CHAN Siu Lung, Daniel

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CURE Efficient Clustering Algorithm for Large
Databases
CHAN Siu Lung, Daniel CHAN Wai Kin, Ken CHOW Chin
Hung, Victor KOON Ping Yin, Bob
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Content

1. Different problem in traditional clustering
   method
2. Basic idea of CURE clustering
3. Improved CURE
4. Summary
5. References

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Different problem in traditional clustering
method
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Partitional Clustering
Different problem in traditional clustering method

• Partitional Clustering
• This category of clustering method try to reduce
  the data set into k clusters based on some
  criterion functions.
• The most common criterion is square-error
  criterion.
• This method favor to clusters with data points as
  compact and separated as possible

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Partitional Clustering
Different problem in traditional clustering method

• You may find error in case the square-error is
  reduced by splitting some large cluster to favor
  some other group.

Figure Splitting occur in large cluster by
partitional method
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Hierarchical Clustering
Different problem in traditional clustering method

• Hierarchical Clustering
• This category of clustering method try to merge
  sequences of disjoint clusters into the target k
  clusters base on the minimum distance between two
  clusters.
• The distance between clusters can be measured as
• Distance between mean
• Distance between average point
• Distance between two nearest point within cluster

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Hierarchical Clustering
Different problem in traditional clustering method

• This method favor hyper-spherical shape and
  uniform data.
• Lets take some prolonged data as example
• Result of dmean

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Hierarchical Clustering
Different problem in traditional clustering method

• Result of dmin

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Problems summary
Different problem in traditional clustering method

1. Traditional clustering mainly favors spherical
   shape.
2. Data in the cluster must be compact together.
3. Each cluster must separate far away enough.
4. Cluster size must be uniform.
5. Outliner will greatly disturb the cluster result.

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Basic idea of CURE clustering
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General CURE clustering procedure.
Basic idea of CURE clustering

1. It is similar to hierarchical clustering
   approach. But it use sample point variant as the
   cluster representative rather than every point in
   the cluster.
2. First set a target sample number c . Than we try
   to select c well scattered sample points from the
   cluster.
3. The chosen scattered points are shrunk toward the
   centroid in a fraction of ? where 0 lt?lt1

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General CURE clustering procedure.
Basic idea of CURE clustering

1. These points are used as representative of
   clusters and will be used as the point in dmin
   cluster merging approach.
2. After each merging, c sample points will be
   selected from original representative of previous
   clusters to represent new cluster.
3. Cluster merging will be stopped until target k
   cluster is found

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Pseudo function of CURE
Basic idea of CURE clustering
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CURE efficient
Basic idea of CURE clustering

• The worst-case time complexity is O(n2logn)
• The space complexity is O(n) due to the use of
  k-d treee and heap.

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Improved CURE
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Random Sampling
Improved CURE

• In case of dealing with large database, we cant
  store every data point to the memory.
• Handle of data merge in large database require
  very long time.
• We use random sampling to both reduce the time
  complexity and memory usage.
• Assume if we need to detect a cluster u present,
  we need to at least capture f fraction of data
  from this cluster fu
• The the required sampling data s to capture can
  be present as follow
• You can refer to proof from the reference (i).
  Here we just want to show that we can determine a
  sample size smin such that the probability of get
  enough sample from every cluster u is 1 - ?

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Partitioning and two pass clustering
Improved CURE

• In addition, we use two-pass approach to reduce
  the computation time.
• First, we divide the n data point into p
  partition and each contain n/p data point.
• We than pre-cluster each partition until the
  number of cluster n/pq reached in each partition
  for some q gt 1
• Then each cluster in the first pass result will
  be used as the second pass clustering input to
  form the final cluster.
• Each one partitions time complexity is
• Therefore, the first pass complexity will be
• And the second pass complexity is
• Overall, the time complexity will become

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Partitioning and two pass clustering
Improved CUR

• The overall improvement will be
• Also, to maintain the quality of clustering, we
  must make sure n/pq must be 2 to 3 times of k.

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Outlier elimination
Improved CURE

• We can introduce outliners elimination by two
  method.
• Random sampling With random sampling, most of
  outlier points are filtered out.
• Outlier elimination As outliner is not a compact
  group, it will grow in size very slowly during
  the cluster merge stage. We will then kick in the
  elimination procedure during the merging stage
  such that those cluster with 1 2 data points
  are removed from the cluster list.
• In order to prevent these outliners from merging
  into proper cluster, we must trigger the
  procedure in proper stage such that we can
  properly remove the outliners. In general, we
  will trigger this procedure when cluster sets
  reduce to 1/3 of total data sets.

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Data labeling
Improved CURE

• Due to the use of random sample. We need to label
  back every remaining data points to the proper
  cluster group.
• Each data point is assigned to the cluster group
  with a representative point nearest to the data
  point.

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Final overview of CURE flow
Improved CURE
Data
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Sample result with different parameter
Improved CURE
Different shrinking factor ?
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Sample result with different parameter
Improved CURE
Different number of representatives c
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Sample result with different parameter
Improved CURE
Relation of execution time, different partition
number p, and different sample points s
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Summary

• CURE can effectively detect proper shape of the
  cluster with the help of scattered representative
  point and centroid shrinking.
• CURE can reduce computation time and memory
  loading with random sampling and 2 pass
  clustering
• CURE can effectively remove outlier.
• The quality and effectiveness of CURE can be
  tuned be varying different s,p,c,? to adapt
  different input data set.

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References

1. GRS97   Sudipto Guha, R. Rastogi, and K. Shim.
   CURE A clustering algorithm for large databases.
   Technical report, Bell Laboratories, Murray Hill,
   1997.
2. ZRL96 Tian Zhang , Raghu Ramakrishnan , Miron
   Livny, BIRCH an efficient data clustering method
   for very large databases, ACM SIGMOD Record, v.25
   n.2, p.103-114, June 1996
3. Sudipto Guha, Rajeev Rastogi, Kyuseok Shim CURE
   An Efficient Clustering Algorithm for Large
   Databases, ACM SIGMOD, 1998.

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