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Bi-Clustering

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

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Bi-Clustering

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  1. Bi-Clustering COMP 790-90 Seminar Spring 2011

  2. 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

  3. 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.

  4. Conversion to Sequence Mining Problem Sequence: Expression Levels A1 A2 A3 A4

  5. 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}

  6. a:3 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

  7. 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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