CACTUS-Clustering Categorical Data Using Summaries Advisor： Dr. Hsu Graduate：Min-Hung Lin IDSL seminar 2001/10/30

Outline Motivation Objective Related Work Definitions CACTUS Performance Evaluation Conclusions Comments

Motivation 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 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 EM algorithm [Dempster et al., 1977] Iterative clustering technique STIRR algorithm[Gibson et al., 1998] Iterative algorithm based on non-linear dynamical systems ROCK algorithm[Guha et al., 1999] Hierarchical clustering algorithm

DEF:Support

DEF:Strongly Connected

DEF:Strongly Connected(cont’d)

Formal Definition of a Cluster

Formal Definition of a Cluster (cont’d) 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 STIRR fails to discover CACTUS correctly discovers all clusters clusters consisting of overlapping cluster-projections on any attribute clusters where two or more clusters share the same cluster projection CACTUS correctly discovers all clusters

CACTUS Three-phase clustering algorithm Summarization Phase Compute the summary information Clustering Phase Discover a set of candidate clusters Validation Phase Determine the actual set of clusters

Summarization Phase Inter-attribute Summaries Intra-attribute Summaries

Clustering Phase Computing cluster-projections on attributes Level-wise synthesis of clusters

Computing Cluster-Projections on Attributes Step 1 :pairwise cluster-projection Step 2 :intersection

Computing Cluster-Projections on Attributes (cont’d)

Level-wise synthesis of clusters

Level-wise synthesis of clusters (cont’d) Generation procedure

Level-wise synthesis of clusters (cont’d) Candidate cluster

Validation Some of the candidate clusters may not have enough support because some of the 2-cluster 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 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 Large Attribute Value Domains Clusters in Subspaces

Performance Evaluation Evaluation of CACTUS on Synthetic and Real Datasets Compared the performance of CACTUS with the performance of STIRR

Synthetic Datasets 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 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},{10212,10527,2315,52}

Real Datasets (cont’d) Database-related Theory-related Mixture

Results CACTUS is very fast and scalable(only two scans of the dataset) CACTUS outperforms STIRR by a factor between 3 and 10

Conclusions 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 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 Pairwise cluster-projection is the NP-complete problem A large number of candidate clusters is still a problem