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Open Access Highly Accessed Methodology article

Methods for simultaneously identifying coherent local clusters with smooth global patterns in gene expression profiles

Yin-Jing Tien1, Yun-Shien Lee23, Han-Ming Wu4 and Chun-Houh Chen5*

Author Affiliations

1 Institute of Statistics, National Central University, Tao-Yuan, 32001, Taiwan

2 Genomic Medicine Research Core Laboratory, Chang Gung Memorial Hospital (CGMH), Tao-Yuan, 33305, Taiwan

3 Department of Biotechnology, Ming Chuan University, Tao-Yuan, 33348, Taiwan

4 Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan

5 Institute of Statistical Science, Academia Sinica, Taipei, 11529, Taiwan

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BMC Bioinformatics 2008, 9:155  doi:10.1186/1471-2105-9-155

Published: 20 March 2008



The hierarchical clustering tree (HCT) with a dendrogram [1] and the singular value decomposition (SVD) with a dimension-reduced representative map [2] are popular methods for two-way sorting the gene-by-array matrix map employed in gene expression profiling. While HCT dendrograms tend to optimize local coherent clustering patterns, SVD leading eigenvectors usually identify better global grouping and transitional structures.


This study proposes a flipping mechanism for a conventional agglomerative HCT using a rank-two ellipse (R2E, an improved SVD algorithm for sorting purpose) seriation by Chen [3] as an external reference. While HCTs always produce permutations with good local behaviour, the rank-two ellipse seriation gives the best global grouping patterns and smooth transitional trends. The resulting algorithm automatically integrates the desirable properties of each method so that users have access to a clustering and visualization environment for gene expression profiles that preserves coherent local clusters and identifies global grouping trends.


We demonstrate, through four examples, that the proposed method not only possesses better numerical and statistical properties, it also provides more meaningful biomedical insights than other sorting algorithms. We suggest that sorted proximity matrices for genes and arrays, in addition to the gene-by-array expression matrix, can greatly aid in the search for comprehensive understanding of gene expression structures. Software for the proposed methods can be obtained at webcite.