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
• Presented by Xiao Pan

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Outline

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

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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

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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

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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?

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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

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CMON Framework
Construction of CB
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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)

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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

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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

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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
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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

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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

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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

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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

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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.

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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)

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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)

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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
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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
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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
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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

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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

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Thank you