On Discovering Moving Clusters in Spatio-temporal Data

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On Discovering Moving Clusters in Spatio-temporal
Data

• Panos Kalnis
• National University of Singapore
• Nikos Mamoulis
• University of Hong Kong
• Spiridon Bakiras
• Hong Kong University of Science and Technology

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What is a Moving Cluster?

• Dense clusters of objects that move similarly for
  a long time period
• Not necessarily the same objects during the
  lifetime of the cluster
• Examples
• Migrating animals
• Convoy of cars
• Military applications
• Solutions
• Efficient exact and approximate algorithms

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Problem Formulation

• Example
• Moving cluster

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Related Work (Static)

• Partition-based clustering (k-medoids)
• Hierarchical clustering (BIRCH, CURE)
• Density-based clustering (DBSCAN)

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Related Work (Moving Objects)

• Grouping trajectories Vlachos et.al, ICDE 02
• Trajectory cluster Constant set of objects
  through its lifetime
• Only similar movement no space proximity
• Dense areas over time Hadjieleftheriou et.al,
  SSTD 03
• Static dense regions
• No common objects between regions in sequence
• Incremental DBSCAN/OPTICS Ester et.al, VLDB 98
• Only a small percentage of objects moves
• Maintaining Data Bubbles Nassar et.al, SIGMOD
  04
• Redistributes updated objects in existing bubbles

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MC1 The Straight-forward approach

• G set of moving clusters
• Apply clustering to next timeslice Si
• Expand moving clusters in G
• Add new moving clusters to G
• Report ending clusters

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Hash-based DBSCAN

• Memory
• 10M objects with 1GB RAM

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MC1 is inefficient!

1. Checks all possible combination of clusters in
   consecutive timeslices
2. Performs clustering for every timeslice

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MC2 Minimizing Redundant Checks

• Clustering in every timeslice
• Select a random object in c1
• Search the object in S2
• Repeat for remaining objects
• Max (1-?)ci objects

c1c2 is a moving cluster
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Ambiguity Cases ?lt0.5
c0c1, c2 c0c2, c1
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MC3 Approximate Moving Clusters

• Intuition Many clusters will remain the same
  even if objects move
• Avoid performing clustering in every timeslice
• For an object o
• If o belongs to cluster c in timeslice Si
• Assume that o also belongs to c in the next
  timeslice (notice objects may have moved)

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Refine clusters

• Hash new clusters in a grid
• Legal cluster
• Does not meet/intersect with other clusters
• It is connected (cells meet)
• Objects in legal clusters are not considered
  further
• For the rest of the objects, perform clustering
• Possible inaccuracies!!!

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Minimize Error

• Perform exact clustering to absorb (may not
  eliminate) the accumulated error
• Period for exact clustering Grows linearly,
  drops exponentially
• Exact clustering If more that aG clusters have
  been added/removed

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Experimental Evaluation

• 10K-50K objects per timeslice
• 50-100 timeslices, up to 5M objects
• Linux, C, 1.3GHz CPU, 1.2GB RAM
• Generator Clusters move/rotate, objects
  appear/disappear

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Varying data size (10K-50K per timeslice)
Avg 87

• ?0.9, a0.1
• Larger dataset larger clusters, more interactions

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Varying number of clusters (100-800 per timeslice)
96
87
73

• 5M objects, ?0.9, a0.1
• Many clusters Reaches error threshold fast

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Varying a

• 5M objects, ?0.9, 800 clusters
• a small may not recover!!!

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Varying a for different agilities

• Low agility Fewer errors ? faster

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MC3 for varying ?

• 5M objects, a0.1, 800 clusters
• ? large incorrect clusters are pruned for not
  satisfying the ? criterion

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Conclusions

• Moving clusters
• Objects may move/change
• Exact and approximate solutions
• Future work
• Automatic setting of parameter a
• Better error estimation
• Constraints (e.g, moving cluster must span at
  least k timeslices)

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Questions?