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2017 ; 73
(3
): 811-821
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Statistical significance for hierarchical clustering
#MMPMID28099990
Kimes PK
; Liu Y
; Neil Hayes D
; Marron JS
Biometrics
2017[Sep]; 73
(3
): 811-821
PMID28099990
show ga
Cluster analysis has proved to be an invaluable tool for the exploratory and
unsupervised analysis of high-dimensional datasets. Among methods for clustering,
hierarchical approaches have enjoyed substantial popularity in genomics and other
fields for their ability to simultaneously uncover multiple layers of clustering
structure. A critical and challenging question in cluster analysis is whether the
identified clusters represent important underlying structure or are artifacts of
natural sampling variation. Few approaches have been proposed for addressing this
problem in the context of hierarchical clustering, for which the problem is
further complicated by the natural tree structure of the partition, and the
multiplicity of tests required to parse the layers of nested clusters. In this
article, we propose a Monte Carlo based approach for testing statistical
significance in hierarchical clustering which addresses these issues. The
approach is implemented as a sequential testing procedure guaranteeing control of
the family-wise error rate. Theoretical justification is provided for our
approach, and its power to detect true clustering structure is illustrated
through several simulation studies and applications to two cancer gene expression
datasets.