1. Incremental Clustering for Trajectories
Zhenhui Li, Jae-Gil Lee, Xiaolei Li, Jiawei Han
Univ. of Illinois at Urbana-Champaign
DASFAA Conference 2010
April, Tsukuba, Japan

2. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

3. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

4. Tracking by GPS/Sensor is becoming more common
Vehicles
Animals
Hurricane

5. Moving object data is accumulated fast
Taxi tracking system tracks 5,000 taxis in San Francisco
Location information received each taxi every minute
After a day, 7.2 million points collected
After a week, 50.4 million points collected
...

6. Online monitoring demand
Trajectory clusters have applications in
discovering common hurricane paths
monitoring hot traffic paths
analyzing animals’ movement
As data is updated along with time, there is need to online monitor the clustering result.
But, it is inefficient to compute the trajectory clusters from scratch every time.

7. New data will only affect local shifts
The key observation is that, the new data will only affect local shifts.
Snapshot Time 1
Snapshot Time 2

8. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

9. TRACLUS: trajectory clustering
Clustering trajectories as a whole could not detect similar portions of the trajectories (i.e., common sub-trajectories)
Example: if we cluster TR1~TR5 as a whole, we cannot discover the common behavior since they move to totally different directions
Jae-Gil Lee, Jiawei Han, and Kyu-Young Whang, “Trajectory Clustering: A Partition-and- Group Framework”, in Proc ACM SIGMOD Int. Conf. on Management of Data (SIGMOD'07), Beijing, China, June 2007.
A common sub-trajectory
TR5
TR1
TR2
TR3
TR4

10. The Partition-and-Group Framework
Consists of two phases: partitioning and grouping
TR5
TR1
TR2
TR3
TR4
(1) Partition
A set of trajectories
A representative trajectory
(2) Group
A cluster
A set of line segments
Note: a representative trajectory is a common sub-trajectory

11. Partition
Identify the points where the behavior of a trajectory changes rapidly; such points are called characteristic points
A trajectory is partitioned at every characteristic point
A line segment between consecutive characteristic points is called a trajectory partition
: characteristic point : trajectory partition

12. Group Group line segments based on density
L1, L2, L3, L4, and L5 are core line segments
L2 (or L3) is directly density-reachable from L1
L6 is density-reachable from L1, but not vice versa
L1, L4, and L5 are all density-connected L1 L3 L5 L2 L4 L6
L L L L L L4
MinLns = 3

13. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

14. TCMM Framework Trajectories received along with time
Partition the trajectory into line segments
A micro-cluster stores a small group of close line segments
A macro-cluster a cluster of micro-clusters

15. Data Preprocess
Finding the optimal partitioning translates to finding the best hypothesis using the MDL principle
H  a set of trajectory partitions, D  a trajectory
L(H)  the sum of the length of all trajectory partitions
L(D|H)  the sum of the difference between a trajectory and a set of its trajectory partitions
L(H) measures conciseness; L(D|H) preciseness

16. Micro-Cluster Definition
Micro-cluster maintains a fine-granularity clustering.
Each micro-cluster holds and summarizes the information of local partitioned trajectories.
A micro-cluster for a set of directed line segments is defined as the tuple:
:number of line segments
:linear sums of the line segments’ center points, angles and lengths
:squared sums of the line segments’ center points, angles and lengths

17. Distance between Micro-Clusters
Representative line segment of a micro-cluster
Distance between two micro-clusters can be defined as the distance between representative line segments of two micro- clusters

18. Creating and updating Micro-Cluster
When a new line segment is received
Find the closest micro-cluster
If the distance is between the new line segment and its closest micro-cluster is less than threshold , add the new line segment into this micro-cluster and update the micro-cluster
If not, create a new micro-cluster, and the new micro-cluster only contains this line segment
are the center, angle, and length of this line segment
are the square of the center, angle and length of this line segment

19. Merging Micro-Clusters
Why merging micro-clusters?
If the number of micro-clusters is large, it is time-consuming to
find the closest micro-cluster when a new line segment is received
do macro-clustering over micro-clusters
And the memory might not be enough to store all the micro- clusters
Merge close micro-clusters to save storage space and save computation time
“closeness” can be simply defined as the distance between two micro-clusters
However, it does not consider the “tightness” of a micro-cluster

20. Merging Micro-Clusters (cont.)
We prefer to merge loose micro-clusters rather than tight ones to better preserve the “tightness” of micro-clusters.
Lose more information when merging two tight micro-clusters.

21. Merging Micro-Clusters (cont.)
Introducing “extent” of a micro-cluster
Extent defines the tightness of a micro-cluster in terms of center, angle and length

22. Merging Micro-Clusters (cont.)
Distance between micro-clusters with extent
Center distance
Angle distance
Length distance

23. Micro-clustering summary

24. Macro-Clustering
Macro-clustering is evoked only when it is called upon by the user
Macro-clustering is performed on the representative line segments of micro-clusters
Similar to the group step in TRACLUS framework

25. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

26. Experiment
Real taxi data in san Francisco, trajectories in a week, 100,000 points in total

27. Experiment (cont.) Effectiveness
SSQ (sum of squared distance) is the average of all the line segments to the centroid of its macro-cluster
TCMM reaches similar quality as TRACLUS

28. Experiment (cont.)
Efficiency
TCMM is much faster than TRACLUS

29. Experiment (cont.) Sensitivity with parameter:
When d_max is larger, the quality is lower but the efficiency is better

30. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

31. Conclusion
We address the problem to incrementally cluster trajectories.
We propose the TCMM (Trajectory Clustering based on Micro- and Macro-clustering) framework.
The definition of extent is proposed to better capture the “tightness” of micro-clusters.
Experiments show that TCMM achieves similar quality as TRACLUS but it is much faster.

32. Outline Motivation Introducing previous work TRACLUS
Trajectory Clustering using Micro- and Macro-clustering
Experiment
Conclusion
Future Work

33. Future Work Efficiency Parameter insensitivity Temporal information
Use an index to find closest micro-cluster
Not easy because our distance function is non-metric
Parameter insensitivity
Make our algorithm more insensitive to parameter values
Temporal information
Take account of temporal information during clustering
Other applications
Incrementally discover outliers and patterns

34. Thank you!