CACTUS-Clustering Categorical
Data Using Summaries
Advisor： Dr. Hsu
Graduate：Min-Hung Lin
IDSL seminar 2001/10/30
Outline
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Motivation
Objective
Related Work
Definitions
CACTUS
Performance Evaluation
Conclusions
Comments
Motivation
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Clustering with categorical attributes
has received attention
Previous algorithms do not give a
formal description of the clusters
Some of them need post-process the
output of the algorithm to identify the
final clusters.
Objective
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Introduce a novel formalization of a
cluster for categorical attributes.
Describe a fast summarization-based
algorithm CACTUS that discovers
clusters.
Evaluate the performance of CACTUS
on synthetic and real datasets.
Related Work
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EM algorithm [Dempster et al., 1977]
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STIRR algorithm[Gibson et al., 1998]
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Iterative clustering technique
Iterative algorithm based on non-linear
dynamical systems
ROCK algorithm[Guha et al., 1999]
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Hierarchical clustering algorithm
DEF:Support
DEF:Strongly Connected
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DEF:Strongly
Connected(cont’d)
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Formal Definition of a Cluster
Formal Definition of a Cluster
(cont’d)
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is the cluster-projection of C on
C is called a sub-cluster if it satisfies
conditions (1) and (3)
A cluster C over a subset of all
attributes
is called a
subspace cluster on S; if |S| = k then C
is called a k-cluster
DEF:Similarity
Inter-attribute Summaries
Intra-attribute Summaries
Experiments
Result
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STIRR fails to discover
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clusters consisting of overlapping clusterprojections on any attribute
clusters where two or more clusters share
the same cluster projection
CACTUS correctly discovers all clusters
CACTUS
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Three-phase clustering algorithm
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Summarization Phase
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Clustering Phase
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Compute the summary information
Discover a set of candidate clusters
Validation Phase
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Determine the actual set of clusters
Summarization Phase
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Inter-attribute Summaries
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Intra-attribute Summaries
Clustering Phase
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Computing cluster-projections on
attributes
Level-wise synthesis of clusters
Computing Cluster-Projections
on Attributes
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Step 1 :pairwise cluster-projection
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Step 2 :intersection
Computing Cluster-Projections
on Attributes (cont’d)
Clusterprojection
Level-wise synthesis of
clusters
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n
Level-wise synthesis of
clusters (cont’d)
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Generation procedure
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Level-wise synthesis of
clusters (cont’d)
Candidate
cluster
Validation
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Some of the candidate clusters may not have
enough support because some of the 2cluster may be due to different sets of tuples.
Check if the support of each candidate cluster
is greater than the threshold: times the
expected support of the cluster.
Only clusters whose support on D passes the
threshold are retained.
Validation Procedure
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Setting the supports of all candidate
clusters to zero.
For each tuple
increment the
support of the candidate cluster to
which t belongs.
At the end of the scan, delete all
candidate clusters whose support is less
than the threshold.
Extensions
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Large Attribute Value Domains
Clusters in Subspaces
Performance Evaluation
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Evaluation of CACTUS on Synthetic and
Real Datasets
Compared the performance of CACTUS
with the performance of STIRR
Synthetic Datasets
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The test datasets were generated using
the data generator developed by Gibson
et al.(1 million tuples, 10 attributes, 100 attributes
values for each attribute)
Real Datasets
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Two sets of bibliographic entries
 7766 entries are database-related
 30919 entries are theory-related
Four attributes: the first author, the second
author, the conference, and the year.
Attribute domains are
{3418,3529,1631,44},{8043,8190,690,42},{1
0212,10527,2315,52}
Real Datasets (cont’d)
Database-related
Theory-related
Mixture
Results
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CACTUS is very fast and scalable(only
two scans of the dataset)
CACTUS outperforms STIRR by a factor
between 3 and 10
Conclusions
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Formalized the definition of a cluster for
categorical attributes.
Introduced a fast summarization-based
algorithm CACTUS for discovering such
clusters in categorical data.
Evaluated algorithm against both
synthetic and real datasets.
Future Work
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Relax the cluster definition by allowing
sets of attribute values are “almost”
strongly connected to each other.
Inter-attribute summaries can be
incremental maintained=>Derive an
incremental clustering algorithm
Rank the clusters based on a measure
of interestingness
Comments
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Pairwise cluster-projection is the NPcomplete problem
A large number of candidate clusters is
still a problem