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

Outline Introduction Problem Definition Algorithms Evaluation Conclusions

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.

Original Problem Definition

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

Problem Definition max_dis=10, min_dur=3;

Problem Definition Definition2. Let P be a mobile group with valid segments s 1, …,s n, and N denotes the number of time points in the database, the weight of P is defined as:

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 {u 2,u 3,u 4 } 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.

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.

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.

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.

Trajectory-based location DB reference_pointvelocitystart_timeend_time o1o1 (1,1)(3,1)03 (7,-11)(1,5)35 (10,-3)(4,3)69 o2o2 (2,2)(2,1)03 (2,-13)(2,6)35 (-4,5)(3,2)610 o3o3 (2,4)(3,1)03 (17.-5)(-2,4)35 (12,35)(-1,-4)58

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

How to convert location data into trajectories Dead reckoning

Determining the distance of 2 objects For trajectories of two objects o 1 and o 2 Synchronize linear pieces Calculate the distance for each time segment Object o 1 : Object o 2 :

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:

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)

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

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.

Apriori Trajectory-based Group Pattern Mining

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)

An example

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

We compare the other two methods for handling untraceable intervals for objects Pessimistic Linear Performance metrics

Performance Evaluation

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