A permutation test for determining significance of clusters with applications to spatial and gene expression data.
Hierarchical clustering is a common procedure for identifying structure in a data set, and this is frequently used for organizing genomic data. Although more advanced clustering algorithms are available, the simplicity and visual appeal of hierarchical clustering has made it ubiquitous in gene expression data analysis. Hence, even minor improvements in this framework would have significant impact. There is currently no simple and systematic way of assessing and displaying the significance of various clusters in a resulting dendrogram without making certain distributional assumptions or ignoring gene-specific variances. In this work, we introduce a permutation test based on comparing the within-cluster structure of the observed data with those of sample datasets obtained by permuting the cluster membership. We carry out this test at each node of the dendrogram using a statistic derived from the singular value decomposition of variance matrices. The p-values thus obtained provide insight into the significance of each cluster division. Given these values, one can also modify the dendrogram by combining non-significant branches. By adjusting the cut-off level of significance for branches, one can produce dendrograms with a desired level of detail for ease of interpretation. We demonstrate the usefulness of this approach by applying it to illustrative data sets.
Harvard Medical School, Boston, Massachusetts, USA.
P J
PJ
Park
J
J
Manjourides
M
M
Bonetti
M
M
Pagano
Proc Natl Acad Sci U S A. 2001 Jul 31;98(16):8961-5
11470909
Science. 1994 Nov 18;266(5188):1202-8
7973702
Bioinformatics. 2006 Jan 1;22(1):58-67
16257984
Bioinformatics. 2002 Nov;18(11):1462-9
12424117
Bioinformatics. 2001;17 Suppl 1:S22-9
11472989
Genome Res. 2002 Oct;12(10):1574-81
12368250
Nature. 2000 Aug 3;406(6795):536-40
10952317
Nature. 2002 Jan 24;415(6870):436-42
11807556
Proc Natl Acad Sci U S A. 2004 Jul 6;101(27):10143-8
15210990
Proc Natl Acad Sci U S A. 1998 Dec 8;95(25):14863-8
9843981
Bioinformatics. 2008 Mar 1;24(5):719-20
18024473
BMC Bioinformatics. 2003 Mar 20;4:10
12659637
Milbank Q. 2002;80(4):677-707, iv
12532644
Forensic Sci Int. 1995 Jun 30;74(1-2):99-113
7665137
Biometrics. 1971 Sep;27(3):501-14
5116570
Genome Biol. 2003;4(5):R34
12734014
Stat Med. 2005 Mar 15;24(5):753-73
15523703
BMC Bioinformatics. 2005 Dec 07;6:289
16336639
Funct Integr Genomics. 2000 Nov;1(3):156-73
11793234