z, t) - coordinates (points) and a time stamp for example GPS data, mobile phone, radar…

  4. Data collection - 2005

  5. Data collection - 2010

  6. Scientific challenge • Find definitions of movement patterns that are: • Useful and • 2. “Computable”

  7. Movement patterns • The REMO framework: • defined a collection of spatio-temporal patterns based on location, motion and direction. • Patterns: flock, leadership, convergence and encounter • Laube and Imfeld, 2002 & 2003 • Laube, van Kreveld and Imfeld, 2004 • Laube, Imfeld and Weibel, 2005 • G, van Kreveld and Speckmann, 2005

  8. REMO model convergence encounter flock Assumption: Fixed direction and constant speed

  9. Flocks & meetings

  10. Kalnis, Mamoulis & Bakiras, 2005 G. & van Kreveld, 2006 Benkert, G., Hubner & Wolle, 2006 Jensen, Lin & Ooi, 2007 Al-Naymat, Chawla & G., 2007 Vieria, Bakalov & Tsotras, 2009 ... Flocks and a new model t2 t3 t4 t1

  11. Flocks and a new model Time = 0 1 2 3 4 5 6 7 8 m = 3

  12. Patterns in trajectories fixed subset variable subset flock meet examples for m = 3

  13. Leadership & followers

  14. front Leadership - definition • A leader? • - Should not follow anyone else! • Is followed by at least m • other entities. • For a certain duration. Andersson, G., Laube & Wolle, 2007

  15. Popular places

  16. Popular place - convergence A region is a popular place if at least k entities visit it. σ σ is a popular place for k  5 Benkert, Djordjevic, G. & Wolle, 2007 ?, ? & ?. ????

  17. Convoy

  18. Convoy m – integer e – distance threshold p directly density–reachable from q  e pNHe(q) q p p,q density connected |NHe(p)|m q p x p & q density-reachable from x Jeung, Yiu, Zhou, Jensen & Shen, 2008Jeung, Shen & Zhou, 2008

  19. Convoy A group of objects forms a convoy C if every pair of objects are density connected. Jeung, Yiu, Zhou, Jensen & Shen, 2008Jeung, Shen & Zhou, 2008

  20. Similarity…

  21. Similarity…measurements Agrawal, Lin, Sawhney & Shim, 1995 Alt & Godau, 1995 Yi, Jagadish & Faloutsos, 1998 Gaffney & Smyth, 1999 Kalpakis, Gada & Puttagunta, 2001 Vlachos, Gunopulos & Kollios, 2002 Gunopoulos, 2002 Mamoulis, Cao, Kollios, Hadjieleftheriou, Tao & Cheung, 2004 Chen, Ozsu & Oria, 2005 Nanni & Pedreschi, 2006 Van Kreveld & Luo, 2007 Gaffney, Robertson, Smyth, Camargo & Ghil, 2007 Lee, Han & Whang, 2007 Buchin, Buchin, van Kreveld & Luo, 2009 Agarwal, Aranov, van Kreveld, Löffler & Silveira, 2010 ...

  22. Fréchet Distance Fréchet Distance measures the similarity of two curves. Dog walking example • Person is walking his dog (person on one curve and the dog on other) • Allowed to control their speeds but not allowed to go backwards! • Fréchet distance of the curves: minimal leash length necessary for both to walk the curves from beginning to end

  23. Fréchet Distance • Fréchet Distance • where α and β range over continuous non-decreasing reparametrizations only • Well-suited for the comparison of trajectories since they take the continuity of the curves into account

  24. Free Space Diagram • Decision version • Is the Frechet distance between two paths at most ε? • Build a free space diagram! [Alt & Godau’95] i α (i,j) (i,j) 1 0 ε 1 2 3 4 5 6 α j [stolen from Brakatsoulas, Pfoser, Wenk and Salas]

  25. Free Space Diagram If there exists a montone path in the free-space diagram from (0, 0) to (p, q) which is monotone in both coordinates, then curves P and Q have the Fréchet distance less than or equal to ε (p,q) (0,0)

  26. Single File Intuitively easy to define Hard to define formally!

  27. Single File Intuitively easy to define Hard to define formally!

  28. Single file We say that the entities a1, … , am are moving in single file for a given time interval if during this time each entity aj+1 is following behind entity aj for j = 1, … ,m-1. Following behind? Time t  Time t’  [t+min,t+max]

  29. Free Space Diagram and Following Behind The time lag means that the path will be restricted to a “diagonal” strip! min max

  30. Extending the free space diagram

  31. Extending the free space diagram Buchin, Buchin & G., 2010

  32. Clustering subtrajectories Buchin, Buchin, G., Löffler & Luo, 2010

  33. Trajectory compression

  34. point (x,y) Problem • where-at(T,t): • location of e at time t. time t • when-at(T,(x,y),L): • time at which e is within • distance L of (x,y). Cao, Wolfson & Trajcevski, 2003 Meratnia & de By, 2004 Benkert, G., Hubner & Wolle, 2007

  35. 7 7 7 6? 6 6 5 2 2 2 4 3 1 1 1 Path simplification Input path Traditional path simplification Aim

  36. Basic tools • Median trajectory: • Buchin, Buchin, van Kreveld, Löffler, Silveira, Wenk & Wiratma, 2010 • Regular patterns: • Hadjieleftheriou, Kollios, Tsotras & Gunopulos, 2006 • Djordevic, G., Pham & Wolle, 2009 • Trajectory compression: • Cao, Wolfson & Trajcevski, 2003 • Meratnia & de By, 2004 • Benkert, G., Hubner & Wolle, 2007 • Trajectory segmentation • M. Buchin, Driemel, van Kreveld & Sacristan, 2010 • Subtrajectory query efficiently • de Berg, Cook IV, G. & Haverkort, 2011

  37. Questions?

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