1. Clustering Moving Objects in Spatial Networks Jidong Chen, Caifeng Lai, Xiaofeng Meng, Renmin University of China Jianliang Xu, and Haibo Hu Hong Kong Baptist University Presented by Xiao Pan

2. 2 Outline Introduction CMON Framework Continuous Maintenance of CBs Periodical Construction of CMON Experiments Conclusions

3. 3 Introduction Clustering Moving Objects in Networks (CMON) Challenge: –For moving objects –Network distance metric Motivations and goals: –Minimize cost of clustering and its maintenance –Minimize network distance computations –Support multiple types of cluster in a single application

4. 4 Introduction How to cluster moving objects? A straightforward approach: –Periodically execute the static snapshot clustering over the entire moving objects –Expensive clustering costs Incremental clustering algorithm: –Create initial global clusters and incrementally maintain them –Expensive maintenance costs

5. 5 Introduction Applications of CMON with different criteria –Identify a convoy of cars that follow same route Minimum distance clustering –Query for dense areas of cars in the road network Density-based clustering –Assign K polices to manage K most congested areas in a road network K-partitioning clustering Whether an unified framework?

6. 6 Our Work CMON Framework –Efficiently support different clustering criteria at the same time Continuous Micro-clusters: Cluster block maintenance –As underlying clustering unit, easy to maintain –As a building block of different types of clusters Snapshot Macro-clusters: CMON construction with different definitions –Reduce the search space and avoid unnecessary computation network distance

7. 7 CMON Framework Clustering results of MO on road network Periodical construction of CMON COMN Framework Continuous maintenance of CB Construct ion of CB Predict split and merge event Process the events Minimum Distance CMON Density based CMON K- partitioning CMON Combination of CBs

8. 8 Cluster Block Assumptions: –A piecewise linear movement: stable speed at an edge segment unless updated explicitly –The route of each object (e.g. home to office) is known Definition of Cluster Blocks (CB): CB= (O, n a, n b, head, tail, ObjNum) –O={o 1,o 2,…,o i,…o n } –(n a,n b ): the edge on which the object moves –(head, tail): position of the CB –ObjNum: numbers of objects in the CB –Dd(o i,o i+1 ) ≤  (1≤i≤n-1) –o i =(n a, n b, pos i, speed, next_node)

9. 9 CB Maintenance Construct initial CBs by traversing network and maintaining their changes (e.g. splitting and merging) Main problems –How to predict splitting time of CB on road segments –How to process splitting event of CB at intersections

10. 10 Predicting Splitting Event Predicting the splitting of CB (occur in two cases) –On arriving the end of the segment –On moving along the segment when distance between any neighboring objects exceeds  Problem: the neighborhood of objects changes over time Solution: dynamically maintain the order of objects over time on the edge

11. 11 Predicting splitting time of CB Predict the initial splitting time on moving along the segment Given a threshold: 7 –Compute the leaving time te –t0: object list {o1,o2,o3,o4,o5} –t1: –t2: –t3: object list {o3,o1,o4,o2,o5} –t4 –t5 Dist(o4,o5)>7 ts is splitting time object list {o1,o3,o2,o4,o5} object list {o1,o3,o4,o2,o5} : object list {o3,o1,o4,o5,o2}

12. 12 Splitting Event Processing Splitting event on the segment Splitting event at the end of segment –A straightforward approach: one-by-one object delete and insert –Group splitting approach: split the CB by next_node

13. 13 CMON Construction Periodically construct CMON Main problems: –How to use CBs construct application-level cluster with different criteria? Distance-based, Density-based, K-partitioning clustering –How to reduce network distance computation among CBs? Incremental network extension

14. 14 Distance-based CMON Definition of Minimum Distance CMON –For each object in an MD-CMON, the minimum network distance with other objects in the cluster is not longer than a user specified threshold δ Threshold δ and  : –δ is a user-defined threshold. –  is a system threshold and independent of δ –δ >=  How CBs are used: –Combination of CBs based on their network distance –Adaptation of the incremental network extension to avoid O(N 2 ) network distance computation between CBs

15. 15 Density-based CMON Definition of Density-Based CMON –For each cluster in the DB-CMON, the average density is higher than a given threshold ρ. Moreover, there is not any empty segment (without any objects on) whose length is longer than E. Implications: –Suppose m objects in a CB, then its density is m/  (m-1) > 1/  –For any object, its nearest object is within a distance of E avoid very skewed clusters How CBs are used: –Requirement of CBs:  ≤ max{E,1/ρ} –Same as the MD-CMON construction, but a dynamic minimum-distance constraint, related to density of candidate CB

16. 16 K-Partitioning CMON Definition of K-Partitioning CMON –Given a set of objects, group them into the K clusters such that the sum of distances between all adjacent objects in each cluster is minimized Intuitive method based on CBs –Iteratively merge closest pairs of CBs until K clusters are obtained –Problem: costly distance computation between all pairs of CBs Improved K-Means method based on CB and Cross-CB –Low-complexity heuristic similar to the K-means algorithm –Initially select K CBs as the seeds for K clusters and assign the remaining CBs to their nearest clusters to make the sum of distances between adjacent objects to be minimum.

17. 17 K-Partitioning CMON Problem: may not lead to the optimal solution –dist(CB2,CB3)<dist(CB2,CB5)< dist(CB3,CB1)<dis(CB2,CB1)< dist(CB3,CB5) –Construct 3 clusters (k=3) {(CB5,CB2),(CB1,CB3),CB4}  Not optimized Introduce the Cross-CB –The minimum distance  across the intersection (e.g. CB2+CB3)

18. 18 Experiments Dataset: MO Generator on Beijing Road Network –Set K hotpots and generate objects moving along their shortest path from the initial hotpot to destination hotpot Main contents –Performance comparison with static clustering (  -link) for entire dataset periodically –Measure the average clustering response time (CB merging) and total workload time (CB maintenance + CB merging)

19. 19 Experiments Clustering Cost Comparison with Different Datasize –CMON is better than the static one in terms of average query latency, yet is still better in terms of total workload time total timeresponse time

20. 20 Experiments Clustering Cost Comparisons of average response time: –Different clustering frequency (at each 5 time units, each 4, … ) –Different monitoring time (different object updates) With clustering frequencyWith monitoring time

21. 21 Experiments Clustering Cost with different parameters ( , δ) –  : effect on the CB maintenance –δ: effect on the CB clustering CMON performance with εCMON performance with δ

22. 22 Related Work Clustering Moving Objects –Li & Han [KDD’04] Moving Micro-Clustering –Kalnis & Mamoulis[SSTD’05] On Discovering Moving Clusters in Spatio-temporal Data –R.V. Nehme & E.A. Rundensteiner[EDBT’06] Scalable Cluster-Based Algorithm for Evaluating Continuous Spatio-Temporal Queries on Moving Objects Clustering Objects on a Spatial Network –Yiu & Mamoulis [SIGMOD’04] Adapt k-medoids, ε-link, & single-link Agglomerative algorithms

23. 23 Conclusions Cluster moving objects in road network An unified framework –Splitting the costs of clustering into different granularity in conjunction with the movement feature in the road network –Application-centered clustering and periodical monitoring the clusters The experimental results show the efficiency of our method

24. Thank you