Mining Mobile Group Patterns: A Trajectory-based Approach

1. Mining Mobile Group Patterns: A Trajectory-based Approach San-Yih Hwang, Ying-Han Liu, Jeng-Kuen Chiu NSYSU, Taiwan Ee-Peng Lim NTU, Singapore

2. Outline • Introduction • Problem Definition • Algorithms • Evaluation • Conclusions

3. Introduction • Many ways can determine the groups an object belongs to. • Grouping based on demographics • Grouping based on purchasing behavior • Groups formed by using spatial-temporal information are useful. • Objects within a mobile group tend to closely influence one another. • Potential applications: • Construction of social network • Animal behavior study • group-based pricing models or marketing strategies • Previous work gives a precise definition about mobile groups and derives algorithms for efficiently identifying mobile groups. • Physical proximity between group members. • Temporal proximity between group members.

4. Original Problem Definition

5. Problem Definition

6. Problem Definition • Definition1. Given a group of users G, a maximum distance threshold max_dis, and a minimal time duration threshold min_dur, a set of consecutive time points [t,t+k] is called a valid segment of G if 1.All users in G are not more than max_dis apart at time t, t+1,…, and t+k; 2.Some users in G are more than max_dis apart at time t-1: 3.Some users in G are more than max_dis apart at time t+(k+1); 4.(k+1)>=min_dur

7. Problem Definition max_dis=10, min_dur=3;

8. Problem Definition • Definition2. Let P be a mobile group with valid segments s1,…,sn, and N denotes the number of time points in the database, the weight of P is defined as:

9. Problem Definition • If the weight of a mobile group exceeds a threshold min_wei, we call it a valid mobile group. • For example, if max_dist=10, min_dur=3, min_wei =50%, the mobile group {u2,u3,u4} is a valid mobile group, since it has valid segments{[1,3][6,8]} and weight 6/10>0.5. • The mobile group mining problem: Given D, max_dis, min_dur, and min_wei, find all valid mobile groups.

10. Pitfalls of the location model • To maintain accurate location tracking, the frequency of sampling users’ locations must be high. (Tracking 1000 users every second will result in 1GB per day) • In reality, moving objects may be disconnected from time to time voluntarily or involuntarily. • It is almost impossible to have perfectly synchronized sampling of users’ locations in reality.

11. Remedies • Use trajectories with untraceable periods to model user locations • The mobile group mining problem has to be redefined. • The algorithms have to be modified.

12. Trajectory model • A trajectory T is a set of piecewise linear functions, each of which maps from a disjoint time interval to an n-dimensional space. • E.g.

13. Trajectory-based location DB

14. How to convert location data into trajectories • The change point detection problem • Recursive linear regression

15. How to convert location data into trajectories • Dead reckoning

16. Determining the distance of 2 objects • For trajectories of two objects o1 and o2 • Synchronize linear pieces • Calculate the distance for each time segment Object o1: Object o2:

17. Determining the distance of 2 objects • Location of object o1 at time t: (1 + 3t , 1 + t) • Location of object o2 at time t:(2 + 2t, 2 + t) • Enclidean distance of o1 and o2 when 0t<3:

18. Determining close intervals • Given a distance function dist(t) of two objects o1 and o2 within an interval I, we would like to identify the subintervals I’ in I such that dist(t)max_dis, tI’. • E.g. • Let 3=max_dis= • [ ][0, 3)= [0, 3)

19. Definitions • For a user group P • Geographically close, far, or undecided at a time point t. • The valid close segments and valid far segments of P can be accordingly defined. • The weight of P is defined as

20. The problem • The problem is to find all valid mobile groups under such a model • Apriori property still holds • if a moble group is valid, all of its subgroup will also be valid.

21. Apriori Trajectory-based Group Pattern Mining

22. Trajectory VG-Growth • The set of valid 2-groups form a graph called VG-graph • The close and far segments of a conditional TVG graph have to be properly updated. • c(o1, o2 | o3) = c(o1, o2)∩c(o1, o3)∩c(o2, o3) • f(o1, o2 | o3) = f(o1, o2)∪f(o1, o3)∪f(o2, o3)

23. An example

25. Performance evaluation DBI: 100M100N DBII: 100M500N DBIII:100M1000N

26. Performance evaluation • We compare the other two methods for handling untraceable intervals for objects • Pessimistic • Linear • Performance metrics

27. Performance Evaluation

28. Conclusions • We have defined the mobile group mining problem on a new location model and proposed algorithms. • Future work • Correcting location measurement error • Calendar-based mobile group mining • Applications using mobile group patterns