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Bi-Clustering. COMP 790-90 Seminar Spring 2011. Definition of OP-Cluster.

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Definition of OP-Cluster

- Let I be a subset of genes in the database. Let J be a subset of conditions. We say <I, J> forms an Order Preserving Cluster (OP-Cluster),if one of the following relationships exists for any pair of conditions.

Expression Levels

A1 A2 A3 A4

when

Problem Statement

- Given a gene expression matrix, our goal is to find all the statistically significant OP-Clusters. The significance is ensured by the minimal size threshold nc and nr.

Ming OP-Clusters: A naïve approach

root

- A naïve approach
- Enumerate all possible subsequences in a prefix tree.
- For each subsequences, collect all genes that contain the subsequences.

- Challenge:
- The total number of distinct subsequences are

a

a

b

c

d

b

b

c

d

a

c

d

…

c

d

d

b

d

b

c

c

d

a

d

…

d

c

d

b

c

b

d

c

d

a

…

A Complete Prefix Tree with 4 items {a,b,c,d}

d:2

d:3

c:2

c:3

Mining OP-Clusters: Prefix Tree- Goal:
- Build a compact prefix tree that includes all sub-sequences only occurring in the original database.
- Strategies:
- Depth-First Traversal
- Suffix concatenation: Visit subsequences that only exist in the input sequences.
- Apriori Property: Visit subsequences that are sufficiently supported in order to derive longer subsequences.

Root

a:1,2

a:1,2,3

a:1,2

a:1,2,3

b:3

d:1

d:1,2,3

d:1,2,3

d:1,3

d:1,3

b:2

a:3

b:1

c:1,3

c:1,2,3

d:2

d:3

c:1

c:2

c:3

References

- J. Yang, W. Wang, H. Wang, P. Yu, Delta-cluster: capturing subspace correlation in a large data set, Proceedings of the 18th IEEE International Conference on Data Engineering (ICDE), pp. 517-528, 2002.
- H. Wang, W. Wang, J. Yang, P. Yu, Clustering by pattern similarity in large data sets, to appear in Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD), 2002.
- Y. Sungroh, C. Nardini, L. Benini, G. De Micheli, Enhanced pClustering and its applications to gene expression data Bioinformatics and Bioengineering, 2004.
- J. Liu and W. Wang, OP-Cluster: clustering by tendency in high dimensional space, ICDM’03.

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