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Clustering Moving Objects in Spatial Networks

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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 – PowerPoint PPT presentation

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Title: Clustering Moving Objects in Spatial Networks


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

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
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
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
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
CMON Framework
Construction of CB
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, na, nb, head, tail, ObjNum)
  • Oo1,o2,,oi,on
  • (na,nb) the edge on which the object moves
  • (head, tail) position of the CB
  • ObjNum numbers of objects in the CB
  • Dd(oi,oi1) ? (1in-1)
  • oi(na, nb, posi, speed, next_node)

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
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
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)gt7
  • 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
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
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
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 d
  • Threshold d and ?
  • d is a user-defined threshold.
  • ? is a system threshold and independent of d
  • d gt ?
  • How CBs are used
  • Combination of CBs based on their network
    distance
  • Adaptation of the incremental network extension
    to avoid O(N2) network distance computation
    between CBs

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 ?.
    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) gt 1/?
  • For any object, its nearest object is within a
    distance of E
  • avoid very skewed clusters
  • How CBs are used
  • Requirement of CBs ? maxE,1/?
  • Same as the MD-CMON construction, but a dynamic
    minimum-distance constraint, related to density
    of candidate CB

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
K-Partitioning CMON
  • Problem may not lead to the optimal solution
  • dist(CB2,CB3)ltdist(CB2,CB5)lt
  • dist(CB3,CB1)ltdis(CB2,CB1)lt
  • dist(CB3,CB5)
  • Construct 3 clusters (k3)
  • (CB5,CB2),(CB1,CB3),CB4
  • Not optimized
  • Introduce the Cross-CB
  • The minimum distance ?
  • across the intersection
  • (e.g. CB2CB3)

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
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 time
response time
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 frequency
With monitoring time
21
Experiments
  • Clustering Cost with different parameters (? , d)
  • ? effect on the CB maintenance
  • d effect on the CB clustering

CMON performance with e
CMON performance with d
22
Related Work
  • Clustering Moving Objects
  • Li Han KDD04
  • Moving Micro-Clustering
  • Kalnis MamoulisSSTD05
  • On Discovering Moving Clusters in Spatio-temporal
    Data
  • R.V. Nehme E.A. RundensteinerEDBT06
  • Scalable Cluster-Based Algorithm for Evaluating
    Continuous Spatio-Temporal Queries on Moving
    Objects
  • Clustering Objects on a Spatial Network
  • Yiu Mamoulis SIGMOD04
  • Adapt k-medoids, e-link , single-link
    Agglomerative algorithms

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
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